Question

DEF Corp is currently trading at $38/share. Consider an option trading strategy consisting of:

1. A long European call on DEF with a strike price of $50, trading at $3.50

2. A long European put on DEF with strike price of $40, trading at $5

a) What are the intrinsic and time value of the call and put?

b) Draw a profit diagram for each option as well as the overall strategy (neat and labelled)

c) Construct the payoff table and profit, max potential loss, and breakeven points (there are 2)

d) If the stock price turns out to be $60 at the maturity date, what is the profit on the strategy?

Answer 1

We are given the following information:

Spot price (S) = $ 38, call price (C) = $3.50, call strike price (SP_c) = $ 50, put price (P) = $5, put strike price (SP_p) = $ 40

Now we can calculate:

call intrinsic value is given by (S - SP_c) and time value is simply (C - Intrinsic Value); however since this option is out of the money, it will not have any intrinsic value or its intrinsic value is zero. Thus the entire option value is time value hence the time value = C = $3.50

put intrinsic value is given by (SP_p - S) and time value is simply (P - Intrinsic Value); however since this option is also out of the money, it will not have any intrinsic value or its intrinsic value is zero. Thus the entire option value is time value hence the time value = P = $ 5

We will first create pay off table, profit, max potential loss and break even points:

Pay off on Long Call = Max (Expiry Price - SP_c - C, -C)

Pay off on Long Put = Max (SP_p - Expiry Price - P, -P)

Since these are long options, the maximum loss is limited to the sum total of the premiums being paid for both the options which is (3.50 + 5) = $ 8.50

For the break even point, we know that if the expiry price is above $38 then the put option will expire worthless and call option will make money only above $50, but to be over all in profit the expiry price should be above $ 58.5 (strike price + combined premium paid for both the options) to break even. Similarly for expiry price below $50, the call price will be worthless but the put will make money only when the expiry price is below $38 however to start making profit the expiry price should be below $29.5 (strike price - combined premium paid for both the options)to break even.

Hence the break even price levels will for expiry price below $29.5 or above $58.50. A profit (or loss table) for various prices is presented below along with the profit diagram:

we can see in the above table (or the pay off diagram) that at expiry price of $ 60 the profit is going to be $ 1.5. The calculations are as below:

Long Call profit = Expiry Price - SP_c - C = 60 - 50 - 3.50 = $ 6.50

Long Put loss = the put expires worthless and the maximum loss is limited to premiumm paid of P = $ 5

Net profit of strategy = (6.50 - 5) = $ 1.50