It contains an introduction to how simulation methods can be used to price American options and a discussion of various existing methods. An application using one of these methods, the regression based method, to the GARCH option pricing model is also provided

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The...

This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics dVt = κt.(θt − Vt).dt λt.Vt.dBt. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility...

This paper extends and refines the method of option pricing by frame projection of risk-neutral densities to incorporate general B-splines, including the cubic basis, and general payoff structures. We introduce a coefficient stabilization method which substantially improves convergence for...

This paper investigates the pricing and weak convergence of an asymmetric non-affine, non-Gaussian GARCH model when the risk-neutralization is based on a variance dependent exponential linear pricing kernel with stochastic risk aversion parameters. The risk-neutral dynamics are obtained for a...

We propose a new nonparametric technique to estimate the CALL function based on the superhedging principle. Our approach does not require absence of arbitrage and easily accommodates bid/ask spreads and other market imperfections. We prove some optimal statistical properties of our estimates. As...

We suggest a semi-nonparametric estimator for the entire call price surface based on a tensor-product B-spline. To enforce no-arbitrage constraints in strike and calendar dimensions we establish sufficient no-arbitrage conditions on the control net of the tensor product (TP) B-spline. Since...

In this paper, we propose a novel parametric approach to extract the implied risk-neutral density function from a cross-section of call option prices. The method is based on the framework proposed by Orosi (2011), who presents a multi-parameter extension of the models of Figlewski (2002) and...

This paper studies the nonparametric identification and estimation of projected pricing kernels implicit in European option prices and underlying asset returns using conditional moment restrictions. The proposed series estimator avoids computing ratios of estimated risk-neutral and physical...

The Libor Market Model describes the evolution of a discrete subset of all interest rates quoted in the market. Generation of the complete yield curve from a simulated set of rates (the so-called "Libor rate interpolation") is one of the basic challenges which are faced by a practical user of...