Leveredhedge.com The Complete Guide to Trading … to Derivatives (6) Fundamentals of Derivatives Pricing (8) Options Greeks (12) Volatility & Volatility Swaps (18)

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The Complete Guide to

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Copyright 2011 lever

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Trading InterviewsV2.0

Copyright 2011 leveredhedge.com

1


Interviews


2

Table of Contents

Word from the Author (3)

Introduction to Sales and Trading (4)

Introduction to Derivatives (6)

Fundamentals of Derivatives Pricing (8)

Options Greeks (12)

Volatility & Volatility Swaps (18)

Introduction to Exotic Equity Derivatives (23)

Bonds (25)

Introduction to Credit Derivatives (29)

Introduction to Interest Rate Derivatives (31)

Interview Tips (33)


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Word from the Author

“Failing to prepare, is preparing to fail”

-John Wooden

Even though the quote above is a household standard, it is one that everybody who wants

to be successful should have on their mind at all times. Success depends on what happens

in the future, and therefore has an element of randomness (I don’t like to use the word luck

as it implies an ability to beat probability). But success also depends on how you position for

the randomness ahead. Preparation and hard work is what allows you to tip the scales of

randomness in your favor, and obtain what every trader requires: edge. Imagine if you are

walking into an interview, and there are 100 possible states that can occur, 50 good (you

get the job) and 50 bad (you don’t get the job). Imagine if one of the bad states is that the

interviewer asks you every question that is in this guide. Through preparation you are able

to alter that bad state into a good one, and obtain a 51 to 49 edge. This is what anything in

life comes down to, edge, and whether you have done the work to obtain it.

I was definitely not the smartest person at any of my assessment centers, and

probably not even the smartest person who rotated on the equity derivatives desk during

my internship. However, I was prepared enough to take advantage of opportunities that

others simply weren’t. Every interview I went into I had the confidence that I knew more

about options than any other candidate that walked in before me, and I used that as my

edge to get a job. Trading desks interview tons of candidates, and most will have

Ivy/Oxbridge/Captain written all over them. What differentiates candidates is their interest.

Therefore congratulations, because by purchasing this guide you have taken the first step to

obtaining an edge.

This guide features 100+ questions on derivatives that you should know walking into

a trading interview. Some are straightforward and will only require one read through, others

are more advanced and will require some thought. I deliberately didn’t over describe the

tough questions because it will do you more good to ‘get it’ yourself. Only this way will you

actually understand the concept rather than have memorized it. Remember, it is no good for

you to be able to answer a question, and then be completely lost by a simple variation of

the same question. If you are stuck on any question, then just log in to the sites member

page and post your question, and I will do my best to help you through it.

Good luck!


4

1) Introduction to Sales and Trading

-What is a market maker?

Market makers are the guys who take on the risk for the bank when a trade goes

through and act as liquidity providers in the market. Let’s say a client rings up the credit

salesperson at an investment bank, saying he needs to sell $100 million of bonds. The

salesperson will ask the trader to make him a market. The trader may reply 98-99,

therefore he is willing to buy at 98, and sell at 99 for a $100 million. This is the bid-ask

spread, and is a large portion of how the trader gets compensated. If the client trades, the

trader now has a position of $100 million worth of bonds at a price of 98. This is the position

of a market maker. He has to make prices for clients to accommodate their requests. It is

important to note that he cannot simply turn around and sell this $100 million of bonds for

99 right away and earn a profit. Market makers are generally stuck with positions no one

wants, and with size that is too big to get rid of. If a market maker wants to get rid of a

position quickly, he will also probably have to become a market taker and hit someone

else’s bid. The skill of the market maker is basically to obtain an inventory that will be

desired by clients in the near future. It can be seen that there is a trade off with various

products. Illiquid products are harder to get rid of but the spread is much wider, whereas

liquid products are easier to get rid of but the spread is much narrower (for example the

spread on Eurostoxx futures is the minimum tick).

-What is the difference between an agency and risk trade?

An equities market maker at an investment bank can take two types of trades. An

agency trade, where all he does is simply executing the trade for the client in the market

place, therefore neither the trader nor the bank takes any risk on the position. On the other

hand the client may ask for a risk trade, which means immediate execution as the trader

takes the position on his book. Risk trades are done if the client needs to move a certain

size and he doesn’t want to wait for it to be executed in pieces in the market.

-Explain how a market maker is also a market taker

As explained in the previous example, a market maker is also a market participant,

and if he needs to unload or needs to take on a certain product and can’t wait until an order

comes to him he will have to act as a market taker.


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-Make me a market on the area of the United States in square miles, 500k wide.

This is a very common question asked in trading interviews. It might not be this

specific example, but the concept is the same. Let’s first go over to what happens to most

candidates, and then what you should do. You have just sat down in front of a head trader

and he tells you:

Interviewer: “Make me a market on the area of the United States in square miles”

There is no way you are expected to know this so take an estimated guess. For example

you estimate that Florida is probably 300 miles long, and it could fit around 5 times on the

east coast, and the US is around twice as wide as is tall. So your first estimate is (300*5)^2

= 2.25 million square miles. So you make a market of 2 – 2.5 million. To this the interview

replies:

Interviewer: “Mine at 2.5, make me another market.”

Now you get frustrated and decide to simply move up your price to 2.5-3 million. Once

again the interviewer buys from you at 3 and asks for another price. You move up again

systematically to 3-3.5 million and the same scenario repeats.

If you simply did what was described above then you missed a large part of what the

question is about.

