Question

Consider a one-step binomial tree on stock with a current price of $200 that can go either up to $230 or down to $170 in 2 years. The stock does not pay dividend. Continuously compounding interest rate is 5%. Compute the payoff of a 2-year $210-strike European call option on the stock if the stock price ends up at the $230 node of the tree in 2 years.

Answer 1

Exercise Price, E = 210

Stock Price at end of 2 years, S = 230

A call option gives an option holder a right to buy the stock in future at an agreed price set today

Clearly, the option holder will exercise the option when E<S , that means he or she can buy the stock at lower price (E) and sell the stock in market at price S making a gain.

In this case, Payoff = S-E

= 230 - 210 =20

Therefore, the option holder has payoff of 20 at end of 2 years.

If we take the Present value of that payoff today, we get

PV = 20 / ert

where r = rate of compounding, t is no. of years

PV = 20 / e0.05*2

= 18.097