Question

RTF Inc. has options traded on the CBOE. As a measure of its volatility, assume the stock price can either go up at $40 or down to $15. Interest rates that apply are 1%. Consider a strike 25 call option. Using this strike price and the two possible binomial prices for the stock, the dollar cash flow that a risk-free hedge will generate under each possible strike price will be?

Answer 1

Price at Upmove = $40

Price at Downmove = $15

Strike Price = $25

Risk free rate = 1%

Now, for creating a risk free hedge, we need to sell the call option and buy the stock. This can be calculated as follows:

Payoff at Upmove: * $40 - Max($40 - $25, 0) = 40 - 15

Payoff at Downmove: * $15 - Max($40 - $25, 0) = 15

Since, it is a risk free combination, both should be equal. So,

40 - 15 = 15

40 - 15 = 15

25 = 15

= 15/25 = 0.6.

Thus, for a risk free hedge, we need to buy 0.6 stock for every call option sold. Thus,

Payoff at upmove = 0.6 * $40 - Max($40 - $25, 0) = 24 - 15 = 9

Payoff at Downmove: 0.6 * $15 - Max($40 - $25, 0) = 9

Dollar Cashflow at both the possible price of this risk free hedge is $9.