When the trader first bought from you at 2.5, you became short at 2.5 million. Therefore

you need to buy for less than this price to make a profit. So after the trader buys for 2.5

million, you move up your price, but you want to make a price where your bid is less than

the average price you have sold for. For example 2.25 – 2.75 million. Now if he sells to you,

you buy back at 2.25 and make a profit. The exception to this is if you receive some sort of

information that hints that your estimate is wrong. Keep in mind that that the trader

probably knows the correct answer, and as long as he is buying you are overestimating. So

the trader buys again at 2.75. Now you have sold 2 at an average price of 2.625, therefore

your next bid needs to be below this number, and so on.

By the way, the correct answer is around 4 million square miles.


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2) Introduction to derivatives -What is a derivative security?

A derivative security is one whose value is based on the price of another security

(referred to as the underlying). Derivatives can be linear, where the derivative moves

linearly relatively to the underlying, or it can be convex/concave/mix. The diagram below

illustrates the difference.

-How are they used?

Derivatives can be used for a wide variety of purposes. They can be used to hedge a

portfolio, i.e. a fund buying put options on an index to protect against a market crash (it is

rumored that the prop trading firm Jane Street Capital uses 10% of its annual profits to buy

puts on the S&P 500 index). Derivatives can also be used for the leverage they provide, as

well as to express a particular view on the underlying. If you believe that the S&P 500 is

going to rise by 10%, but are confident not by more, you can improve your risk-reward by

buying a call spread (long call option at a lower strike and a short call option at a higher

strike). This way you can in essence fund your view and make it cheaper to enter that

strategy.

Linear Derivative

Price of Derivative

Price of

Underlying

Price of

Underlying

Price of Derivative

Non Linear Derivative


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-What is the difference between a future and a forward?

Both a future and forward are the obligation to buy an underlying at a specific price

at a future date. The difference between the two is that a future is traded on exchanges that

is standardized and is marked to market, while a forward is an over the counter product.

Marked to market means that an investor has to put up margin when they buy the product,

and if the product drops in value, they might have to put up more margin as collateral.

Example: Crude Oil is trading at $80 per barrel. An airline wants to hedge its exposure to

the price of oil for the next 6 months. They set up a forward contract with an investment

bank that means they have to buy a certain amount of oil in 6 months at $85 per barrel.

Therefore they have locked in that price. Let’s say they bought futures contracts instead. If

they bough contracts worth a total of $100 million, a 10% margin requirement means they

have to put up $10 million as collateral. Now if the value of the contracts they bought fall to

$95 million, they will have to increase the amount of collateral. This is marked to market.

-Underlying is at 100, 1 year interest rate is 10%, what is the 1 year forward?

Pricing of forwards and futures doesn’t actually require any forecast of the future

price of the underlying, just a simple no arbitrage formula.

�� = �� ∗ �(��)� Where c are the storage costs associated with holding the underlying and d is any benefit

(i.e. dividends). Imagine if this equality did not hold. If the forward was greater than the

right hand side of the equation, you could simply sell the forward, buy the underlying today

and hold it until the forward expires. Then deliver the forward for a profit. Therefore:

� = 100 ∗ ��.� = 110.5

-What is backwardation and contango?

Backwardation: This is the case when the spot price is higher than the forward price. As can

be seen from the above equation, this occurs if the holding benefits are greater than the

interest rate and holding costs.

Contango: A case where the forward is higher than the spot price.


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-What is a call/put option?

Call option: the right to buy a security at a certain price (known as the strike price) within a

certain time period. The important point is that the holder of a call option has no obligation

to buy the underlying.

Put option: the right to sell a security at the strike price within a certain time period.

-What is the difference between American and European options?

European options can be exercised only on the day of expiry, while American options

can be exercised at expiry or at any point before that.

On both graphs, the bold line represents the payoff of the options at expiry, while the

dashed line represents the pre expiry price. An option has extra value because the investor

has to pay for the one sided payoff. As time approaches expiry the dashed line converges to

the final payoff.

Example: Shares of Microsoft are trading at $28. Let’s say you buy a European option with a

strike of $25 and 3 months until expiry. You pay $5 for this option. If in 3 months Microsoft

is trading at $30, you can exercise your option and therefore buy it for $25. This is an

immediate profit of $5. However, you paid $5 for this option so you actually breakeven.

Call Option

Call Price Put Price

Underlying

Put Option

Underlying


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3) Fundamentals of Option Pricing

-What is the Taylor expansion, and how does it relate to option pricing?

A Taylor expansion is a mathematical method of fitting a curved function. Since

options have convex profiles, a Taylor expansion can be used to estimate the payoff curve

in the graph in section 1.

-Describe convexity of options in terms of expected value.

Convexity of options means that downside is limited, while the upside is unlimited.

This means that if we take a simplified model where a stock is at 100, and has a 0.3

probability of moving to 90, 0.3 probability of moving to 110, and 0.4 probability of staying

at 100, the expected value for a 100 strike call option is calculated as:

�� = 0.3 ∗ (110 − 100) = 3

This is different to a linear payoff where the expected value would take account of the

downside as well.

-What is Ito’s Lemma?

Ito’s lemma is a mathematical technique that helps solve the Black-Scholes equality,

and therefore generate the Black-Scholes pricing formula. It is the stochastic version of the

chain rule in calculus.

-What is the Black-Scholes equation?

The BS formula is one of the most widespread option pricing models, and relies on a no

arbitrage argument.

�� = ��(!��)"(��) − #��(!��)"(�$) �� = ln (�#) + (� − � + 12 ,$) (- − )

,.- −

�$ = �� − ,.- − Where S is the underlying price, d is the dividend yield, T-t is the time to maturity, X is the

strike price, r is the interest rate, , is the implied volatility, and N() is the cumulative

density function.

-What makes Black-Scholes different from the preceding option pricing methods?

