Question

A stock price is currently $50. It is known that at the end of one year it will be either $40 and $60. The exercise price of a one-year European call option is $55. The risk-free interest rate is 5% per annum. Construct a binoamial tree to show the payoff of the call option at the expiration date. (5%) Based on the binomial tree model, what is the value of the call option? (15%) Address the relation between the binomial tree model and the Black-Scholes model. (5%)

Answer 1

Strike Price (X) = $55

Stock Price (S) = $50

Time (t) = 1 Year

Rate of interest = 5% p.a.

Calculation of Higher Probability (HP) = Stock price*((1 + r) ^ t) – Low Price /

(Higher Price – Low Price)

                        HP = $50 * ((1+0.05) ^ 1) – $40/ ($60 - $40)

                              = $12.5 / $20

                              = 0.625

Lower Probability (LP) = 1 – HP = 1- 0.625 = 0.375

Working: -

The binomial Model and the black Scholes model is the two different method of calculating the option price by using the varied assumptions and theories.

In the Black Scholes Model we use to calculate the call price theoretically while considering the five key determinants like the stock price, strike price, volatility, expiration time and interest rate.

While in the binomial distribution we calculate the value of call price by considering the stock price, strike price, time expiration, interest rate and probability for upward and downward movement.