Question

XYZ stock is trading at $100. The effective 3 month interest rate r = 1%. 3 month options on XYZ are trading at the following prices:

Strike Price	Call Price	Put Price
95	7.05	1.81
100	4.11	3.86
105	2.14	6.88

1. Buy XYZ for $100 and buy a 95 strike put.

a) What is the cost for this position?

b) Construct the payoff and profit graphs for this position.

c) Take the same amount of cash as in a) and instead buy the 95 strike call and invest the rest in 3 month zero coupon bonds yielding r.

d) Construct payoff and profit graphs for this position.

e) How do your graphs from b) and d) compare?

Answer 1

1. Buy Stock for $100 and buy a 95 strike Put (Also called as Protective Put)

Protective Put buyer is bullish in view on the underlying and buys Put option to protect from the losses when stock value goes down. Hence the downside loss is limited to the premium paid, and upside potential is unlimited.

a)Cost involved for this position = $1.81

Trader owns the stock and buys Put option.

Below is the pay off and profit diagram for Protective Put:

c) Own stock and sell call

This strategy is also called as Covered Call. Trader is stable on the underlying with low volatility expectation. Hence when stock goes up, call buyer exercises the option and the Trader has obligation to exercise the short Call. Call writer owns the stock and shorts Call. He forgoes upside profit for premium received upfront for selling the call. Below is the Payoff and Profit diagram for the same:

d)Difference between the Payoff is, Protective Put has unlimited upside potential gains whereas Covered Call writer limits his profits for the upfront premium received. However, both traders benefit from upswing in the stock.