Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least...

Recently, simulation methods combined with regression techniques have gained importance when it comes to American option pricing. In this paper we consider such methods and we examine numerically their convergence properties. We first consider the Least Squares Monte-Carlo (LSM) method of...

Both barrier options and the Heston stochastic volatility model are omnipresent in real-life applications of financial mathematics. Therefore, we apply the Heath-Platen (HP) estimator as first introduced by Heath and Platen to price barrier options in the Heston model setting as an alternative...

The Fourier inversion method solves the Heston option pricing formula. However, this method does experience the noteworthy disadvantage of a computationally sedate solution process. As a result, the literature introduces faster approximations with accuracies later improved by the joint...

In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target...

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...

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

At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution...

A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov-backward-equation is...

We consider the saddlepoint approximation methods for pricing derivatives whose payoffs depend on the discrete realized variance of the underlying price process of a risky asset. Most of the earlier pricing models of variance products and volatility derivatives use the quadratic variation...