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Calibration problems – An inverse problems view

In this article, Heniz W. Engl discusses the model parameters from market prices of liquid instruments.

Heinz W. Engl
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Can anyone solve the smile problem?

In this paper, the authors explore whether the smile problem can be solved and provide a general reflection of the problem. 

Elie Ayache, Philippe Henrotte, Sonia Nassar and Xuewen Wang
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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.

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Knock-in/out Margrabe

In this paper, Espen G. Haug and Jorgen Haug push the Black-Scholes-Merton (BSM) formula to the limit by using it to value exchange-one-asset-for-another options with knock-in or knock-out provisions that depend on the ratio of the two asset prices.

Espen G. Haug and Jorgen Haug
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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
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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
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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
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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
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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