I can just remember that short straddles have unlimited loss but how would you work that out mathematically?
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Short calls have unlimited risk. The investor is selling someone the ability to buy the stock at a specific price. If the counterparty exercises the call, the selling investor will need to buy the stock at the current (higher) market price to fill the order. Although they made received the premium, they will lose money on difference between the current market price and the strike price.
Consider a short ABC 10 call with a premium of 1:
- At a market price of 10, this option is at the money, the investor makes $1
- At a market price of 20, this option has $10 of intrinsic value, the investor loses $9
- At a market price of 120, this option has $100 of intrinsic value, the investor loses $99
- At a market price of 1020, this option has $1000 of intrinsic value, the investor loses $999
The market price could theoretically rise forever, so the maximum loss is unlimited.
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