We implement 15 simulation schemes for the Cox–Ingersoll–Ross (CIR) square root process
and 10 schemes for Heston's stochastic volatility model to generate draws that we …

This paper presents a comprehensive simulation study on estimating parameters for the
popular Heston stochastic volatility model. Leveraging high-frequency data, we explore, in a …

In this paper, we extend the classical constant elasticity of variance (CEV) model to a
subdiffusive CEV model, where the underlying CEV process is time changed by an inverse α …

With splitting technique, a new semi-analytical scheme with predictable strong convergence
order 1.0 is proposed for the transformed Heston model, where the variance process is …

This thesis studies the role of higher moments, that is moments behind mean and variance,
in continuous-time, or diffusion, processes, which are commonly used to model so-called …

In order to sample asset price more accurately under the non-affine Heston model in the
situation where the Feller condition was unsatisfied, we proposed the key technique of …

A new discretization scheme ES-QE by combining the exact simulation (ES) and quadratic
exponential (QE) scheme is proposed to simulate the volatility process and price process of …

This chapter presents my motivations for working on numerical methods involving model
uncertainty in financial markets. These motivations are accompanied with a brief introduction …

We provide a tractable introduction to option pricing models and examine how the complex
analysis concept of branch-cutting influences financial mathematics. The Black-Scholes …

This article applies four popular discretization schemes, ie Andersen's quadratic exponential
(QE) scheme, Zhu's scheme, semi-analytical (SA) scheme, and Alfonsi's second-order …