When calculating the volatility or covariance matrix of stock returns for the purpose of pricing a vanilla option on an underlying, it is difficult to choose the window over which the volatility should be calculated. What are the pros and cons of using a window length equal to the maturity of the option, compared to hard-coding a single window size? This is in the context of naively applying a standard model to price several contracts either with volatility calculated over the same window or each depending on their own maturities, rather than say dynamically calibrating a volatility surface.

  • $\begingroup$ I remember an old paper by S. Figlewski (NYU) that showed that using the historical volatility for the last N months when pricing an N months option gave fairly good results, so he recommended this approach. Keep in mind however that using historical volatility is backward looking and somewhat simplistic by today's standards. $\endgroup$
    – noob2
    Apr 15 at 13:04
  • $\begingroup$ I will have a look for the paper, thank you! I completely agree it is not the way to go in practice, however this will only be used for an example in an introductory resource into options pricing, rather than any real-world application or advanced courses. $\endgroup$
    – user54806
    Apr 15 at 13:32
  • $\begingroup$ I think it was called Forecasting Volatility Using Historical Data and is from the mid 1990's $\endgroup$
    – noob2
    Apr 15 at 13:34

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