FINA3204 03 Options Basics

The Hong Kong University of Science and Technology

FINA 3204: Derivative Securities Andrew Chiu

Derivative Securities FINA 3204

Options Basics

Andrew Chiu, PhD [email protected]



Course Overview

Forwards & Futures

Market Mechanics

Hedging Strategies

Pricing

Options

Market Mechanics

Properties Trading

Strategies Pricing

Binomial Tree

Black-Scholes

Greeks

Other Derivatives

Warrants, CBBC Swaps Convertible

Bonds Structured Products



Review of Option Types

A call is an option to buy

A put is an option to sell

A European option can be exercised only at maturity

An American option can be exercised at any time



K = Strike price, ST = Price of asset at maturity

Payoff Payoff

ST ST K

K

ST ST K

K

Payoffs from Options What is the Option Position in Each Case?



Payoffs in Equation Form

Long Call: max( 0, ST K )

Short Call: - max( 0, ST K )

Long Put: max( 0, K ST )

Short Put: - max( 0, K ST )



Underlying Asset

Stocks, FX, stock indices, futures

Expiration date (T)

Quarterly, Monthly, Weekly expirations, LEAPS

Strike price (K or X)

European or American

Most options are American style

Call or Put

Settlement (Cash or Physical) http://www.hkex.com.hk/eng/sorc/frontend/stk_opt_faq_3.htm#04

https://www.interactivebrokers.com/en/index.php?f=deliveryExerciseActions&p=optionEx

Options Contract Specification



Terminology

Moneyness At-the-money option (ATM)

In-the-money option (ITM)

Out-of-the-money option (OTM)

Intrinsic Value The value derived from the options moneyness

Time Value The part of option value that is in excess of its

intrinsic value



Margins are required only when options are written

Hong Kong Stock Option Margin Requirements: http://www.hkex.com.hk/eng/sorc/margin_data/margin_data

_search.aspx

Chicago Board of Options Exchange http://www.cboe.com/micro/margin/introduction.aspx

If you own the stock and you write a call on the stock, should you be subject to the same margin

requirement?

Portfolio Margin

Margin



Options Exchanges U.S.

CBOE (major options exchange)

CME Group (futures options)

Asia-Pacific

HKEX http://www.hkex.com.hk/eng/prod/drprod/so/classlist_so.htm

Australian Securities Exchange

Tokyo Stock Exchange

Korea Exchange (index option only)

Singapore Exchange (index option only)



c: European call option price

p: European put option price

S0: Stock price today

K: Strike price

T: Life of option

s: Volatility of stock price

C: American call option price

P: American put option price

ST: Stock price at option maturity

D: PV of dividends paid during life of option

r Risk-free rate for maturity T with cont. comp.

Notations



Effect of Variables on Option Pricing

Variable c p C P

S0 + +

K + +

T + (no div) ? (with div)

+

+ +

s + + + +

r + +

D + +



Bounds for European or American Call Options (No Dividends)



Bounds for European and American Put Options (No Dividends)



c max( S0 Ke -rT , 0 )

Simple Bounds on Option Prices

p max( Ke -rTS0, 0 )

c S0

C S0

p Ke rT

P K

Upper Bounds

Lower Bounds

C c

P p



Suppose that

Is there an arbitrage opportunity?

c = 3 S0 = 20

T = 1 r = 10%

K = 18 D = 0

Calls: An Arbitrage Opportunity?



Suppose that

Is there an arbitrage opportunity?

p = 1 S0 = 37

T = 0.5 r = 5%

K = 40 D = 0

Puts: An Arbitrage Opportunity?



If this relationship is violated, then there exists an arbitrage opportunity because the payoffs are the same on both sides.

This applies only to European options.

Can you identify the following popular strategies in this equation?

Protective Put using put option to insure against price drop

Capital Guaranteed Fund

Covered Write

Synthetic Futures

Put-Call Parity for European Options

c + Ke -rT = p + S0




c + Ke -rT = p + S0

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Pay

off

Stock Price at Expiration



Put-Call Parity for European Options c - p = S0 - Ke

-rT

c - p = [F0 K]e -rT

-40

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60

Pay

off





S0 - c = Ke rT - p

0

5

10

15

20

25

30

35

0 10 20 30 40 50 60

Pay

off




Using Put-Call Parity for Replication

In the real-world, we can substitute a call with a put and vice versa.

This is sometimes useful if one option is more liquid or have tighter bid-ask spread than the other.

Can you create a straddle using only call options? Only put options?



Suppose that

What are the arbitrage possibilities when

p = 2.25 ?

p = 1 ?

c= 3 S0= 31

T = 0.25 r = 10%

K =30 D = 0

Put-Call Parity Arbitrage Example



c max( S0 PV(D) Ke rT, 0 )

Effects of Dividend

p max( Ke -rT S0 + PV(D), 0 )

Lower Bounds

Put-Call Parity

c + Ke -rT = p + S0 PV(D)



Early Exercise of American Options

Should you exercise or sell the option?

An American call on a non-dividend paying stock should never be exercised early

Call option price is always larger than intrinsic value, so it is better to sell on the market

In this case, we have C=c

In reality, a large number of calls are exercised

It is optimal to exercise an American put on a non-dividend paying stock if it is deep in-the-money

Ex: Imagine a stock falls to $0.01, the put option has almost reached maximum value and has very little to gain by waiting.



Early Exercise of American Options

With dividends, it is more complicated.

Sometimes it is optimal to exercise call options before an ex-dividend date

In general, it is optimal to exercise if the dividend amount is larger than the options time value. When you exercise, you give up the time value in return for

receiving the dividend by holding the stock.



Early Exercise Example (Call) Assume rf = 0 One day before

Ex-Dividend Date Ex-Dividend Date

Stock S=100 S = 99, Div = 1

European Call (X=90) c =9.20 c > S Div K

American Call (X=90) Suppose C = 9.20 (too low!)

Buy call: -9.20 Exercise: -90 (receive stock in 2 days) Short Stock: +100

Receive Div = 1 to pay borrower Arbitrage Profit: 0.80 C >= S K

American Call (X=90) Short-dated Suppose C = 10.30

Exercise: pay -90 to buy stock Cost of call: -10.30

S = 99 Div = 1 Loss = -0.30 (better to exercise)

Dont Exercise Cost of call: -10.30

C = 9.30 Loss: -1

American Call (X=90) Long-dated Suppose C = 12

Exercise: pay -90 to buy stock Cost of call: -12

S = 99 Div = 1 Loss = -2

Dont Exercise Cost of call: -12

C = 11 Loss = -1 (better NOT exercise)

When exercising is optimal, then the market price will be C = S - K



Dividend Capture

Assume rf = 0 Before Ex-Dividend Date Ex-Dividend Date

S = 100 American Call (X=90) Suppose C = 10 Buy Stock: -100 Sell Call: +10

Counterparty Exercises: Sell stock for X=90: +90

Profit = 0

Counterparty Doesnt' Exercise: S=99, Div=1 C = 9 Buy back call: -9 Sell stock: +99 Receive Dividend: +1 Profit = +1 Even if S deviates from 99 by small amounts, the profit is still +1

Buy stock and Sell in-the-money calls to capture dividend when the counterparty does not exercise the call.

Documents

FINA3204 03 Options Basics