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Pricing Credit Derivatives with Uncertain Default Probabilities

In this article, the author presents a model for pricing credit spread options in an environment where the rating transition probabilities are uncertain parameters.

Vivien Brunel
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Option Pricing with Radial Basis Functions: A Tutorial

In this article, Alonso Pena describes the method of radial basis functions (RBF) and how it can be used for the numerical solution of partial differential equations in finance.

Alonso Pena
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Swaptions: 1 Price, 10 Deltas, and … 61/2 Gammas*

This article compares simple risk measures (first and second order sensitivity to the underlying yield curve) for simple instruments (swaptions).

Marc Henrard
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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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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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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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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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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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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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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

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