Question

Use the two state call option value in this problem. Data: S0=130 ; X=143 ; 1+r=1.1. The two possibilities for ST are 160 and 109. Calculate the value of a call option on the stock with an exercise price of $143.

Answer 1

10.3

Step-by-step explanation:

The computation of the value of a call option is shown below:

But before that we need to do the following calculations

P = (r - d) ÷ (u - d)

where

r = 1.1

d = down price ÷ current price

= 109 ÷ 130

= 0.838

u = up price ÷ current price

= 160 ÷ 130

= 1.231

Now placing these values

= (1.1 - 0.838) ÷ (1.231 - 0.838)

= 0.6667

Now the value of the call option is

= (cu × p) + cd × (1 - p) ÷ R

= (17 × 0.6667) + 0 × (1 - 0.6667) ÷ 1.1

= 10.3

The cu could come from i.e. payoff in that case when the option is exercised

= 160 - 143

= 17

cd = payoff in that case when the option is not exercised