After the recent financial crisis, the market for volatility derivatives has expanded rapidly to
meet the demand from investors, risk managers and speculators seeking diversification of …

In this chapter, we present recent developments in using the tools of continuous-time Markov
chains for the valuation of European and path-dependent financial derivatives. We also …

In this paper we develop a new delta expansion approach to deriving analytical
approximation to the transition densities of multivariate diffusions using the Itô-Taylor …

It is extremely challenging to design a model calibrating both SPX and VIX option prices. A
long‐standing conjecture due to Julien Guyon is that it may not be possible to calibrate …

Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of
the recent research results in pricing models of derivatives on discrete realized variance and …

This paper studies a class of tractable jump-diffusion models, including stochastic volatility
models with various specifications of jump intensity for stock returns and variance …

This paper shows that a small-time Hermite expansion is feasible for multivariate diffusions.
By introducing an innovative quasi-Lamperti transform, which unitizes the diffusion matrix at …

This article extends the solution proposed by Aït-Sahalia, Fan, and Li for the leverage effect
puzzle, which refers to a fact that empirical correlation between daily asset returns and the …

Abstract The Heston-Dupire model is a well-established stochastic local volatility model that
offers a non-parametric representation. This model is known to closely match the implied …

We study the first hitting time of integral functionals of time-homogeneous diffusions, and
characterize their Laplace transforms through a stochastic time change. We obtain explicit …