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Measuring Monthly Mark-to-Market Returns for Long-Dated Index Puts

Article Quant Q&A · Author: nzc
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Summary

The document raises a backtesting problem for a systematic strategy that repeatedly buys one-year, 90% strike equity index puts and rolls them shortly before expiry. It proposes repricing the option each month with Black–Scholes using the current spot, remaining time, and volatility while keeping the original strike fixed between rolls. This captures changes in option value from both delta and vega, unlike tracking intrinsic value alone.

The central question is how to express monthly performance when percentage changes in a low-priced option can look disproportionately large. The document does not provide a solution, empirical results, or a preferred return convention. It identifies the need to distinguish the option’s price change from the return on the strategy’s capital or risk budget. Any backtest would also depend on its volatility inputs, pricing assumptions, and treatment of premiums and roll dates.

Key ideas

  • A monthly option mark can reflect spot, volatility, and time-to-expiry changes while the strike remains fixed between rolls.
  • Intrinsic value alone omits the effects of volatility and time value on the option mark.
  • Percentage changes in a low-priced option can be large and may not describe strategy-level performance well.
  • The document poses the return-measurement question but supplies no method or backtest evidence.

Tags

OptionsEquitiesVolatilityBacktesting
Full text
# Accounting of a stock put option for Monthly % Changes


# Accounting of a stock put option for Monthly % Changes












am looking to backtest a strategy of systemic put buying on an equity index (e.g SPX Index) so say a strategy of buying 1Y 90% SPX Puts rolled 1 day prior to expiry.

As opposed to only calculating the intrinsic value of the option prior to rolling (ITM/OTM/ATM), I would like to calculate the monthly MtM of the strategy so I can get exposure to the vega/delta effects.

Am able to calculate the price of the option at the end of each month via BSM as a function of Spot,Time,Vol while keeping the initial strike constant but am having issues with how to best calculate the Monthly Returns of the option since a simple % chng from the option price is going to have especially outsized % p/ls which isnt entirely representative.

Any help would be appreciated! Thanks.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.