8/7/2019 Embeded option

http://slidepdf.com/reader/full/embeded-option 1/6

What is an embedded option in a bond? List the types of option that can be

embedded in a bond and discuss the impact of the embedded option on the value

of a bond.

Answer: An Embedded option is a component of a financial bond or other security,

and usually provides the bondholder or the issuer the right to take some action against

the other party. There are several types of options that can be embedded into a bond.

Some common types of bonds with embedded options include callable bond, puttable

bond, convertible bond, extendible bond, and exchangeable bond. A bond may have

several options embedded if they are not mutually exclusive.

Bonds with Embedded Options: Many bonds have embedded option features, like-

Callable Bonds: Give issuer right to redeem the issue call price (par).

Callable Bond = Straight Bond -Call Option

• Higher yield due to call option premium received

• As yields decline, value of call option increases, hence pricecompression

Pricing of callable bonds

• Price straight (i.e. non-callable) bond

• Price call option

Interest rate option model

Pr ice (CB) = Price (NCB)-Price (CO)

• Putable Bond

• Yield sensitivity

• Price compression

• Option-adjusted convexity & duration

• Yield to call: Calculate yield of bond assuming its expected cash flows arecoupon payments to the first call date plus call price.

• Yield to worst: Calculate yield to call for all call dates and pick the lowest

• Yield spread

• Static spread

• Option adjusted spread

• Monte-Carlo techniques

8/7/2019 Embeded option

http://slidepdf.com/reader/full/embeded-option 2/6

The Effects of Embedded Options on Bonds:

Options on bonds can be granted to both the issuer and the holder. Those options

most commonly granted to the issuer are call options, prepayment options,

accelerated sinking fund options and the cap on a floater. The first three are all

options that can be exercised in the case of falling interest rates so that the issuer may

refinance to take advantage of the lower market rates. A cap on a floater is basically

an option that requires no action. The issuer has the right to not pay more than the

cap. In this case this option becomes more valuable as rates increase.

Common options granted to the holder are conversion, put, and floor on a floating

interest rate. The value of converting the bond into stock is dependent upon the price

of the stock and the strike price of the option. Puts will get exercised in the case of 

rising interest rates and floors guarantee a minimum payment in a falling rate

environment.

Because of the value of the call or the put to either the issuer or the holder, the value

of bonds with an embedded option can be thought of as holding a portfolio of a bond

without an option and an option on the bond. The relationship is as follows:

Price of a callable bond = price of an option free bond – price of an embedded

call Price of a putable bond = price of an option-free bond + price of an

embedded put

To properly value a bond with embedded options you have to create a model that

takes into account the probability that the option will be exercised and the behaviour 

of issuers and borrowers to determine when they would exercise the option.The

difficulty that comes with valuing a bond with an embedded option is the uncertainty

of future cash flows that depend on uncertain future interest rates. This is called

expected yield volatility. Volatility has the effect of making options more valuable

but because of the relationship between the value of a put and a call to the holder,

the value of the bond itself can either rise or fall in an environment of increasing or 

decreasing volatility. This relationship is summarized in the following table:

8/7/2019 Embeded option

http://slidepdf.com/reader/full/embeded-option 3/6

Two bonds have identical times to maturity and coupon rates. One is callable at 105, the other at 110?

Answer: The call price is irrelevant for yield to maturity. With identical maturities andcoupon rates, the higher yield to maturity is whichever of the two bonds is trading at a lower price in the market.

The call price is important for yield to call. If all other aspects of the bonds are equal, thebond with the higher call price will have the higher yield to call.

Expected Interest Rate Callable Bond Price Putable Bond Price

Volatility

Increases Falls Rises

Decreases Rises Falls

8/7/2019 Embeded option

http://slidepdf.com/reader/full/embeded-option 4/6

Discuss the shortcomings of the P/E ratio as an analytical tool?

Answer:

P/E is short for the ratio of a company's share price to its per-share earnings. 

P/E Ratio = Market Value per Share

Earnings per Share (EPS)

Using the P/E Ratio: A stock’s P/E ratio tells us how much investor are willing to pay per 

dollar of earnings. For this reason it's also called the "multiple" of a stock. In other words, a

P/E ratio of 20 recommends that investors in the stock are willing to pay $20 for every $1 of 

earnings that the company generates

Problems with the P/E: The P/E ratio can help us determine whether a company is over-

valued or under-valued. But P/E analysis is only valid in certain circumstances and it has its

pitfall. Some factors that can undermine the usefulness of the P/E ratio include:

Inflation: P/E ratios tend to be lower during times of high inflation because the market seems

earnings as artificially distorted upwards. As with all ratios, it's more valuable to look at the

P/E over time in order to determine the trend. Inflation makes this difficult, as past

information is less useful today.

