A perpetual option is one that never expires. (Such an option must be of American style.) Use Exercise 6 to show that the value of a perpetual call on a non-dividend-paying stock is \(C=S\).

Data from Exercises 6

Consider a European call option on a non-dividend-paying stock. The strike price is \(K\), the time to expiration is \(T\), and the price of one unit of a zero-coupon bond maturing at \(T\) is \(B(T)\). Denote the price of the call by \(C(S, t)\). Show that

[Consider two portfolios:

purchase one call,

purchase one share of stock and sell \(K\) bonds.]

Transcribed Image Text:

C(S,1) max[0,S-KB(T)].