Jingtang Ma

TL;DR: A hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump–diffusion, Markov regime switching models, and the finite moment log stable (FMLS) models.

TL;DR: This paper for the first time establishes the exact second-order convergence rates of the CTMC methods when applied to the prices and Greeks of Asian options and proposes a new set of error analysis methods for these path-dependent derivatives, whose payoffs depend on the average of asset prices.

TL;DR: A priori error estimations for the finite-element-method semi-discretization of the given problem are established by defining a suitable Ritz–Volterra projection operator: here, the key point in the proof is the fact that the definition of the Ritz-VolterRA projection operator that is not related to the neutral term.

TL;DR: In this article, the stochastic area swept by a regular time-homogeneous diffusion till a stopping time was studied. And the Laplace transform and integer moments were characterized in terms of the eigenfunctions of the associated diffusion.

TL;DR: In this paper, the second order convergence rate of the continuous-time Markov chain (CTMC) approximation method for pricing options under the general framework of stochastic local volatility (SLV) models is established.