Empirical martingale simulation for asset prices

Article Abstract:

The empirical martingale simulation (EMS) is proposed as a method for computing the prices of derivative securities. This approach , a simple modification to the standard Monte Carlo simulation procedure, eliminates the need for the latter to be repeated time and again to obtain an arbitrary degree of accuracy through simulation. The EMS imposes a martingale property upon the simulated sample and ensures that the simulated price satisfies rational option-pricing bounds. The new methodology is applied to Asian and European call options under the Black-Scholes and GARCH frameworks to investigate the impact of path-dependency in payoffs and/or asset price dynamics. The findings show that EMS generates substantially reduced variance especially for in- and at-the-money or longer-maturity options.

Usage, Derivatives (Financial instruments), Pricing, Simulation methods, Simulation, Monte Carlo method, Monte Carlo methods, Martingales (Mathematics)

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Approximating American option prices in the GARCH framework

Article Abstract:

An efficient method for determining prices of financial options is obtained by combining decision trees and a moments of cumulative return formula.

United States, Capital funds & cash flow, Valuation

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Improving lattice schemes through bias reduction

Article Abstract:

A modified lattice approach to option pricing is proposed.

Canada, Models, Lattice theory

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