abstract:
The Heston Model is a popular stochastic volatility model in mathematical finance. In its classical form the volatility process is given by a CIR process, whereas in the generalized form the volatility follows a mean-reverting CEV process.
While there exist several numerical methods to compute functionals of the Heston price, the convergence order is typically low for discontinuous functionals. In this talk, we will study an approach based on the integration by parts formula from Malliavin calculus to overcome this problem: The original
function is replaced by a function involving its antiderivative and by a Malliavin weight. Using the drift-implicit Euler scheme for the square root of the volatility, we will construct an estimator for which we can prove that it has $L^2$-convergence order $1/2$ even for discontinuous functionals. This leads to an efficient multilevel algorithm, also in the multidimensional case. |