Question

Question one

Consider a two-period binomial model in which a stock currently trades at a price of K65. The stock price can go up 20 percent or down 17 percent each period. The risk-free rate is 5 percent.
(i) Calculate the price of a put option expiring in two periods with exercise price of K60.
(ii) Calculate the price of a call option expiring in two periods with an exercise price of K70.

(iii)‘Risk management is not about elimination of risk’, Discuss.

Answer 1

As time has not given in question , assumed 1 year , with 2 steps Binomial model as,

for PUT option with strike price = 60

At each node:
Upper value = Underlying Asset Price
Lower value = Option Price
Values in red are a result of early exercise.
Strike price = 60
Discount factor per step = 0.9753
Time step, dt = 0.5000 years, 182.50 days
Growth factor per step, a = 1.0253
Probability of up move, p = 0.5235
Up step size, u = 1.20
Down step size, d = 0.80

Value = 3.212

For Call option: with strike price of 70.

Strike price = 70
Discount factor per step = 0.9753
Time step, dt = 0.5000 years, 182.50 days
Growth factor per step, a = 1.0253
Probability of up move, p = 0.5235
Up step size, u = 1.2001
Down step size, d = 0.8332

Value of Call = $ 6.15.

Answer iii) Risk management is systematic process for identification , analysis and treatment of identified risk in such a way that it creates a positive return for investors . This is different from risk elimination. The risk management has many aspects as

• Risk reduction
• Risk aversion
• Risk acceptance
• Risk increment in expectation of higher return.