Payoff and Loss Limits for a Covered Call
Summary
The document asks how to determine the loss limit for a short European call combined with a long stock position, given an initial stock price, call premium, and zero interest rate. The responses describe the position’s terminal outcomes: if the option expires unexercised, the stock can be sold at its market value; if exercised, the stock is delivered at the strike. These cases determine the position’s profit or loss relative to the purchase price and premium received.
One answer clarifies that the stock’s market value at exercise is observed rather than calculated in advance. Another gives conditional payoff expressions and explains how the maximum loss depends on whether the call was initially out of the money or in the money. The discussion is informal and uses inconsistent notation, so the formulas should be checked carefully against the trade’s entry cash flows and exercise assumptions before applying them. The key point is that a covered call limits upside and can still lose money when the stock falls.
Key ideas
- A covered call combines a long stock position with a short call.
- If the call is exercised, the stock is sold at the strike; otherwise, it can be closed at its market price.
- The position’s loss depends on the stock’s terminal value, strike, initial purchase price, and option premium.
- The source’s notation and cash-flow presentation warrant careful checking before using its formulas.
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Full text
# Computing loss of Call / Stock Purchase # Computing loss of Call / Stock Purchase A seller of an European Call, can, subjectively have unbounded losses. This loss may be mitigated by buying the stock (covered call). In this case,, the loss will be bounded at A. How would one compute the value of A? in this case, the interest rate is 0, the initial stock price is S, the price of call is C, and C is greater then S. Also, there is no position at t=0. Now you sell call and buy the stock. Because S is greater then C, you borrow S - C. Additionally, at expiration, you must pay this back. How would one even begin to compute A here? I have no clue. ## Answer by AfterWorkGuinness (score 0) https://quant.stackexchange.com/a/21278 $A$ is the market value of the stock at the time of exercise - making the loss to the short covered call $A_T−K$ where $A_T$ is the market price of the stock at exercise and $K$ is the strike. You observe $A$, not calculate it (at least in the context of your question). ## Answer by HyperVol (score 0) https://quant.stackexchange.com/a/24340 Let's say the exercise time is T , and you bought the stock at time t < T. p would be your premium for the transaction you just mentioned , your PNL at the exercise time depends on following 2 cases :- - if not exercised ( ie ST < X ) : p - St + ST , i.e. you closed your long position at exercise time. - if exercised ( ie ST > X ) : p - St + X Assuming that you sold an OTM option (which would be a fair consideration ) ,then St < X , meaning payoff for Case 2 is always Hence , if you sold an OTM option , your loss would be capped at ( from Case 1 ) : St - ST and if you sold an ITM option , your loss would be capped at ( from both cases ) MAX ( St - ST , St - X - p )
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