Option Pricing using Black-Scholes. Lecture XXIX. The European Call Option. First, we construct the payoff function for a security on which the option is written as: where x j ( k ) is the payoff a share of security j purchased an exercise price of k . .
where xj(k) is the payoff a share of security j purchased an exercise price of k.
where is the time preference parameter
where is the correlation coefficient.
or that future consumption is discounted at the risk-free rate of return.
which is implicitly the pricing condition of stock in period 0 given its utility distribution in period 1 (enforces a zero arbitrage condition on the stock price).