Question

Problem 1: A call option of strike K > 0 is a financial contract that payoffs S>K dollars if S > K and 0 dollars otherwise where S is the stock price of the company at maturity.

I shall use ![.] for the indicator function, and φ(z)-(2π)-1/2e-0.5? Problem 1: A call option of strike K > 0 is a financial contract that payoffs S -K dollars if S> K and 0 dollars otherwise where S is the stock price of the company at maturity (i.e. a date in the future specified in the contract). Assume S is a continuously distributed random variable having density function with support (0, oo) given by n)-m where m and σ > 0 are real paramete, and Ln is the logarithmic function. Let Z denote the random variable having density function ф. Show that the expected payoff of the call option is given by emto2/2PIZ > d1]-KPlZ > dal where di-(Ln(K)-m-p?)/ - (Ln(K)-m)/σ. This is a simplified version of the Black and Scholes model ( 'The Pricing of Options and Corporate Liabilities'. Fischer Black and Myron Scholes, Journal of Political Economy, 1973, vol. 81). σ and d2 Hint: the payoff is equal to (S- K)> K]

Answer 1