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# P2.T5.412. Exotic options: forward start, compound and chooser

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
AIM: Identify and describe the characteristics and pay-off structure of the following exotic options: forward start, compound, and chooser

Questions:

412.1. The price of a vanilla (non-exotic) at-the-money European call option, today, with a one year maturity is $15.05; if we extend the maturity to two years, the price of the option is$22.58. Now consider a forward start at-the-money European call option, on the same underlying stock, that will start in one year (T1 = 1.0 year) and mature one year later, two years from today (T2 = T1 + 1.0 year = 2.0 years). The continuous dividend yield on the underlying stock is 5.0% per annum, and the riskfree rate is 3.0% per annum; both are expressed with continuous compounding. Which is nearest to today's price of the forward start option?

a. $13.89 b.$14.32
c. $14.61 d.$21.48

412.2. Consider the four main types of compound options:

I. call on a call,
II. call on a put,
III. put on a call,
IV. put on a put

With respect to the value of the compound option as a function of the underlying asset price, which of these compound option's value is (are) a DECREASING function of the underlying asset price?

a. None, the compound values are all (each) an increasing function of asset price
b. IV. only (put on a put)
c. II. and III. (call on a put; put on a call)
d. III. and IV. (put on a call; put on a put)

412.3. Consider a chooser option where the underlying is Microsoft's stock (ticker: MSFT). The options underlying the chooser are both European and have the same strike price (i.e., simple chooser) of $35.00. The choose date is six months (T1 = 0.5 years) and the maturity of the options is one year (T2 = T1 + six months = 1.0 year). The riskfree rate is 3.0% per annum with continuous compounding. A long position in this chooser option is most similar to which of the following trading strategies, and how does the initial cost compare to the similar strategy? a. Long straddle but chooser is cheaper b. Short straddle but chooser is more expensive c. Long calendar spread with similar cost d. Long Butterfly spread but chooser cheaper Answers here: #### ivojekle ##### New Member Probably I don't see something, but I really don't understand 412.1. Why is the value of the European option with maturity 2 years different than the option which starts in one year and mature one year later. Both options have the same maturity date (two years from today) and we value them on the same date. I would undesrtand if options were American, but if they are European seem to be fundamentaly the same. Thanks for answer Ivo #### Alex_1 ##### Active Member Hi, as I read the text of the question: the two options don't have the same maturities: for one T = 1, for the other T = 2 ("(T2 = T1 + 1.0 year = 2.0 years")? So they have different time values and so different overall values, if I am not mistaken. BR, Alex #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi @ivojekle I agree with @Alex_1 but there is even another difference (there are two difference). First, consider the "standard" two-year ATM call option with price of$22.58. Let's say that is based on current stock price of \$100.00 (my examples are generally based on actual inputs, but I don't have these assumptions handy). This is an ATM call such that T = 2.0, S = 100, and K = 100. Not only does the one-year forward start have a maturity of one-year but, as of today (T0), the strike price is unknown. The forward start will be struck at the money in one year, so while the two-year option has a strike of 100, the expected strike of price of the one-year forward is higher.

Additional evidence is provided if we simply assume no dividend on the stock. As the price of a forward start = c*exp(qT), where q = 0, as Hull shows, the price of the forward = c. In the above question, if we eliminate the dividend yield, then the price of the one-year forward is 15.05 (equal to the price of the current one-year call option). This one year forward will expire in two years, on the same maturity date as the current two-year option, but the price is considerably less than 22.58. I hope that helps,

#### ivojekle

##### New Member
Thanks both,

now I understand - strike is not fixed - it it ATM.

Ivo