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I want to estimate the historical price of out of the money puts on equities.

I do have about 10 years history of implied volatility (IV) but I would like more.

I had the naïve idea modeling the IV with historical vol (HV) and calibrate my model on the 10 year data I have.

Any better suggestions / ideas?

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  • $\begingroup$ How are you going to use these estimates? $\endgroup$ – Bob Jansen♦ Mar 22 '17 at 17:03
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    $\begingroup$ It's not clear to me what you mean by "I would like more"? Also what is the objective ? price a fixed moneyness fixed time to expiry put option as time goes by (historically)? Or do you want the full market-implied volatility surface each day? It is not clear either IMHO $\endgroup$ – Quantuple Mar 22 '17 at 19:18
  • $\begingroup$ Actually I would like a historical surface. $\endgroup$ – Jean-Christophe Curtillet Mar 23 '17 at 10:59
  • $\begingroup$ Bloomberg provides IV for various moneyness and expiries only up to 2008. Actually I am looking at the performance of reverse convertibles (RC)over time. A RC is just a bond plus a put (mostly out of the money) on an equity. Such that I would like to estimate the price of the puts before 2008. I dot not need a tradable price but a rough estimate. $\endgroup$ – Jean-Christophe Curtillet Mar 23 '17 at 11:06
  • $\begingroup$ So you are looking for the implied volatility surfaces that historically prevailed on some past trading days, before 2008, for which you have no options' data and only historical prices series for the equity, is that right? If it is, please edit your question to make it clear please. $\endgroup$ – Quantuple Mar 30 '17 at 14:51
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You can't estimate historical prices because they are given to you already. If you're trying to estimate future implied volatility based on historical implied volatility and historical volatility, then that is possible.

  1. Use any statistical package or code to calculate HV based on underlying asset
  2. Take your IV data and calibrate your HV model somehow (this part is up to you)
  3. Project new IV into the future via Black-Scholes
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    $\begingroup$ I thinks he's just looking to derive historical implied volatilities from historical "classic" volatilities. No prediction. $\endgroup$ – SRKX Mar 23 '17 at 3:46
  • $\begingroup$ Thanks SRKX for the clarification. You are correct. Bloomberg provides IV for various moneyness and expiries only up to 2008. I need to go further. I am looking at the performance of reverse convertibles (RC)over time. A RC is just a bond plus a put (mostly out of the money) on an equity. Such that I would like to estimate the price of the puts before 2008. I dot not nee a tradable price but a rough estimate. Thanks $\endgroup$ – Jean-Christophe Curtillet Mar 23 '17 at 11:09

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