Martingale option pricing

Option Pricing with v. G. Martingale Components

A Martingale Control Variate Method for Option Pricing with Stochastic Volatility

A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control v...

Learning Martingale Measures From High Frequency Financial Data to Help Option Pricing

We provide a framework for learning risk-neutral measures (Martingale measures) for pricing options from high frequency financial data. In a simple geometric Brownian motion model, a price volatility, a fixed interest rate and a no-arbitrage condition suffice to determine a unique risk-neutral measure. On the other hand, in our framework, we relax some of these assumptions to obtain a class of ...

Minimal Relative Entropy Martingale Measures and their Applications to Option Pricing Theory

In this paper we review the relative entropy meathods for the option pricing theory in the incomplete markets. First we summarize the known results with respect to the existence of minimal relative entropy martingale measure (MEMM), and then we give several examples of the pricing models related to the MEMM (for example, the [Geometric Lévy & MEMM] pricing model). After that we explain the math...

Meshfree Methods in Option Pricing Meshfree Methods in Option Pricing

A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation ...