Consider a European call option on a non-dividend-paying stock. The strike price is S. The expiration...

 

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Consider a European call option on a non-dividend-paying stock. The strike price is S. The expiration date is T. The current price of the stock is Ko. The price of one unit of a zero-coupon bond maturing at T is q. Notice that by definition, a zero-coupon bond pays one unit of payoff at time T. Denote the price of the call by Oc, show that Oc max (Ko Sq, 0). - [Hint: Compare two portfolios: (a) purchase a call, (b) purchase one share of stock and sell S units of bonds.] Based on this inequality, prove that the price of a perpetual call must be Oc = Ko. The perpetual option is the one that never expires (i.e., no expiration. Such an option must be of American style.) [Remember to argue that Ko Oc.] Consider a European call option on a non-dividend-paying stock. The strike price is S. The expiration date is T. The current price of the stock is Ko. The price of one unit of a zero-coupon bond maturing at T is q. Notice that by definition, a zero-coupon bond pays one unit of payoff at time T. Denote the price of the call by Oc, show that Oc max (Ko Sq, 0). - [Hint: Compare two portfolios: (a) purchase a call, (b) purchase one share of stock and sell S units of bonds.] Based on this inequality, prove that the price of a perpetual call must be Oc = Ko. The perpetual option is the one that never expires (i.e., no expiration. Such an option must be of American style.) [Remember to argue that Ko Oc.]

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Proof using Portfolio Comparison Part 1 Call Option vs Stock and Bond Portfolio We can prove the inequality using a noarbitrage argument This means that we cant create a riskfree portfolio with guaran... View the full answer