Question

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

Strike (in $)                 call                  put

15.0                             1.6                   2.0

17.5                             1.2                   2.5

20.0                             0.9                   3.2

please write the solving process without using excel

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) Here actually you can see that there are three breaking points: 15,17.5,20

So let discuss the payoffs case by case

case 1 : when price is less than 15:

Here the one long call with strike 15 and 20 will not be exercised because price is less than the stirke so we have to loose the price of the options which we have paid already.

Also the two short calls will of strike price 17.5 will also not exercised as price is less than the strike price

payoff gain or loss(prices of respective calls) = -1.6 + 2*1.2 - 0.9 = (-)0.1 that is loss to us

Case 2nd : when price is in between 15 and 17.5

here the long call of strike price 15 will be exercised only and other calls will not

payoff = (Stock price - Strike price) -1.6+2.4-0.9 = (S - X) of 15 one - 0.1

Case 3rd when price is between 17.5 and 20

only the call of long 20 will not exercise

payoff = (Stock price of 15 one call - strike price of 15 one call) + 2 x [ -(Stock price of 17.5 one - Strike price of 17.5 one ) -0.1

Case 4th when price is above 20

all calls will be exercised

so payoff will be = (Stock price of 15 one call - strike price of 15 one call) + 2 x [ -(Stock price of 17.5 one - Strike price of 17.5 one ) + (stock price of 20 - Strike of 20) -0.1

b) here S(t) = 16

case 2 will apply

payoff = (16 - 15)-0.1 = 0.9 profit

c) in straddle we purchase the call and put option or in other words take long position in them.

here both call and put have strike price of 15 and also their price is 1.6 and 2

here will be 3 situation

when price is less than 15

then only put will be exercised and pay off will be = (Strike price of put - stock price) -2-1.6 = (Strike price of put - stock price) - 3.6

when price is 15

no one will be exercised

payoff = -3.6

when price is above 15

call option will be exercised :

payoff = (Stock price - strike price at call ) - 3.6

d) sorry i am not sure for which part it is asking for plz clarify .

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