Question

The Amazon stock price is currently $200. The quarterly compounding risk-free

interest rate is 4% per annum. Amazon stock will have an expected return of 10% with volatility of 25% per year. What is the value of a 3-month European call option on the Amazon stock with a strike price of $200?

Answer 1

Using Binomial model,

Probability ie P= R-d/u-d

where, R= Risk free interest

d = down side volatality

u = upside volatality

R = 4% p.s(assume continuously compounded)

= (1.04)3/12 =1.009% (approx)

Therefore,

u = 1.25

d= 0.75

P =1.009-0.75/1.25-0.75

= 0.518

= 0.52(approx)

1-P = 1-0.52

=0.48

As per Binomial model,

Call ie C0 =[P*Cu + (1-P)Cd] / Rf

where ,

Cu = 200*1.25-200

= $50 ie value if call option exercised

Cd = 0 ie value if call lapses

Thereore,

C0 = [0.52 * 50 +0.48*0]/1.009

= $25.77 (approx) ie value of Call option