Pricing and Rick Analysis in Hyperbolic Local Volatility Model with Quasi‐Monte Carlo

Abstract

Local volatility models usually capture the surface of implied volatilities more accurately than other approaches, such as stochastic volatility models. We present the results of application of Monte Carlo (MC) and quasi‐Monte Carlo (QMC) methods for derivative pricing and risk analysis based on Hyperbolic Local Volatility Model. In high‐dimensional integration QMC shows a superior performance over MC if the effective dimension of an integrand is not too large. In application to derivative pricing and computation of Greeks, effective dimensions depend on path discretization algorithms. The results presented for the Asian option show the superior performance of the QMC methods, especially for the Brownian Bridge discretization scheme.

Speeding up the Euler scheme for killed diffusions

“…Here ν > 0 is the level of volatility, and β ∈ (0, 1] is the skew parameter. First introduced in Jäckel [31], this behaves similarly to the constant elasticity of variance (CEV), this model and has been widely used in quantitative finance for numerical experiments in Hok et al [25,26,24]. A practical advantage of this model is that zero is not an attainable boundary, which in turn avoids some numerical instabilities present in the CEV model when the underlying asset price is close to zero (see e.g.…”