European Call Option Valuation using a Binomial Model

A trader is evaluating a European call option on a stock using a two-period binomial model. The stock is currently priced at $50, with an up factor of 1.2 and a down factor of 0.8. The risk-free interest rate is 5% per annum, compounded continuously. After two periods, if the stock goes up twice, it will be worth $72.00; if it goes up once and down once, it will be worth $48.00; and if it goes down twice, it will be worth $32.00. The trader needs to determine the value of the European call option with a strike price of $55.

To do this, the trader constructs the binomial tree to find the call option values at expiration and then uses backward induction to determine the present value of the option.