The BS formula itself is actually very similar to preceding pricing formulas

(Bachelier/Thorp). However, BS is the first formula to use an argument of replication. This

means that an option can be replicated by holding a certain amount of stock and a certain


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amount of bonds shorts. Think of the formula as a recipe. Therefore if you hold a long call,

you can short stock and buy bonds in certain quantities to ensure that you are properly

hedged. Because of this replication strategy, you do not actually need any sort of directional

guess to price options, only the volatility of the underlying between now and expiry.

-What is delta in the BS equation?

Delta is the hedge ratio, or the amount of shares you have to hold short if holding a

call to be hedged against small moves in the underlying (see more in the next section). In

the BS equation, delta is equal to: �� = "(��)

-What are the assumptions behind the BS equation?

1. Constant volatility over the lifetime of the option

2. Constant and known interest rates

3. Lognormally distributed returns

4. No transaction costs

5. A continuous stock price process

-How do traders correct for these assumptions?

Assumption number 3 is most easily corrected for. A trader accommodates for this

by introducing a skew structure in the options prices. By pricing lower strike options with a

higher implied volatility (despite the fact that they are options on the same underlying

which will only have one realized volatility over the life of the option), a trader can introduce

the distributional skew found in historical returns. More on skew and implied volatility in

section 4.

-What are the two components of an option’s price?

The price of an option consists of the intrinsic value (underlying price – strike), and

the time value. It would not make sense for the option in the above example to be trading

at $3 (intrinsic value), because a call option has a one sided payoff. A buyer is charged a

premium for this one sided payoff as his downside is limited, and the upside unlimited.

-What is the lower and upper bound for calls so that there is no arbitrage?

/�� = 01#(0, � − 3)


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Therefore a call price cannot be below it’s intrinsic value. If it was lower, you could simply

buy the call, short the stock at S, and then at expiry buy the call at K and cover your short

stock position. Since you paid less than S-K for the call, and net S-K from the stock, there is

an arbitrage opportunity.

4�� = �

If the call price is greater than the spot price, you can simply sell the call and use a portion

of the proceeds to buy the underlying. If the call is exercised, you deliver the stock and

keep an arbitrage profit.

-What is the lower and upper bound for puts so that there is no arbitrage?

/�� = 01#(0, 3 − �) Just like the call, a put cannot trade below it’s intrinsic value, otherwise there is an arbitrage

opportunity. If the put is trading below K-S, simply buy the put, buy the underlying for S,

and at exercise sell the stock for K.

4�� = 3

The maximum profit on a put option is the strike price, and only in the case that the

underlying goes to 0. Therefore a price higher than the maximum possible payoff is

impossible.

-Is it ever optimal to exercise an American option before expiry?

As was covered in the first section, American options can be exercised at any point

within the life of the option. Is it ever optimal to exercise early though? To answer we need

to look at the costs and benefits of exercising versus not exercising.

Call Option:

Benefits: the convexity of the option, represented by the time value; earn interest on the

strike price amount

Costs: dividends

Therefore the dividend has to be greater than the time value and interest earned on the

strike to exercise. It turns out the only optimal time to exercise a call option is the day

before the last dividend is paid. Otherwise, it is better to sell the call instead of exercising it.

Put Options:

Only time it is optimal to exercise put options early is if the underlying price is very close to

0, therefore when there is not much more upside left.


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-What is Put-Call Parity?

Put-Call parity is a no arbitrage relationship that equates the pricing of calls and puts

of the same strike. The following has to hold otherwise there is an arbitrage opportunity:

5 − = 6�(�) − 6�(3) = � − 6�(3)

Where c is the cost of a European call option, p the cost of a European put option; S the

current spot price, F is the forward price that corresponds to the maturity of the options and

K the strike price. The best way to think about this is to consider the final payoffs of a

strategy of long call and short put:

5 − = 6�[01#(� − 3, 0) − 01#(� − �, 0)]

Because the payoff of this is either F-K or –(K-F), you can see from this that this simply

translates to:

5 − = 6�[01#(� − 3, 0) − 01#(� − �, 0)] = � − 6�(3)

The consequence of this is that holding a long call and short put is the same as holding a

long stock position and borrowing the present value of the strike price. Imagine the case

where c – p is greater than the stock strategy. You can do the following arbitrage:

S(T) > K S(T) = K S(T) < K

Short Call -S(T) + K + c +c +c

Long Put -p -p K-S-p

Long Stock S(T)-S(0) S(T)-S(0) S(T)-S(0)

Borrow PV(K) -(K-PV(K)) -(K-PV(K)) -(K-PV(K))

P&L at expiration c – p – S(0) + PV(K) c – p – S(0) + PV(K) c – p – S(0) + PV(K)

Since we borrow PV(K), we have to pay back K at the end and therefore our P&L for that is

-(K-PV(K)). It can be seen that the profit is positive whatever the final stock price, and

therefore an arbitrage is possible.


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4) Greeks

Delta -What is it?

Delta is the sensitivity of the option value to changes in the underlying. Therefore

delta will be positive if the option rises in value when the underlying rises in value. Delta is

also the amount of the underlying you need to hold to be delta hedged. If you are long a

call option, you can short the delta amount of the underlying (and long the underlying if

holding a put option). This way if the underlying moves a small amount, your gain/loss on

the option is offset by a loss/gain on the stock.

-How does it change with the underlying?

-How does it change with volatility?

Delta

Underlying

Delta of a call option takes a value

between 0 and 1, with at the money

option having a delta of 0.5.

Intuitively, when an option is deep in

the money it behaves like the

underlying itself, therefore delta will

be closer to 1. On the other hand, if

an option is deep out of the money, it

will not be sensitive to changes in the

underlying as the probability of it

expiring in the money is low.

