Question

Given the following parameters use risk-neutral valuation to value a call option.

Current stock price:	$65.00
Stock will increase or decrease next year by:	15 pct.
Call Option strike price:	$60.00
Time to expiration:	1 year
Risk free rate:	8 pct.

A) Value of call: $9.44

B) Value of call: $13.66

C) Value of call: $10.47

Answer 1

Select - Option - (C) ........ $ 10.47

Explanation.

Step - 1 ............Find the values for " u ' and ' d '

u = Ratio if price goes up = 1.15 ......... ( 1 + 15%)

d = Ratio of price goes down = 0.85........( 1 - 15 % )

Step - 2 ..........Determine the probabilities

Probability to go up .......Using risk neutral approach ( also called binomial approach )

Pu = ( 1 + r - d ) / ( u - d ) = ( 1 + 0.08 - 0.85 ) / ( 1.15 - 0.85 )

= 0.23 / 0.30

= 0.766666667

Pd = Probability to go down = 1 - Pu

= 1 - 0.766666667

= 0.233333333

Step - 3 .........Find the values for Call option ........ Cu ( price increases ) and Cd ( when price decreases )

Cu = 65 * 1.15 - 60 = 14.75

Cd = Maximum of ( 65 * 0.85 - 60 , 0 )

= Max ( - 4.75, 0 )

= 0

Step - 4

Value of a Call = [ Cu * Pu + Cd * Pd ] / ( 1 + r )ⁿ

Here " n " = Number of years = 1

= [ 14.75 * 0.766666667 + 0 * 0.233333333 ] / (1.08)

= 11.3083 / 1.08

= $ 10.47