Question

The current price of a stock is $30, and at the end of one year its price will be either $33 or $27. The annual risk-free rate is 3.0%, based on daily compounding. Based on the binominal option pricing model, what is the present value of a 1-year call option with an exercise price of $26?

Answer 1

Using Risk neutral binomial Oprion pricing -

Current Stock Price S0 = 30, Su = 33 and Sd = 27

Since there is no probability mentioned for upside or down side it is safe to assume risk neutral and hence the probability is 0.5

Strike price Sk = 26

Therefore pay off at both upper and lower movement -

Payoff U = 33-26 = 7

Payoff D = 27-26 = 1

Cost of option at C1 (at the end of 1 year) = 7*0.5 + 1*0.5 = 4

Present Value of Option = 4 / (1+r)^1

   = 4 / (1.03)^1 = 3.88  

Therefore, Present Value of Option = $ 3.88