Delta

Underlying

Higher volatility means that out of the

money options are pushed less out of

the money, and in the money options

are pushed less in the money.

Therefore delta rises for out of the

money options, as there is a higher

chance it will end up in the money,

and delta falls for in the money

options.

1

0

High Vol

Low Vol

ATM ITM OTM

ATM ITM OTM


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-How does it change with time?

Gamma

-What is it?

Gamma is the sensitivity of the option delta to changes in the underlying. Therefore

gamma will be positive if the delta rises in value when the underlying rises in value. When

the underlying rises, the delta of the option rises (and this rise in delta is the gamma).


Delta

Underlying

An increase in the time to maturity

has the same effect on delta as an

increase in volatility.

Gamma

Underlying

Gamma is highest at the money. This

is because at the money delta is most

sensitive to changes in the underlying.

This can be seen by the fact that the

slope of delta against the underlying is

highest at the money.

ATM ITM OTM

ATM ITM OTM

Long expiry

Short expiry


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Vega

-What is it?

Vega is the sensitivity of the option value to changes in implied volatility. Therefore

Vega will be positive if the option rises in value when implied volatility rises in value. An

intuitive way to look at it is that Vega is the sensitivity to implied volatility changes; gamma

is the sensitivity to realized volatility of the stock.

Gamma

Underlying

As a rise in volatility pushes out of the

money options closer to at the money,

ITM and OTM options experience an

increased gamma, while ATM options

experience a decreased gamma.

Gamma

Underlying

Increasing the time to maturity has

the same effect on gamma as an

increase in volatility.

High Vol

Low Vol

ATM ITM OTM

ATM ITM OTM

Long expiry

Short expiry


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Vega

Underlying

Option prices are most sensitive to

volatility changes at the money. This

is because this is where the

probability of the option ending in the

money is the most sensitive.

Intuitively, a deep out of the money

option is going to be a lot less

sensitive to changes in implied

volatility compared with an at the

money option.

Vega

Underlying

Higher volatility increases OTM and

ITM Vega as it pushes these strikes

closer to at the money.

Vega

Time to Maturity

As options move closer to expiry, they

become less sensitive to changes in

implied volatility. It can be seen that

short expiry options are more

sensitive to changes in the underlying

(high gamma, low Vega), whereas

longer dated options are more

sensitive to changes in implied

volatility (high Vega, low gamma).

ATM ITM OTM

ATM ITM OTM

High Vol

Low Vol


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Theta

-What is it?

Theta is the sensitivity of the option value to the passage of time. Theta is always

negative for a long position, as passage of time occurs in only one direction. Theta is

basically the decay of the options time value as time passes.



Theta

Underlying

Theta is highest at the money because

the option has the most time value at

this point.

Theta

Underlying

Rise on volatility has the same effect

on theta as on Vega. This is because

the time value OTM and ITM increases

more relative to ATM after a rise in

implied volatility.

ATM ITM OTM

ATM ITM OTM

High Vol

Low Vol


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Interest Rates and Dividend Sensitivity

-How do interest rate and dividend changes affect calls and puts?

The most intuitive way to think about it is what happens to the Forward price. An

increase in interest rates increases the forward price, while an increase in dividends

decreases it. The reason why this happens can be seen by looking at the Forward pricing

formula in section 1. Intuitively, as interest rates rise, it becomes more attractive to hold

the forward rather than the underlying asset. On the other hand, an increase in dividends

makes it more attractive to hold the underlying rather than the forward. Therefore call

options value rises with interest rates and falls with dividend increases, and vice versa for

puts.

-Are calls or puts more sensitive to interest rates?

There are two effects at play. The first one has been covered, and is the effect of

interest rates on the forward price. In this case puts fall with increases in interest rates and

calls rise. In addition to this, increases in interest rates decrease the value of financial

instruments that have a payment in the future due to discounting. This effect drags down

the price of both calls and puts. Therefore puts are more sensitive as the two effects work in

the same direction.

Theta

Time to Maturity

Theta decreases as the time to

maturity decreases. This is because

the option simply has less time value

to lose as it decreases as time passes.


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5) Volatility

-What is the difference between implied and realized volatility?

Realized volatility is the fluctuation of the underlying over a certain historical time

frame. Implied volatility is the projected volatility for a future period of time. Traders

generally observe the market price, and then back out the implied volatility that the option

is being priced at. In options markets, most traders use implied vols rather than monetary

price when quoting.

-What would you expect to be higher historically, implied or realized?

Historically, implied volatility can be seen to be higher than realized volatility.

Although this depends on the method used to measure realized volatility, the main reason

for this is that market agents are willing to pay a premium (irrationally or not) for being

long volatility. This is because being short volatility can easily wipe you out in a market

crash, and therefore holders of short options need to be compensated for the risk of going

bust.

-Why would you want to measure realized volatility relative to 0 rather than the

mean?

The simplest way of calculating realized volatility is to calculate the standard

deviation of the log natural returns:

, = 9:(ln(;) − ln(;))$<

However, what if the stock rises 1% each day for 5 days? Using the above method The

realized volatility is calculated as 0. However, to a trader the stock has not had a realized

volatility of 0. That is why on trading desks the calculation is done not relative to the mean

but to 0.

, = 9:(ln(;) − 0)$<

-What is the volatility skew/smile?

The skew is the phenomenon of lower strike options being priced at a higher implied

volatility than higher strike options, despite them referencing the same underlying which

will have a single realized volatility. In certain situations and in FX markets, the structure is

more of a smile shape, where both higher and lower strikes are priced higher relative to at

the money strikes.


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-What are the reasons behind the skew?

1. Downside protection buying: buying low strike puts is a common method of crash

protection for a portfolio; therefore these strikes are naturally bid up in the market

place.

