Question

The current price of Estelle Corporation stock is $ 23.00. In each of the next two​ years, this stock price will either go up by 19 % or go down by 19 %. The stock pays no dividends. The​ one-year risk-free interest rate is 7.3 % and will remain constant. Using the Binomial​ Model, calculate the price of a​ one-year put option on Estelle stock with a strike price of $ 23.00.

Answer 1

Binomial Distribution requires calculation of probabilty of either the stock price rising or declining in the said period.

Current Stock price (S) = $ 23

Change % = 19% (Both rise and decline)

New price in case of rise = 23*1.19 = $27.37

New price in case of decline = $18.63

Calulation of Probabilty: (r-d) / (u-d)

r = interest received = 1 + 7.3% = 1.073

u = increase percntage

d = decline percentage

Probabilty of increase in the price = (1.073 - 0.81) / (1.19 - 0.81)

= 0.62

Probabilty of decrease in the price = 1- 0.62 = 0.38

In the given diagram, as it can be seen the price either rises or falls. Rise will lead to $27.37 and fall will lead to $18.63. As the buyer of the call will exercise the option only when the strike price is less than the spot price. The buyer will exercise option only when the price rises as in the other case the spot price will be less than $ 23.

For calculation of Call price, the exercise price will be multiplied with the probabilty. The same will be discounted with the interest rate as we need the price of the call option in the present value.

Price of Call Option = ($27.37*0.62) / 1.073 = $ 15.815

Using Call Put Parity theoem:

Call + PV of Strike Price = Put + Stock Price

Strike price will be discounted with the interest rate as we need the strike price in the present value.

Put Option = $ 15.815 + ($ 23/1.073) - $23 = $ 14.25