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Numerical Methods for the Markov Functional Model

Some numerical methods for efficient implementation of the 1- and 2-factor Markov Functional models of interest rate derivatives are proposed.

Simon Johnson
Thu 4 Nov 2021
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Order Statistics for Value at Risk Estimation and Option Pricing

We apply order statistics to the setting of VaR estimation. Here techniques like historical and Monte Carlo simulation rely on using the k-th heaviest loss to estimate the quantile of the profit and loss distribution of a portfolio of assets. We show that when the k-th heaviest loss is used the expected quantile and its error will be independent of the portfolio composition and the return functions of the assets in the portfolio.

Frederik Herzberg & Christoph Bennemann
Tue 12 Oct 2021
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Pricing Rainbow Options

A previous paper (West 2005) tackled the issue of calculating accurate uni-, bi- and trivariate normal probabilities. This has important applications in the pricing of multiasset options, e.g. rainbow options. In this paper, we derive the Black—Scholes prices of several styles of (multi-asset) rainbow options using change-of-numeraire machinery. Hedging issues and deviations from the Black-Scholes pricing model are also briefly considered.

Peter Ouwehand & Graeme West
Tue 12 Oct 2021
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Valuation of American Call Options

The purpose of this paper is to provide an analytical solution for American call options assuming proportional dividends. Proportional dividends are more realistic for long-term options than absolute dividends and the formula does not have the flaws known from absolute dividend formulae.

Ralph Villiger
Thu 5 Aug 2021
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Option Pricing and the Dirichlet Problem

Laplace’s equation is ubiquitous in physics. Yet, despite the equation’s importance in physics, it has not been important so far in finance. In this article, Joshi will relate it to options’ pricing.

Mark S. Joshi
Mon 8 Feb 2021
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Financial Option Prices in Excel

In this article, both Marcin and Jeremy discuss the use of algorithms from the NAG Library to calculate prices for financial options.

Fri 4 Apr 2014