2. Negative correlation between spot and volatility: it can be observed that stocks are

more volatile on the way down.

3. Non lognormal distribution of returns: the true historical distribution can be seen to

exhibit larger moves down than predicted by the normal distribution. The skew is the

market’s way of taking account for this, since the Black-Scholes pricing model does

not.

-When do you think the skew first appeared in option markets?

The skew first appeared following the October 1987 crash. Before that the volatility

structure across strikes was fairly flat.

-What happens to the skew structure of a target in a takeover bid?

If a stock is rumored to be taken over, the implied volatility on the higher strikes

rises and you can see a smile shape. This is because if a takeover bid is announced, the

stock will jump higher closer to the tender offer.

-Why is there more of a smile structure in FX?

The reason that there is a consistent smile shape in FX options is that a high strike

call on EURUSD, is basically also a low strike put on USDEUR.

-Describe what a delta hedge is.

Assume you are holding a call option with strike 100, and the underlying is currently

at 100. The delta of this option is 0.5, and the gamma is 0.02. Therefore you are long a call

and short 0.5 of the underlying. The following price schedule explains the effect of the delta

hedge. The profit on the option is calculated by taking the average delta over a move,

multiplied by the move:

�=��>� �� = �� + (�� + >�??� ∗ ?�=�)2 ∗ ?�=�


21

S=90 S=95 S=100 S=105 S=110

Call -4

0.5 + (0.5 − 5 ∗ 0.02)2 ∗ 5= −2.25

0

0.5 + (0.5 + 5 ∗ 0.02)2 ∗ 5= 2.75

6

Stock 5 0.5 ∗ 5 = 2.5 0 0.5 ∗ −5 = −2.5 5

Total 1 2.5 − 2.25 = 0.25 0 2.75 − 2.5 = 0.25 1

It can be seen that with a positive gamma, you make a profit in a delta hedge whether the

underlying moves up or down, and you make proportionally more the larger the underlying

move. This occurs because of the convexity of the option. The stock hedge is linear.

Therefore if the stock moves up, the option rises more than the linear hedge. If the stock

moves down, the option falls by less than the linear hedge. The bigger the move, the bigger

the difference between the convex options and the linear stock hedge. In the above

example, if the stock moves to 105, we can choose to rehedge at the new delta and become

delta neutral again. In this case we lock in a profit of 0.25, and the 105 becomes the new

100. However, by locking in a profit, you take away the chance of an even bigger gain if the

underlying moves farther in that direction. As you can see, with delta hedging options

become a trade on the level of volatility of a stock.

-If you buy a call option at 16% implied volatility and delta hedge, how much does

the underlying have to move per day to break even on your hedge?

The breakeven move is calculated simply by scaling down the volatility with square

root of time. Volatilities in the market are always expressed on an annual basis, and there

are 252 trading days in the year. Therefore the breakeven volatility is 16% annual, which

transfers to:

16 ∗ 9 1252 = 16 ∗ 116 = 1%

When a trader buys an option and delta hedges, he will make money on moves of

the underlying through the delta hedge as described above, but will lose money through

theta. Therefore the stock has to move enough every day for the trader to breakeven. If the

option is priced at a certain implied volatility, this is the annual realized volatility the trader

needs to break even. To transfer this to a move per day you simply scale down by the root

of time.


22

-If on a delta hedge you make money when the underlying moves up or down, why

not just always buy options and then delta hedge?

Because you paid a premium for this convexity of the option. Therefore the

underlying has to move up or down enough to counter theta loss of the option, which is an

erosion of the premium that was paid for the option. A trader pays theta every day, and the

stock needs to move enough throughout the day so that he can make more on the delta

hedge than what he loses on theta.

-How does correlation between the underlying and volatility affect a risk reversal?

A negative correlation is generally observed between the underlying and volatility.

Assuming a regular skew structure holds (lower strikes have higher implied volatility), if you

buy a risk reversal (long lower strike call, short higher strike call), then you are actually

short theta (as you are paying more to hold the lower strike call due to the higher implied

volatility that results from the skew), but at the same time you are short gamma (as a

higher volatility call has lower gamma). Therefore you are paying time decay and being

short gamma at the same, a bad position to be in.

-Let’s say an option is priced at 16% implied vol, but you think that its true value

should be 20%. Therefore you decide to buy the option and delta hedge. What

volatility input do you use to calculate your delta hedge ratio?

There is no correct answer to this question. You have two choices, you can either use

the implied volatility in the market (16%), which you know is wrong, or the implied volatility

you believe is correct (20%). If you use the market implied volatility your P&L will always be

positive throughout the life of the option, but the final payoff has randomness in it. On the

other hand hedging with 20%, your P&L at the end is pre determined, but the path of the

P&L can experience negative swings.

-What is dispersion trading?

There is a relationship that exists between an index’s volatility, and the volatility of

the underlying constituents:

,CD�EF = GH IC,C$ + 2 H H ICIJ,C$,J$5��C,J Therefore the index volatility is equal to the weighted square root of constituent covariance.

Dispersion trading consists of taking a long (short) volatility position in the index and a

short (long) volatility position in the underlying constituents. If it’s the former, then you are


23

betting that the correlations between the constituents that are implied by the market price

are too high. If the correlations fall, then the volatility of the basket of constituents will fall

and the short position will make money.

-What is a volatility swap?

A volatility swap is a contractual agreement between two parties to exchange

realized variances. A buyer of a volatility swap receives the realized volatility over a certain

time period in exchange for paying a set reference volatility. The final payoff is:

6�K�LL = (,M − 3NOP) ∗ "

Where ,M is the realized volatility, K is the reference volatility and N is the notional amount

per volatility point of the contract.

-What is a variance swap?

