Question

Suppose you are given the following prices for the options on ABC stock:

CANNOT BE ON EXCEL

Strike (in $)                 call                  put

15.0                             1.6                   2.0

17.5                             1.2                   2.5

20.0                             0.9                   3.2

1. Suppose you take the following position: long one call with strike 15.0, short two calls with strike 17.5, and long one call with strike 20.0. Please draw the payoff at maturity.
2. What would be the total gain (loss) on the above position if the stock price at maturity turned out to be S(T) = 16 (taking into account the price of the options)
3. Suppose you decide to buy a 15.0 straddle (1 long call + 1 long put with the same strike of 15.0). Please draw the payoff at maturity.
4. Over what range of underlying stock price (at maturity) will you lose money (after taking into account the price you paid for the options)?

Answer 1

a.

The graph can be drawn after tabulating the payoff of different options and its payoff and profit(considering option price). Red colour is total Profit diagram( considers the option price as well) and Blue colour is total Payoff( without considering cost of option)

b.

Total gain(loss) if stock price at maturity is 16$; = Payoff of all options- cost of options

=1+0+0-(1.6-2.4+.9)= .9$

c.

Total Payoff is Blue line (without considering option price ; Total Profit is red line( with option price)

d.

From the graph, when the stock Price is between 12 - 18 $ (11.4$-18.6$ to be exact); the Straddle at 15$ strike price will loose money after considering the option prices into account.

Proof: when stock price at 11.4$ ;

Profit for straddle at 15$= (15-11.4)-1.6-2= 0$ ;

When Stock price at 18.6$;

Profit= (18.6-15)-1.6-2 = 0$ ;

In between these price range profit goes negative.