How can we compute the expected value of P&L assuming the option price is given? Do we need to have more information to calculate P&L?

  • $\begingroup$ The option expires worthless no? $\endgroup$
    – simsalabim
    May 10 at 19:02
  • $\begingroup$ @simsalabim: assume it is before expiration. $\endgroup$
    – Ken
    May 10 at 19:28
  • $\begingroup$ If you have the option price, you can obtain the implied volatility. This implied volatility parameter you need to transfer somehow into the volatility of the spot. If you have done that, you can construct the underlying time series to a certain degree. Then you do Monte-Carlo simulation to obtain $N$ time series for $M$ trials. You then do your trading on these series. You then obtain a vector with PnL's then you do the statistics etc etc etc $\endgroup$
    – simsalabim
    May 10 at 19:56
  • $\begingroup$ @simsalabim: Thanks, could you please provide a reference with more details? $\endgroup$
    – Ken
    May 10 at 19:59
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    $\begingroup$ Isn't the current value of an asset equal to its expected payoff discounted at the risk-free rate? Insofar, your Pnl is expected to be zero. If it were not, who would be willing to sell something to you if you would be better off? Or why would you buy it if you expect a loss? If you use implied vol in MC as simsalabim suggested, you would still need to have an idea of the underlying process. If it is not as BS suggests, why would you use BS to model the price. If it is, you will end up with the expected payoff, which after discounting, will be you premium. $\endgroup$
    – AKdemy
    May 10 at 20:56

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