A variance swap is the same as a volatility swap except instead of volatility, it is the

realized variance that is being traded. Therefore the final payoff is:

6�K�LL = (,M$ − 3NQ�) ∗ "

-Why would someone want to trade volatility/variance swaps?

Vol/Var swaps are basically plays on the level of the stocks realized volatility, so why

not just use options and delta hedge as we saw in previous sections? The reason is that the

delta hedging strategy is extremely path dependent. A stock can have a realized volatility

higher than the implied you bought an option for and you can still lose money because your

P&L is largely determined by when you rehedge your deltas. This isn’t a problem with

vol/var swaps, as they take away the path dependence and allow a trader to solely profit

from any volatility difference between realized and implied.

-How would you go about hedging a variance swap?

The key to hedging a variance swap is creating a portfolio that has a constant

sensitivity to the stocks variance regardless of where the underlying is trading. If you buy a

string of call options weighted by the inverse of the square of the strike price, this portfolio

has a constant sensitivity to the stocks variance. This concept has a mathematical proof

behind it, but an intuitive grasp is enough.


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6) Introduction to Exotic Equity Derivatives -What is a Barrier Option?

It is an option where the option to exercise depends on the underlying crossing or reaching

a given barrier.

• Up and out: Barrier set above current spot price, and the option is cancelled if the

spot reaches the barrier

• Down and out: Barrier set below current spot price, and the option is cancelled if the

spot reaches the barrier

• Up and in: Barrier set above current spot price, and the option has to reach the

barrier to come into play

• Down and in: Barrier set below current spot price, and the option has to reach the

barrier to come into play

-How can barrier options lead to attempts at market manipulation?

If a market maker has sold a down and out barrier option, if there is low liquidity he

may attempt to push the price to hit the barrier.

-What is a Cliquet?

It is a series of at the money options (a chain where another option starts when one

ends). Therefore it is an option with a readjusting strike. The premium paid for this chain of

at the money options is determined in advance.

-What is a Compound Option?

It is an option on another option. A compound option therefore has two strike prices

and two expiration dates (as the underlying is also another option).

-When would a Compound Option be useful?

Compound options are mainly used for cases when a market maker needs to hedge

the possibility of being assigned options.

-What is a Binary Option?

It is an option that pays either nothing or a fixed value.


25

-What is the difference between a binary and a regular option in terms of gamma?

A long option is always positive gamma. However, as the binary moves into the

money, the gamma becomes negative as movements of the underlying make the probability

of ending up in the money lower.

-What is the Black Scholes Formula for a binary call that pays 1 if in the money?

The equation is simply the risk neutral probability of the option ending up in the

money multiplied by the payoff if in the money.

R = S�TUV(WX) ∗ X

-What is a Lookback Option?

It is an option that allows for the determination of the payoff at the end of the

options life. The payoff is determined to be the optimal value for the buyer. The payoff is

the maximum value of the asset over the time period, minus the strike. Lookbacks can be

either floating strike or fixed strike, referring to when the strikes are set.

-What is a Rainbow Option?

It is an option on the best or worst performer of several underlyings. The option is

basically a correlation trade, as this is a major factor in determining the value of the option.

For example if you buy a best of rainbow option on 10 different stocks, your payoff will the

same as a regular call option on the best performing stock of those 10.


26

7) Bonds

-What is the yield to maturity of a bond?

The YTM of a bond is the holding rate of return if an investor purchases the bond at

todays market price and holds it until the bond matures. It can be calculated by solving for

the discount rate in the bond formula that makes the value of the bond equal the current

market price. If the YTM is below the coupon rate of the bond, the bond is trading at a

premium to its face value, and if the YTM is above the coupon rate, the bond is trading at a

discount.

-Why is Yield to Call sometimes used instead of Yield to Maturity?

YTC is sometimes used if the bond is callable, therefore the issuer can repurchase it

before maturity. This shortens the life of the bond and reduces the number of cash flows.

The YTC is the holding return assuming the bond is called by the issuer.

-What is the relationship between a bond’s price and yield to maturity?

When prices of a bond go up, the yield to maturity goes down, and vice versa. This

is not a cause and effect relationship, but a relationship by definition. If an investor has to

pay more for a bond (where the repayment schedule of coupons and face value is held the

same throughout the life of the bond), then the holding rate of return by definition goes

down.

-What is duration and convexity of a bond?

Duration has two definitions when it comes to bonds. It can be looked at as average

time it takes to receive cash flows, therefore the weighted maturity of the cash flows. This is

called the Macauley duration and is calculated using the following:

YZ[\ = H U] ^_]^_`abWbc

Duration can also be defined as the sensitivity of a bonds price to changes in interest rates.

As can be seen on the following graph, the bond price is negatively related to interest rate

changes.


27

Modified duration measures the linear sensitivity of the bond price to interest rate changes,

and is calculated using the following:

YaW\ = − Xd ∗ edeT

As can be seen from the above graph, the bond price does not react linearly to changes in

interest rates, but rather in a convex fashion. The duration only estimates the slope of the

red straight line, while the bond actually behaves as described by the blue line. The

convexity of the bond measures the curvature of the bond price and is calculated using the

following formula: R = Xdf ∗ ef^_`abWeTf

Therefore a bond with a higher convexity will be more sensitive to interest rate changes

than one with lower convexity.

-What is the relationship between the coupon rate and convexity?

The lower the coupon rate, the higher the convexity. Zero coupon bonds can be seen

to have the highest convexity. This is because a low coupon’s bond value is more

concentrated at the end of the bond’s maturity because of the face value repayment, and

therefore the bond is more sensitive to changes in interest rates.

-When can a bond experience negative convexity?

