Asymptotic analysis of the Heston model and its statistical and financial applications

Abstract

AbstractTransform inversion algorithm is a popular method in the areas of Statistics and Financial Engineering. However, it is often difficult to guarantee its accuracy due to the lack of error control, which depends heavily on the asymptotic feature of the transform function. This article characterizes the asymptotic behavior of the Heston stochastic volatility model, by which one can derive computable error bounds and achieve any pre‐specified error tolerance in the transform inversion algorithm. Moreover, a universal method is proposed to specify a closed‐form upper bound of the discretization error. Numerical examples indicate that the resulting inversion algorithm with our computable error bounds is reliably accurate and efficient, for parameter estimation and option pricing under the Heston model.