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I have designed a call writing option strategy, where I am rolling the options upon expiry, i.e., my portfolio consists of one short call position at any given time.

I have a time series of the value of the option for each day. At expiry, I have a 0 if the option ends OTM and my payoff liability otherwise.

What is the correct approach for calculation my daily P&L time series?

How do I then summarise the performance of this strategy? Do I simply annualise this daily return time series?

TIA

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The main problem with your description is that one option is not a consistent quantity when it comes to a portfolio strategy.

  1. The $ exposure of your option changes as the underlying price of the option changes.

  2. If you look at it from a portfolio basis. Assuming your strategy makes money, the value of the option you sell will become less and less significant in comparison to the portfolio value.

To compute a daily time series, I would suggest redefining your strategy to either sell premium that is a constant proportion of your portfolio, or sell a number of options whose notional is a constant proportion of your portfolio.

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  • $\begingroup$ Although, a portfolio that includes an option with a varying exposure should still have a return! $\endgroup$ – Jared Sep 3 '18 at 16:55
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I think I could've been more specific with my question. I'm just selling call options on the same stock with price $S$, and at every point in time, I never have more than one short call position in my book.

The option is always written on $1$ share of the underlying.

So everyday (except $T_0$) I can mark-to-market my short call option position with the Black-Scholes formula, with the current $S, r, \sigma \text{ and } \tau$. My P&L on day $t$, $PnL_t$, $PnL_t = V_{t-1}-V_{t}$ (if I was long call It'd be $PnL_t = V_{t}-V_{t-1}$). I have a daily P&L time series but this is not my daily return.

This is where I'm stuck, I've seen examples where people taking this daily P&L time series and divide by the strike of the current option, so their return on day $t$, $r_t$, is $r_t=\frac{PnL_t}{K}$. Does this make sense?

Thanks

VB

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  • $\begingroup$ The key question is how much capital will you employ in this strategy. Without knowing the capital you can't define the return or the risk. If the capital is equal to the strike price (which seems like interesting/reasonable assumption, at least as a starting point) then yes you could define the return as $r_t=\frac{PNL_t}{K}$ $\endgroup$ – Alex C Sep 9 '18 at 16:32

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