0
$\begingroup$

I would like to compute the evolution of the P&L of an FX plain vanilla option. Unfortunately, I am not sure about the correctness of my reasoning.

Let's imagine that I sell a 1W call option on a Monday. On that day, I will receive a premium which in my case, is computed using Garman and Kholagen pricing method. Let's say that the premium is \$10, can I say that my P&L is +\$10 right after having sold the option ? In my opinion, at the time, the P&L is \$0, not +\$10.

Let's imagine that on Day 2, if we recompute the option with the new market data, we obtain a premium of \$9. On Day 2, is it right to say that my P&L is (10-9) = \$1 ? My reasoning is that I sold at \$10 something that now only worth \$9.

If that reasoning is correct, I would continue like that until the end of life of the option.

If on top of that, I have to delta-hedge my position on a daily basis. Is it correct to do the following ?

Let's imagine that on Day 1, the ∆ is -0.5, I will buy 0.5 of spot. On that day, the P&L of the delta hedging is 0.

Let's imagine that on Day 2, the spot moved from 1.1 to 1.2. Can I compute the P&L as follows: -∆*(1.2-1.1) = 0.5*0.1 ?

I would be a great help if someone can confirm or not my reasoning.

Thanks

$\endgroup$
3
  • 3
    $\begingroup$ P&L is profit and loss, not earnings or money spent. So on Day 1 PnL is zero because you earned \$10 for something that is worth \$10 to your conterpart. No profit, no loss. Same principle applies to hedging which is permanently trading in the underlying creating realized profits or making losses. $\endgroup$
    – Kurt G.
    Mar 18, 2022 at 13:15
  • $\begingroup$ Thanks for you answer @KurtG. Regarding the reasoning for the following days, do you agree ? $\endgroup$ Mar 21, 2022 at 10:47
  • $\begingroup$ '@MaximeWillemet' . I agree. $\endgroup$
    – Kurt G.
    Mar 21, 2022 at 10:56

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.