Question

A Show Work 5 Question Help 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 20% or go down by 20%. The stock pays no dividends. The one-year risk-free interest rate is 8.6% 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 The price of the one-year put option is $ (Round to the nearest cent.) 4.6))

Answer 1

The current price of Estelle Corporation stock is $ 23. the stock price will either go up or down by 20% for the next 2 years. But the put option is for 1-year only so we consider price change only for 1 year.

In the binomial Model, we find the option price by using probability and estimated future prices of stock and options.

The binomial model for the given question is as follows :-

Put Option Price 1 Year 27.6 18.4 4.6

Buying a Put Option gives you a right to sell the stock underlying at a future date. Thus,

Value of Put Option at expiry is zero if the price of stock is more than the Strike Price.

If value of stock is less than the stock price then,

Put Option Price at expiry = Strike Price - Stock price on expiry

The option price at the end of one year will be as follows :-

1. If stock price goes up by 20%, then Put option Price will be zero as stock price ($ 27.6) is more than strike price of put option ($ 23).

2. If stock price goes down by 20%, then

Put option Price = Strike Price - Stock price on expiry

= 23 - 18.4

Put option Price = $ 4.6

The price of the stock will either go up or down by 20%. Thus, the probability of both the options is 50%.

Value of Put Option on Expiry = ( Probabilty1 * Price1) + (Probabilty2 * Price2)

Value of Put Option on Expiry = ( 50% * 0 ) + (50% * 4.6 )

Value of Put Option on Expiry = 0 + 2.3 = $ 2.3 per option for one share.

We found the value of Put Option on expiry which is 1 year from now, but we need value of Put Option as on today.

Thus, we discount the price at the risk free rate i.e, 8.6% for one year and we will get the price of put option today.

Present Value = Future Value * (1+r)"

were r = Discount Rate per period

n = number of periods

Present Value of Put Option = 2.3 * (1+0.086)

Present Value of Put Option = $ 2.1179 = $ 2.12 per option for one share.

Thus, the price of one-year Put option with a strike price of $ 23 on Estelle Corporation stock is $ 2.12 per option for one share.