Option Pricing under Heston Stochastic Volatility with Time-dependent Parameters

Pricing option under Heston stochastic volatility is challenging because it has a closed formula only when the parameters are constant or piecewise constant (Mikhailov and Nogel, 2003).  Applying Wei-Norman theorem (Wei and... [ view full abstract ]

Pricing option under Heston stochastic volatility is challenging because it has a closed formula only when the parameters are constant or piecewise constant (Mikhailov and Nogel, 2003).  Applying Wei-Norman theorem (Wei and Norman, 1963), we derived an approximate analytical formula for pricing a vanilla call option for any time-dependent model parameters.  The error crrection can be calculated numerically and in turn gives a more accurate result than the volatility expansion based model (Benhamou, Gobet and Miri, 2010) for time-dependent parameters.  In addition, the accuracy can be further improved by reiterating the calculation of error correction.