Question

A stock is currently priced at $45. It will either increase by 20% or decrease by 10% over the next two months. If you sold a put option with exercise price of $45 and two months to maturity, how many shares of stock should you buy or sell to hedge the option?

Doesn't give risk free rate.

Answer 1

Current Stock Price = $ 45 | Upstate = 20% | Downstate = 10%

Exercise Price of Put option = $45

First we will look at the stock prices in each state.

Upstate Stock Price = 45 * (1+20%) = 54

Downstate Stock Price = 45 * (1 - 10%) = 40.5

Now using the Upstate and Downstate prices, we can find the payoffs from selling the put option.

By selling put option, you are giving the right to sell the shares at Exercise price, hence, you will be receiving the shares at Price of $ 45

Payoff in Upstate = Upstate Price - Exercise Price = 54 - 45 = $ 9

Payoff in Downstate = Downstate Price - Exercise Price = 40.5 - 45 = $ - 4.5

As you would be receiving the shares at Rs 45, therefore, to hedge the option, you must sell one share at the Spot price to complete the position.

Following payoff will occur by selling 1 share in spot market.

Payoff from Spot market in Upstate = Stock Price - Upstate Price = 45 - 54 = $ -9

Payoff from Spot market in Downstate = Stock Price - Downstate Price = 45 - 40.5 = $ 4.5

The Payoff from Spot market are opposite of Put Option's payoff. Hence, Selling of one share in spot market will hedge the position.