Many Interpretations: A low P/E ratio does not necessarily mean that a company is undervalued.

Rather, it could mean that the market believes the company is headed for trouble in the near future.

Stocks that go down usually do so for a reason. It may be that a company has warned that earnings

will come in lower than expected. This wouldn't be reflected in a trailing P/E ratio until earnings are

actually released, during which time the company might look undervalued. 

Accounting: In general, it's difficult to say whether a particular P/E is high or low without

taking into account growth rates and the industry. Changes in accounting rules as well as

differing EPS calculations can make analysis difficult.

8/7/2019 Embeded option

http://slidepdf.com/reader/full/embeded-option 5/6

Subject: Analysis - Price-Earnings (P/E) Ratio (article)

Last-Revised: 27 Jan 1998Contributed-By: E. Green, Aaron Schindler, Thomas Busillo, Chris Lott

P/E is shorthand for the ratio of a company's share price to its per-share earnings. For 

example, a P/E ratio of 10 means that the company has $1 of annual, per-share earnings for 

every $10 in share price. Earnings by definition are after all taxes etc.

A company's P/E ratio is computed by dividing the current market price of one share of a

company's stock by that company's per-share earnings. A company's per-share earnings are

simply the company's after-tax profit divided by number of outstanding shares.

P/Es are traditionally computed with trailing earnings (earnings from the past 12 months,

called a trailing P/E) but are sometimes computed with leading earnings (earnings projected

for the upcoming 12-month period, called a leading P/E). Some analysts will exclude one-

time gains or losses from a quarterly earnings report when computing this figure, others willpossibility of a late earnings report from a company; computation of a trailing P/E based on

incomplete data is rather tricky. Even worse, some methods use so-called negative earnings

(i.e., losses) to compute a negative P/E, while other methods define the P/E of a loss-making

company to be zero. The many ways to compute a P/E may lead to wide variation in the

reporting of a figure such as the "P/E for the S&P whatever." Worst of all, it's usually next to

impossible to discover the method used to generate a particular P/E figure, chart, or report.

Like other indicators, P/E is best viewed over time, looking for a trend. A company with a

steadily increasing P/E is being viewed by the investment community as becoming more and

more speculative. And of course a company's P/E ratio changes every day as the stock price

fluctuates.

The price/earnings ratio is commonly used as a tool for determining the value the market has

placed on a common stock. A lot can be said about this little number, but in short, companies

expected to grow and have higher earnings in the future should have a higher P/E thancompanies in decline. For example, if Amgen has a lot of products in the pipeline, I wouldn't

8/7/2019 Embeded option

http://slidepdf.com/reader/full/embeded-option 6/6

mind paying a large multiple of its current earnings to buy the stock. It will have a large P/E.

I am expecting it to grow quickly.

PE is a much better comparison of the value of a stock than the price. A $10 stock with a PE

of 40 is much more "expensive" than a $100 stock with a PE of 6. You are paying more for 

the $10 stock's future earnings stream. The $10 stock is probably a small company with an

exciting product with few competitors. The $100 stock is probably pretty staid - maybe a

buggy whip manufacturer.

It's difficult to say whether a particular P/E is high or low, but there are a number of factors

you should consider. First, a common rule of thumb for evaluating a company's share price is

that a company's P/E ratio should be comparable to that company's growth rate. If the ratio ismuch higher, then the stock price is high compared to history; if much lower, then the stock 

price is low compared to history. Second, it's useful to look at the forward and historical

earnings growth rate. For example, if a company has been growing at 10% per year over the

past five years but has a P/E ratio of 75, then conventional wisdom would say that the shares

are expensive. Third, it's important to consider the P/E ratio for the industry sector. For 

example, consumer products companies will probably have very different P/E ratios than

internet service providers. Finally, a stock could have a high trailing-year P/E ratio, but if the

earnings rise, at the end of the year it will have a low P/E after the new earnings report is

released. Thus a stock with a low P/E ratio can accurately be said to be cheap only if the

future-earnings P/E is low. If the trailing P/E is low, investors may be running from the stock 

and driving its price down, which only makes the stock look cheap.