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There seems to be a puzzling behaviour with "Theoretical Price" of option contracts computed via QuantLib. Including an example backtest.
First, let's start with
option.PriceModel = OptionPriceModels.BlackScholes();IV results seem reasonable given that interest and yield are apparently both set to flat 1% in QC. Zero values are consistently returned for the TheoreticalPrice.
Now, compare to binomial tree pricing, such as:
option.PriceModel = OptionPriceModels.BinomialJoshi();
option.PriceModel = OptionPriceModels.BinomialJarrowRudd();In these cases, TheoreticalPrice values are non-zero but very different from the mid-spread. Those unusual values are reproducible between backtests. Take this contract for example:
TimeAndContract,Right,Expiry,Strike,Bid,Ask,Last,TheoreticalPrice,OI,Underlying,IV,HV
(BS)
2017-08-14 16:00:00 SPY 190118P00245000,Put,1/18/2019 12:00:00 AM,245.00,16.270,16.760,16.500,0.000,0,246.520,0.0858,0.1604
(binomial)
2017-08-14 16:00:00 SPY 190118P00245000,Put,1/18/2019 12:00:00 AM,245.00,16.270,16.760,16.500,7.980,0,246.520,0.0858,0.1604Specific questions:
- TheoreticalPrice in Black-Scholes case: Why all zeroes?
- TheoreticalPrice in binomial models: Do those values carry any meaning?
- Could interest rate and dividend yield be set by a user? E.g., force ConstantQLRiskFreeRateEstimator(0.03) in C# API?
- (Somewhat separate topic) Underlying volatility model (historical, for the spot price, as in this line , security.VolatilityModel): What is the default? Over what historical period? What happens if only a few days are given as a warm-up? Any intraday models here?
Jing Wu
Hi Pavel, these are the models all we have
here is the default estimators used by all models
private static IQLUnderlyingVolatilityEstimator _underlyingVolEstimator = new ConstantQLUnderlyingVolatilityEstimator();private static IQLRiskFreeRateEstimator _riskFreeRateEstimator = new ConstantQLRiskFreeRateEstimator();
private static IQLDividendYieldEstimator _dividendYieldEstimator = new ConstantQLDividendYieldEstimator();
For the blacksholes model
https://github.com/QuantConnect/Lean/blob/21cd972e99f70f007ce689bdaeeafe3cb4ea9c77/Common/Securities/Option/OptionPriceModels.cs#L50To
In order to create a BlackScholes with different estimators, you can duplicate the function and use custom estimators. The default volatility model is the standard deviation of returns, the time period is 30 days.
Pavel Paramonov
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