3
$\begingroup$

Assume that I long ATM Call option on a stock at 20% implied volatility. This Call option will expire in 1 month. If, over this coming month, the underlying moves with 30% volatility and I delta-hedge this option. I expect to get profit from Gamma scalping. My expected P&L would be positive.

How would my P&L accumulate, on average,

Does P&L grow linearly over time, or does P&L grow exponentially over time?

Does moneyness of option affect accumulated P&L shape?

$\endgroup$
  • 5
    $\begingroup$ It accumulates randomly, depending on the specific path the stock price takes. The profit rate is determined by the current value of $S_t^2 \Gamma$ . $\endgroup$ – Alex C Feb 10 '17 at 4:06
  • $\begingroup$ Thank you, @AlexC. Can I say that P&L is path-dependent, but expected P&L is path-independent? $\endgroup$ – Jack JackGuRae Feb 10 '17 at 4:18
  • 1
    $\begingroup$ Well an expectation is by definition an average over all paths so the last part does not really make sense to me. See this related question here: quant.stackexchange.com/questions/30397/… $\endgroup$ – Quantuple Feb 10 '17 at 8:05
  • 1
    $\begingroup$ @Jack JackGuRae, also please have a look at Exhibit 2.1.1. here: trade2win.com/boards/attachments/f112/… $\endgroup$ – Quantuple Feb 10 '17 at 14:50

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.