A callable bond has a bond price ceiling, at which it will be called, and therefore at

lower yields the bond price has negative convexity due to the fact the bond price cannot go

higher than call price. This creates a limit. You can imagine in the above graph if the bond

price had an upper limit. At lower yields the blue line would lose convexity as it reaches the

limit.

-What is the difference between an off the run and an on the run bond?

An issuer has various bond issues at various stages. Off the run and on the run

refers to the newness of a bond issue. For example the US treasury may issue 30 year

bonds, and 2 months later issue more 30 year bonds. Now both of these bonds are pretty

much 30 year bonds, but the newer one will have more liquidity and is called the on the

run. One of the strategies of the notorious hedge fund LTCM was to short the on the run and

go long the off the run, as the two generally showed small mispricing.


28

-What is the value of a bond paying $10 annually forever with no principal

repayment and a 10% discount rate?

This type of bond is called a perpetuity, and can be valued by the following formula,

with CF standing for cash flow per year, and r standing for the appropriate discount rate:

^ = H Rg(X + T)U = RgT = Xcc. Xhc

= Xcc

-What does it mean for a bond to be callable/putable?

A callable bond is one where the issuer has the right but not the obligation to buy

back the certain bond at a certain price before maturity. This price is generally higher than

the face value of the bond. Basically, the issuer is long a call option on the bond. As the

holder is short a call option, a callable bond offers a higher yield compared to a straight

bond. An issuer might want to redeem a bond if it can issue debt at a lower interest in the

current conditions.

A putable bond gives the holder of the bond the right but not the obligation to sell

the bond back to the issuer at a certain price.

-Apart from being short a call option, why are callable bonds bad for investors?

An issuer will want to redeem bonds at a time of low interest rates. Therefore if a

bond holder receives the face value at this time, he can reinvest at a lower interest rate.

This is called reinvestment risk.

-What is DV01?

DV01, or dollar value of one basis point, is a risk measure used by interest rate

traders that calculates how much is made or lost for a 1 basis point move in the yield of the

underlying (1 basis point = 0.01%). Traders will have a sliding scale of their P&L for

various movements of yields but DV01 is the most basic and most crude risk measure

available. It is calculated by taking the average absolute P&L resulting from a basis point up

move and a basis point down move.

-What is the advantage of a municipal bond?

A municipal bond is a bond that is issued by a local government entity such as a

city, district, state, public school system or utility development organizer. The advantage of

municipal bonds is that they are exempt from federal tax and therefore provide an

advantage for buyers in a higher tax bracket. Municipal bonds are usually issued for a

specific project and provide returns from that project.


29

-What is a TIPS bond?

A Treasury Inflated Protected Security is a bond issued by the United States

Treasury and has the unique characteristic that the coupon and face value are adjusted

periodically for inflation. A bond that has a coupon rate of 3%, but the inflation rate is 4%

will in essence have a coupon rate of -1%. Especially with longer term bonds this can be a

problem for investors.

-What is the difference between a clean and a dirty price?

Since coupon payments are done semiannually/annually, at any point in between

coupon payments, the bond has an accrued interest. The clean price is the price of the bond

not including this accrued interest, while the dirty price is including the AI. Traders often

use the clean price instead of the dirty price because it is more stable, as the dirty price

provides daily fluctuations simply because of the effect of the accrued interest.

-What is the difference between the current yield and the nominal yield?

The nominal yield is the coupon rate of a bond, while the current yield is the coupon

divided by the current clean price of the bond.


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8) Introduction to Credit Derivatives

-What is a Credit Default Swap?

A Credit Default Swap is a contract that allows a bond holder to buy protection on

corporate/sovereign debt without having to sell any of the underlying. Let’s say that an

investor is holding 100 million of bonds on which he wants to buy protection. The investor

pays x% per year for the duration of the CDS and if the underlying experiences a credit

event (default etc), the buyer of the CDS receives 100 million less the recovery value of the

bond. Note that a CDS can be bought without owning the underlying debt, and ultimately

acts as a short position. The x% is referred to as the premium paid and the value of the

underlying protected is called the notional.

-What is a Constant Maturity CDS?

A CMCDS is similar to a regular CDS, except that the premium is referenced to a

CDS of a constant maturity. Therefore the premium is always calculated off of the same

maturity of CDS.

-What is a Credit Default Swaption?

It is an option to buy or sell protection on a reference entity exercisable in the

future. They are generally European (i.e. exercisable only on one date).

-What is the asset swap spread?

ASW is the difference in the yield of a bond and the maturity corresponding LIBOR

rate. It is used to look at the credit risk of a bond.

-What is the Z Spread?

The Z spread is the spread you would have to add to the treasury curve to arrive at

the market price. Imagine the curve of the yield of a bond and the treasury curve. The

spread between them isn’t constant along the curves. The Z spread finds a single measure

for the difference in the two curves.

-What is the CDS basis?

Both the asset swap spread and the CDS premium are measures of a bond’s

riskiness. The CDS premium less the LIBOR rate should equal the asset swap spread. The

difference between the two is called the CDS basis. However, in reality oftentimes the CDS


31

basis can either be positive or negative due to market forces and liquidity constraints. If the

bond is very illiquid, the asset swap spread might trade above the CDS premium. For a

great discussion see Choudry’s book ‘CDS Basis’.

-What are the key CDS indices?

• CDX NA IG: 125 investment grade names – North American

• CDX NA HY: 100 high yield names – North American

• CDX NA Crossover: 35 names that are at the crossover point between investment

grade and junk rated – North American

• CDX NA IG Hvol: 30 names from the CDX NA IG with the highest volatility – North

American

• iTraxx Main: 125 most actively traded names in the 6 month period before the index

roll - Europe

• iTraxx Crossover: 50 sub investment grade names - Europe

You can find daily levels at: http://www.markit.com/markit.jsp?jsppage=indices.jsp

-Describe how a Collateralized Default Obligation transforms risk?

