Question:
In regard to exotic options:
(i) If c = value of a European call option, what is the value of the same but where it is a forward start option?
(ii) If we increase the frequency of observing the asset price, what happens to the value of a lookback call? What happens to the value of a barrier option?
(iii) Warren Buffet has argued that executive stock options ought to be indexed to the Standard and Poor’s 500 index, instead of striking with a fixed exercise price (since the owner of such an option profits from even riskless appreciation in the stock)? Which exotic valuation can be used for this sort of indexed stock option?
Answer:
(i) The value is c. For a non-dividend paying stock, the value of a forward start is the same as the value of a regular at-the-money option with the same life as the forward.
(ii) The lookback becomes more valuable as we have more chances to observe a lower minimum. Regarding the barrier, it DEPENDS on the type of barrier option. More frequency = greater chance of triggering the barrier: a knock-out goes DOWN in value, but an knock-in goes UP in value.
(iii) This is tantamount to an EXCHANGE option because the exercise is indexed to another asset (the S&P;500 index). As such, it can be valued by a variant of the Black-Scholes called the Margrabe. (Hull 6th Edition, p 540).
