Option price sensitivity to errors in stochastic dynamics modeling

摘要

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 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) as a proxy for volatility.