A CDO pools cash flows from a wide source of assets, and chops them up. Let’s say

that there are 100 assets that pay an expected return of µ with a volatility of σ. There are

also 100 investors. Instead of each investor owning each asset and receiving (µ, σ), the

payments can be pooled together and split up so that each investor gets 1/100 of each

assets cash flow. If these assets are independent, each investor now has an expected return

of µ, but with a volatility of σ/100.

In addition to this pooling effect, CDO’s are created with tranches, where the CDO

has to lose a certain amount of its value in order for a tranche to fall in value. For example

a two tranche CDO will have a junior and senior tranche, where the senior tranche only

experiences losses until the junior tranche holders have been wiped out. Therefore out of a

series of assets, another security was formed with a lower level of risk.

9) Introduction to Interest Rate Derivatives -What is an interest rate swap

An interest rate swap is a contractual agreement for two parties to exchange cash

flows at certain dates. The following are variations of a vanilla swap:

• Fixed for Floating (same c

semiannual basis

• Floating for Floating (same currency):

rate, usually LIBOR in exchange for another key rate + spread

• Fixed for Floating (cross

floating rate in another currency

• Floating for Floating (cross currency)

• Fixed for Fixed (cross currency)

In cross currency swaps, the parties exchange the notional at the beginning and the end of

the transaction. For example if party A enters into a contract with party B where it receives

fixed GBP and pays fixed USD on a $100 million notional, then at the beginning of the

contract party A will pay $100 million in GBP to party B, and party B will pa

party A.

-What is LIBOR?

LIBOR is the London Interbank Offer Rate, or the interest rate at which A rated

banks are willing to lend to each other. The following chart shows the 1 month L

over the past 3 years and shows how it ac

Copyright 2011 lever

) Introduction to Interest Rate Derivatives & Swaps

wap, and what are the different vanilla variations?


flows at certain dates. The following are variations of a vanilla swap:

Fixed for Floating (same currency): A party exchanges a fixed rate for LIBOR on a

Floating for Floating (same currency): A party exchanges a floating rate for a floating

rate, usually LIBOR in exchange for another key rate + spread

Fixed for Floating (cross currency): A party exchanges LIBOR in one currency for a

floating rate in another currency

Floating for Floating (cross currency)

Fixed for Fixed (cross currency)


e transaction. For example if party A enters into a contract with party B where it receives


contract party A will pay $100 million in GBP to party B, and party B will pay $100 million to


banks are willing to lend to each other. The following chart shows the 1 month L

over the past 3 years and shows how it acts as a gauge of market health.


32

, and what are the different vanilla variations?


A party exchanges a fixed rate for LIBOR on a

A party exchanges a floating rate for a floating

A party exchanges LIBOR in one currency for a


e transaction. For example if party A enters into a contract with party B where it receives


y $100 million to


banks are willing to lend to each other. The following chart shows the 1 month LIBOR rate


33

-The LIBOR curve only goes out to 12 months, ideas on how you can extend it?

The LIBOR curve can be extended by looking at swap rates which extend out much

further. This is because the floating rate is LIBOR and therefore you can interpolate the

LIBOR curve by looking at the fixed rate corresponding to the desired maturity.

-How would you go about pricing an IR swap?

An interest rate swap is simply a series of cash flows, and therefore can be valued

through present value formulas. In a fixed for floating swap, the present value of the

floating stream is set to equal the present value of the fixed stream. Therefore the fixed

rate is set so that the initial value of the swap is equal to 0.

-What is an inflation swap?

It is a swap contract where the floating rate is tied to the inflation rate for the

reference period.

-What is a total return swap?

In a total return swap, the protection buyer and pays all interest and positive price

changes of an asset in return for LIBOR + spread and any negative price changes. In the

case of an asset default, the price is assumed to go to 0 and the protection buyer receives

the full market price.

-What is a Eurodollar futures contract?

A Credit

-What do you think the shape of a sovereign yield curve is under expectations of

an economic downturn?

A Credit


34

10) Interview Tips

Market Awareness

• Market indicators: know current level, trend over past 6 months and have an opinion

on the future movement

o Equities (Bloomberg.com)

� US: DJIA, S&P 500, VIX

� Europe: Estoxx, FTSE 500, VStoxx

� Asia: NIKKEI

o Credit (published on markit.com)

� Corporate: CDX NA IG, CDX NA HY, iTraxx Europe, iTraxx XO

� Sovereign: SovX WE, SovX CEEMEA

� Realized volatility on these indices

o FX (Bloomberg.com)

� EURUSD, USDJPY, GBPUSD

o Commodities ( Bloomberg.com)

� Crude, Gold

o Interest Rates (Bloomberg.com)

� LIBOR, EURIBOR, BOE rate, ECB rate, Fed Funds Rate

� UK 2yr, UK 10yr

� US 2yr, UK 10yr

� PIIGS developments

• Trade ideas

o You should be able to answer the following questions on each trade idea:

� What is your stop loss and why? What is your profit target and why?

� What is the timeframe for the trade and why?

o 2 long stock ideas (1 is fine)

o 2 short stock ideas (1 is fine)

o 1 FX idea

o 1 global macro (cross asset) idea

o 1 volatility idea (if you have access to a Bloomberg or Reuters terminal)

• News

o Know the 5 themes currently going on in the market

o Read the FT/WSJ on the morning of the interview, and remember a key story

and have an opinion on it

Documents

Leveredhedge.com The Complete Guide to Trading … to Derivatives (6) Fundamentals of Derivatives Pricing (8) Options Greeks (12) Volatility & Volatility Swaps (18)