Exhibit 22.5
Use the Information Below for the Following Problem(S)
The information provided is relevant in the context of a one period (one year) binomial option pricing model. A stock currently trades at $50 per share, a call option on the stock has an exercise price of $45. The stock is equally likely to rise by 25% or fall by 25%. The one-year risk free rate is 2%.
-Refer to Exhibit 22.5.Estimate n,the number of call options that must be written.
A) -1.4286
B) -2.9286
C) -2.8571
D) -2.5714
E) -1.1111

Question

Quizplus · Accepted Answer

Current stock price = $50
Exercise price = $45
Risk free rate = 2%
Price in one year if stock rises = 50(1.25)= $62.50
Price in one year if stock declines = 50(1.25)= $37.50
Intrinsic value of call option if stock rises to $62.50 = Max[0,62.50 - 45] = $17.50
Intrinsic value of call option if stock falls to $37.50 = Max[0,37.50 - 45] = $0
Estimate the number calls needed by setting:
The hedge portfolio will consist of one share of stock held long plus some number of call options written.
Value of hedge portfolio if stock rises = Value of hedge portfolio if stock falls
62.50 + (17.5)(n)= 37.50 + (0)(n)
n = -1.4286

Exhibit 22.5 Use the Information Below for the Following Problem(S)