When asset prices are modelled by stochastic dynamics, the model parameters are estimated from financial data. We study how estimation errors on model parameters impact the computed option prices, in the case where asset price and volatility follow the classical joint stochastic differential equations (SDEs) parametric model of Heston. Model parameters are estimated by an approximate maximum likelihood approach studied in [4] which presented an implementable computation of the covariance matrix for the errors in model parameters estimation. We then study and compute the sensitivity of optimal option prices to errors on the model parameters. This is achieved by numerically solving the partial differential equations (PDEs) verified by the derivatives of the option price with respect to model parameters. Combining these evaluations of derivatives with the computed covariance matrix of errors on model parameters, we obtain the errors on option price due to parametric estimation errors. We apply our method to the Standard & Poor's (S&P) 500 index options using the implied volatility index (VIX) [29] as a proxy for volatility.
IntroductionIt is common practice in finance applications to model the price of securities and other assets using stochastic differential equations. The models are estimated using available data and are then used for forecasting or for computing the price of financial instruments.We study the impact of errors in model estimation on the price of options where the underlying asset is assumed to verify the estimated model. We study how errors on each individual parameter affect option prices. We compute a bound on the error in the option price due to model error. Our study of parametric error sensitivity does not depend on the choice of method used for the calibration of the asset pricing model.Extensions of the Black-Scholes models to local volatility ([8], [9]) and stochastic volatility models ([19], [25]) are often used in practice. Local volatility models allow for the instantaneous volatility to be a
