Question

Selling a straddle with a strike price K_L has unlimited risk. We can mitigate this risk by buying a call option with a higher strike K_H. What is K_H if the maximum loss for the combined position is the same as the loss if S_T = 0 (stock price)?

Answer 1

Note: You can understand the solution better if you "ignore" the option price "P". We can assume 'P'=0 for this question. But you may get a question in exam where you need to consider the option price "P" in calculation.

A sell Straddle or a Short straddle involves simultaneously doing 2 things

a) Sell a PUT of stock 'S' with strike price 'X' and expiry date 'T'.

b) Sell a CALL of stock 'S' with strike price 'X' and expiry date 'T'.

When you sell a straddle with strike price 'KL', the pay-off diagram as shown below. 'P' is the price of PUT and CALL option.

For the Straddle, if Stock Price (ST)=0, there will be a LOSS. This LOSS= KL-2P.

The Loss is unlimited if the stock price keeps rising above "KL+2P".

To mitigate this risk, you buy a CALL with strike price 'KH' where (KH > KL) at price '2P'.

If Maximum LOSS allowed = "KL-2P".

Accordingly, let us calculate the value of KH.

We buy CALL because, the Short Straddle looses money if Stock Price increases beyond 'KL+2P'.

If Max loss= "KL-2P".

Then KH= (KL+2P) + { KL-2P}

KH= 2*KL.