Question

A trader buys a put on a stock having a certain strike price and buys a put on the same stock having a higher strike price. She also writes (sells) two puts having a strike price in the middle of the other two strike prices.

            a. Illustrate the resulting payoff pattern (profits for different possible stock prices at the expiration date) this position will give the trader. Explain.

            b. If you didn’t include the answer to this question for “a,” include it now: if the stock price at expiration turns out to be higher all three strike prices, what will the payoff turn out to be? Explain why.

Answer 1

a) A put option is an option in which the buyer have right to sell the the stock at predetermined price to the seller of the option at some put price.

So let say we have a put price of $2 and we purchased and sell the puts as under.

Purchase 1st put - at strike price of $x

Sell two puts at strike price of $y

and purchase 2nd put at strike price of $z where X<Y<Z

So there may be different situation for payoffs that are explained as under:

case 1: when price is less than x, then all the puts will be exercised because stock price is less than strike price in all cases

so Payoff will be = (X - Stock price) - 2*(Y-stock price) + (Z-stock price) +2+2-2-2

Case 2nd when price is in between X and Y then the put of X will not be exercised but the later one will be

so payoff will be = -2*(y-stockprice)+(z-stock price) +2+2-2-2

Case 3 when stock price is bewtween y and z then only z one will be exercised

payoff = (z-stock price)+2+2-2-2

case 4 when price is above z then no one will be exercised so payoff will be

payof =2+2-2-2 = 0

b) so as we can see in a also that if the price is higher than all 4 puts then there will be no loss or no gain provided that all puts are same price. otherwise answer wll change accordingly.

for example if put price is 2 for all

payoff will be = 2+2-2-2 = 0

if different let say he purchase put at 3 and sell puts at 2

then payofff will be = -3-3+2+2 = -2 loss

thanks

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