Question

consider a 2-year european call option. the strike price is $90. the current stock price is $115. consider a two-step binomial tree with each step equal to one year. in each time step, the stock price either moves up by 20% or moves down by 20%. a dividend of $6 will be paid in time 1. the one-step risk-free interest rate is 6% (in periodic compounding). a) (3 pts) calculate the price of the call option. b) (3 pts) find the replicating strategy at time 0 and time 1.

Answer 1

The problem requires calculating the price of a 2-year European call option and finding the replicating strategy using a binomial model, including adjustments for dividends and using the risk-free rate for option valuation.

Step-by-step explanation:

The question asks to calculate the price of a 2-year European call option using a two-step binomial tree method and then find the replicating strategy at time 0 and time 1. When dealing with option pricing, one must take into account the possible future movements of the stock price, the strike price of the option, dividend payments, and the risk-free interest rate. In this case, the current stock price is $115, the strike price is $90, the stock can either go up or down by 20%, a dividend of $6 is paid after one year, and the one-step risk-free interest rate is 6%.

To calculate the option price, we build a binomial tree for the stock price, adjust stock prices for dividends, and then use risk-neutral valuation to back-calculate the option price from the possible prices at expiration. The replicating strategy involves determining the number of shares and the amount of risk-free bonds needed at each node of the binomial tree to replicate the option's payoff.