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### Comparison between Heston models calibrated by historical time series and instant option prices.

Posted: **March 6th, 2015, 4:33 am**

by **EdisonCruise**

Is it possible to make a volatility trading strategy like this: (1) Use SP500 historical time series to calibrate Heston model, then calculate the expected realized volatility v1 in the period T.(2) Use SP500 option prices to calibrate Heston model, then calculate the expected realized volatility v2 in the same period T.If v1<<v2, it means the market over estimates the future volatility. Then one can short the option, and delta-hedge it with v1 under the black-scholes framework. The expected profit should be the difference between option price with volatility v2 and option price with volatility v1.If v2<<v1, we can do this in an opposite direction.Is this a practical method?

### Comparison between Heston models calibrated by historical time series and instant option prices.

Posted: **March 6th, 2015, 12:44 pm**

by **Alan**

You are trying to capture the volatility risk premium. If you think about it, the introduction of the Heston model is not necessary.For example, the implied vol associated to OTM SPX puts is well-known to be higher than justified by the historical SPX time series.The actuarial expected profit from selling such puts repeatedly is significantly positive. So, why not just sell those and do your delta-hedging?The answer is: you will indeed likely capture that risk premium "on average". But you won't capture it risklessly and when your strategyis losing the most, that when equities in general will be crashing. That's why it's a "risk premium" and not an "inefficiency" or an "arbitrage opportunity".I will guess that, if you tried your Heston model strategy, the results would generally be similar to the SPX put case.As a general rule, risk premiums are drift effects and drift effects do not translate into arbitrage opportunities. However, you don't need me. You can easily simulate your strategy under some assumptions and see the pattern of the gains and losses.Be sure to include highly stressed markets, perhaps with a crash or two, in your simulations.

### Comparison between Heston models calibrated by historical time series and instant option prices.

Posted: **March 10th, 2015, 8:10 am**

by **EdisonCruise**

Thank you Alan. Trading the difference between OTM option's vol and historical vol (caluclated by annualized standard deviation) is indeed on risk premium.Howevver, if one calibrate Heston model by historical data, then he should also be able to get a "vol surface" as the implied vol calibrated from market option data. For the option with the same strike and the same expiration date, no matter ATM or OTM, the volatiltiy must be different. This difference, if big enough, may indicate the option at that strike and expiration be overvalued or undervalued from historical point. This strategy is not simply trading the risk premiem, but the view of volatility at different aspect. It is applicable to ATM, OTM, ITM options. It seems this is not a common trading method, but what make people think it is impractical?

### Comparison between Heston models calibrated by historical time series and instant option prices.

Posted: **March 10th, 2015, 1:11 pm**

by **Alan**

Letting a model help you develop a valuation opinion is fine. You can test any proposed trading strategy on historical option data, monitor your trading results, and try to improve your models and strategies. I did this kind of thing for many years. You can bring as much "science" to the process as you want. I will simply point out some of the many, many issues: -model dependence and lack of realism in many models, -sensitivity to the historical data time period, -vol and equity risk premiums,-failure of historical data to be forward looking, in contrast to the market implied vols.-diversification, strategy issues, liquidity