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:
[tex] H = \frac{C_u - C_d}{uS - dS} [/tex]
Where,
Cu = uS - X
= 120 - 100
= $20
[tex] H = \frac{20 - 0}{120 - 80} = \ftac{1}{2}[/tex]
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 [tex] = \frac{80}{1 + 0.10} = 72.73 [/tex]
Value = exercise price - value of option
$72.73 = $100 - 2C
Find call option, C
[tex] C = \frac{100 - 72.73}{2} = 13.64 [/tex]
Call option's value = $13.64
