Question

Harbin Manufacturing has 10 million shares outstanding with a current share price of $24.07 per share. In one​ year, the share price is equally likely to be $30 or $20. The​ risk-free interest rate is 6%.

a. Using the​ risk-neutral probabilities, what is the value of a​ one-year call option on Harbin stock with a strike price of $25​?

b. What is the expected return of the call​ option?

c. Using the​ risk-neutral probabilities, what is the value of a​ one-year put option on Harbin stock with a strike price of $25​? d. What is the expected return of the put​ option?

Answer 1

First of all we shall look up at the formula of risk neutral probability for an up move.

= (1 + r - d) / (u - d), where

r = risk free interest rate

d = down move factor which is calculated as stocks down price divided by stocks current price

u = up move factor which is calculated as stocks up price divided by stocks current price

Now we shall answer the questions

a) value of one year call option

up move probability = (1 + 0.06 - 0.83) / (1.25 - 0.83)

= 0.55

Probability of down move = 1 - probability of up move = 1- 0.55 = 0.45

Value of call option in an upmove = stocks expected price - stocks strike price = 30 - 25 = 5

Value of call option in an downmove = stocks expected price - stocks strike price = 20 - 25 = 0 (Since the maximum loss in case of call option is zero in case stocks moves below its strike price)

So value of call option is

= 0.55 x 5 + 0.45 x 0 = 2.75. In order to get the present value , we need to divide the same by one year discount rate i.e.

=2.75 / 1.06 = $ 2.59

b) Expected return of call option is given by

Stock price - strike price - option premium

= 30 - 25 - 5 = 0

c) Value of one year put option is as follows:

Value of put option in an upmove = stocks strike price - stocks price = 25 - 30 = 0 (Since the maximum loss in case of put option is zero in case stocks moves above its strike price

Value of put option in an downmove = stocks strike price - stocks price = 25 - 20 = 5

The risk neutral probabilities would be computed similarly as computed in above part i.e. 1.25 for up move and 0,83 for down move.

So the value of put option is

0.55 x 0 + 0.45 x 5 = 2.25.

In order to get the present value , we need to divide the same by one year discount rate i.e.

=2.25 / 1.06 = $ 2.12

d) Expected return of put option is

Strike price - stock price - option premum

= 25 - 20 - 5

= 0