Implementation problems and solutions in stochastic volatility models of the heston type

In Heston stochastic volatility framework, the main problem for implementing Heston semi-analytic formulae for European-style financial claims is the inverse Fourier integration. Without good implementation procedures, the numerical results obtained from Heston formulae cannot be robust, even for customarily used Heston parameters, as the time to maturity is increased. We compare three major approaches to solve the numerical instability problem inherent in the fundamental solution of the Heston model and show that the simple adjustedformula method is much simpler than the rotation-corrected angle method of Kahl and Jäckel and also greatly superior to the direct integration method of Shaw if taking computing time into consideration. In this chapter, we used the fundamental transform method proposed by Lewis to reduce the number of variables from two to one and separate the payoff function from the calculation of the Green function for option pricing. Furthermore, the simple adjusted formula is shown to be a robust option pricer as no complex discontinuities arise in this formulation even without the rotation-corrected angle.