Question

You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $120 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%.Based upon your assumptions, calculate your estimate of the the call option's value using the two-state stock price model.

Answer 1

Answer:

$13.64

Explanation:

Given:

Exercise price,X = $100

Current price = $100

Value when price is up, uS = $120

Value when price is down, dS= $80

Risk free interest rate = 10%

First calculate hedge ratio, H:

$H = \frac{C_u - C_d}{uS - dS}$

Where,

Cu = uS - X

= 120 - 100

= $20

$H = \frac{20 - 0}{120 - 80} = \ftac{1}{2}$

A risk free portfolio involves one share and two call options.

Find cost of portfolio:

Cost of portfolio = Cost of stock - Cost of the two cells.

= $100 - 2C

This portfolio is risk free. The table below shows that

_______________

Portforlio 1:

Buy 1 share $80; Write 2 calls: $0; Total: ($80 + 0) $80

____________________

Portforlio 2:

Buy 1 share: $120; Write 2 calls: -$40; Total: ($120 - $40) $80

Check for oresent value of the portfolio:

Present value $= \frac{80}{1 + 0.10} = 72.73$

Value = exercise price - value of option

$72.73 = $100 - 2C

Find call option, C

$C = \frac{100 - 72.73}{2} = 13.64$

Call option's value = $13.64