Question

Let’s assume that, on any given week, a stock is equally likely to increase or decrease by $1 in price. We will assume that the price movements are independent from week to week also. Suppose that the current price of a stock that we’re interested in is $50. I agree to buy a "call option" that lets me purchase the stock for $55 after 10 weeks if the share price is greater than $55. If the price is less than $55 after 10 weeks, then the option is not exercised. Assuming no transaction fees and an interest rate of 0%, what is a "fair" price to pay per share for the option?

Answer 1

The fair price of a call option can be determined using probabilistic methods involving the expected payoff, considering the stock's potential price paths and the terms of the option contract.

Step-by-step explanation:

The question pertains to calculating the fair price of a call option on a stock with a current price of $50, where the stock price has an equal chance of increasing or decreasing by $1 each week, independently. To determine the fair price of the option, one would use probabilistic methods from financial mathematics, often involving a binomial pricing model, that considers the various possible stock price paths over the 10-week period and the payoff of the option if it is in the money (exercise price above $55). However, to provide an exact answer, one would need to perform a detailed calculation that includes all possible outcomes, their probabilities, and the corresponding payoffs. In this scenario with no transaction fees and a 0% interest rate, the option price would be the present value of the expected payoff.