Question

The current price of a stock is $50. In 1 year, the price will be either $65 or $35. The annual risk-free rate is 10%. Find the price of a call option on the stock that has an exercise price of $55 and that expires in 1 year. (Hint: Use daily compounding.)

Answer 1

                                            65

50                                          

                                           35                                              

Since the option is call option, where exercise price is $ 55

C_u = Max [65-55, 0] = 10

C_d = Max [35-55, 0] = 0

So the intrinsic value in one period binomial model is (A) $ 10 and $ 0

r = (1+.10) = 1.10

Upside factor (u) = 65/50 = 1.30,

Downside factor (d) = 35/50 = 0.70

P = (r-d)/(u-d)

= (1.10-0.70)/(1.30-0.70)

= 0.6667

With the value of probability we can find out the present value of the expected payout as follows:

= {10*0.6667+0(1-0.6667)}/1.1

= 6.667/1.1

= $ 6.06

So the Call option price is $ 6.06