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37
Pricing earlyexercise and discrete barrier options by Fouriercosine series expansions
 Numerische Mathematik
"... We present a pricing method based on Fouriercosine expansions for earlyexercise and discretelymonitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C ∞ [a, b] ∈ R) transitional pr ..."
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Cited by 28 (8 self)
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We present a pricing method based on Fouriercosine expansions for earlyexercise and discretelymonitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth (C ∞ [a, b] ∈ R) transitional probability density functions. The computational complexity is O((M − 1)N log N) with N a (small) number of terms from the series expansion, and M, the number of earlyexercise/monitoring dates. This paper is the followup of [22] in which we presented the impressive performance of the Fouriercosine series method for European options. 1
Intensity gamma: a new approach to pricing portfolio credit derivatives. Working paper
, 2006
"... Abstract. We develop a completely new model for correlation of credit defaults based on a financially intuitive concept of business time similar to that in the Variance Gamma model for stock price evolution. Solving a simple equation calibrates each name to its credit spread curve and we show that t ..."
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Cited by 27 (0 self)
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Abstract. We develop a completely new model for correlation of credit defaults based on a financially intuitive concept of business time similar to that in the Variance Gamma model for stock price evolution. Solving a simple equation calibrates each name to its credit spread curve and we show that the overall model can be calibrated to the market base correlation curve of a tranched CDO index. Once this calibration is performed, obtaining consistent arbitragefree prices for nonstandard tranches, products based on different underlying names and even more exotic products such as CDO 2 is straightforward and rapid. 1.
A Multivariate JumpDriven Financial Asset Model
, 2005
"... c ○ 2006 by Elisa Luciano and Wim Schoutens. Any opinions expressed here are those of the authors and not those of the Collegio Carlo Alberto. We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the b ..."
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Cited by 26 (6 self)
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c ○ 2006 by Elisa Luciano and Wim Schoutens. Any opinions expressed here are those of the authors and not those of the Collegio Carlo Alberto. We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behavior of a series of stocks or indexes and to study a multifirm, valuebased default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including nonGaussian dependence. We use a stochastic timechange technique and provide the details for a Gamma change. The main feature of the model is the fact that opposite to other, non jointly Gaussian settings its risk neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.
Pricing CDOs with Correlated Variance Gamma Distributions
, 2006
"... The purpose of this article is to show that the correlation smile in liquid CDS index tranches can be explained by the same ideas that have proven to explain the volatility smile in equity options. First, we extend a structural model proposed by Luciano and Schoutens [2005] that models firm values b ..."
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Cited by 23 (0 self)
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The purpose of this article is to show that the correlation smile in liquid CDS index tranches can be explained by the same ideas that have proven to explain the volatility smile in equity options. First, we extend a structural model proposed by Luciano and Schoutens [2005] that models firm values by Variance Gamma processes. We show that these extensions can explain the index spread curves and tranche quotes of DJ iTraxx 5 year simultaneously. Second, we extract the resulting dependence structure into a factor copula approach. The resulting VG copula shares the advantages of the well known Gaussian copula that underlies the most important industry models like CreditMetrics and KMV. We apply this approach to weekly spreads of DJ iTraxx 5 year. We show that this approach fits significantly better to the correlation smile than comparable copula approaches. 1 In the 1980s, Collateralized Debt Obligations (CDOs) were introduced for balance sheet risk management. The emergence of credit derivatives in the 1990s offered the possibility of synthetic risk transfer of a portfolio of bonds or loans, too. Since 2003, credit risk of
Exotic Options under Lévy Models: An Overview
, 2004
"... In this paper we overview the pricing of several socalled exotic options in the nowdays quite popular exponential Lévy models. ..."
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Cited by 17 (0 self)
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In this paper we overview the pricing of several socalled exotic options in the nowdays quite popular exponential Lévy models.
On maxima and ladder processes for a dense class of Lévy processes
 Journal of Applied Probability
"... Abstract. Consider the problem to explicitly calculate the law of the first passage time T(a) of a general Lévy process Z above a positive level a. In this paper it is shown that the law of T(a) can be approximated arbitrarily closely by the laws of T n (a), the corresponding first passages time for ..."
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Cited by 15 (0 self)
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Abstract. Consider the problem to explicitly calculate the law of the first passage time T(a) of a general Lévy process Z above a positive level a. In this paper it is shown that the law of T(a) can be approximated arbitrarily closely by the laws of T n (a), the corresponding first passages time for X n, where (X n)n is a sequence of Lévy processes whose positive jumps follow a phasetype distribution. Subsequently, explicit expressions are derived for the laws of T n (a) and the upward ladder process of X n. The derivation is based on an embedding of X n into a class of Markov additive processes and on the solution of the fundamental (matrix) WienerHopf factorisation for this class. This WienerHopf factorisation can be computed explicitly by solving iteratively a certain fixed point equation. It is shown that, typically, this iteration converges geometrically fast.
Stochastic evolution equations in portfolio credit modelling with applications to exotic credit products.
, 2011
"... Abstract We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a s ..."
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Cited by 10 (4 self)
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Abstract We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a stochastic partial differential equation and we establish existence and uniqueness for the solution taking values in a suitable function space. The loss function of the portfolio is then a function of the evolution of this density at the default boundary. We develop numerical methods for pricing and calibration of the model to credit indices and consider its performance pre and post credit crunch.
The Lévy Libor model with default risk
 J. Credit Risk
, 2006
"... In this paper we present a model for the dynamic evolution of the term structure of defaultfree and defaultable interest rates. The model is set in the Libor market model framework but in contrast to the classical diffusiondriven setup, its dynamics are driven by a timeinhomogeneous Lévy proces ..."
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Cited by 9 (5 self)
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In this paper we present a model for the dynamic evolution of the term structure of defaultfree and defaultable interest rates. The model is set in the Libor market model framework but in contrast to the classical diffusiondriven setup, its dynamics are driven by a timeinhomogeneous Lévy process which allows us to better capture the realworld dynamics of credit spreads. We present necessary and sufficient conditions for absence of arbitrage in the dynamics of the spreads, and provide pricing formulae for defaultable bonds, credit default swaps and options on credit default swaps in this setup. 1
Default swap games driven by spectrally negative Lévy processes. Stochastic Process
 Appl
"... ABSTRACT. This paper studies gametype credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model b ..."
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Cited by 7 (4 self)
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ABSTRACT. This paper studies gametype credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Lévy processes, we apply the principles of smooth and continuous fit to identify the equilibrium exercise strategies for the buyer and the seller. We then rigorously prove the existence of the Nash equilibrium and compute the contract value at equilibrium. Numerical examples are provided to illustrate the impacts of default risk and other contractual features on the players ’ exercise timing at equilibrium.
Fast valuation and calibration of credit default swaps under Lévy dynamics
 Journal of Computational Finance
"... In this paper we address the issue of finding an efficient and flexible numerical approach for calculating survival/default probabilities and pricing Credit Default Swaps under advanced jump dynamics. We have chosen to use the firm’s value approach, modeling the firm’s value by an exponential Lévy m ..."
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Cited by 6 (0 self)
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In this paper we address the issue of finding an efficient and flexible numerical approach for calculating survival/default probabilities and pricing Credit Default Swaps under advanced jump dynamics. We have chosen to use the firm’s value approach, modeling the firm’s value by an exponential Lévy model. For this approach the default event is defined as a first passage of a barrier and it is therefore possible to exploit a numerical technique developed to price barrier options under Lévy models to calculate the default probabilities. The method presented is based on the Fouriercosine series expansion of the underlying model’s density function.