Sensitivity estimates for portfolio credit derivatives using Monte Carlo

Chen, Zhiyong; Glasserman, Paul

doi:10.1007/s00780-008-0071-y

Cited by 18 publications

(19 citation statements)

References 15 publications

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“…On practical grounds, one can remark that prices of credit default swaps and CDO tranches are Markovian processes in this framework and, by Feynman-Kac's theorem, they are also solutions of particular partial differential equations (PDE) 17 .…”

Section: I8 Hedging Credit Portfolio Derivatives In Multivariate Strmentioning

confidence: 99%

“…We will also try to highlight the commonalities (if any) between the approaches. 17 In the case of CDS, these PDE can be solved numerically either using finite difference methods or algorithms based on recombining trees. Regarding CDO tranche prices, the dimension of the PDE is too large to consider a direct numerical resolution method.…”

Section: I9 Comparison With Other Approachesmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Cousin¹,

Laurent

2011

Credit Risk Frontiers

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Section: I8 Hedging Credit Portfolio Derivatives In Multivariate Strmentioning

confidence: 99%

Section: I9 Comparison With Other Approachesmentioning

confidence: 99%

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Cousin¹,

Laurent

2011

Credit Risk Frontiers

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“…As a numerical test ground we consider the case of Basket Default Options [12]. In this context, the random factors X i represent the default time τ i of the i-th name, e.g., the time a specific company in a reference pool of N names fails to pay one of its liabilities as specified by the terms of the contract priced.…”

Section: Numerical Testsmentioning

confidence: 99%

“…, M }/T k < τ ], and s k is the premium payment (per unit notional) at time T k . In order to apply the Pathwise Derivative method to the payout above, the indicator functions in (16) and (15), need to be regularized [1,12]. One simple and practical way of doing that is to replace the indicator functions with their smoothed counterpart, at the price of introducing a small amount of bias in the Greek estimators.…”

Section: Numerical Testsmentioning

confidence: 99%

Fast Correlation Greeks by Adjoint Algorithmic Differentiation

Capriotti

Giles

2010

SSRN Journal

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We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illustrate the method for a copula-based Monte Carlo computation of claims written on a basket of underlying assets, and we test it numerically for Portfolio Default Options. For any number of underlying assets or names in a portfolio, the sensitivities of the option price with respect to all the pairwise correlations is obtained at a computational cost which is at most 4 times the cost of calculating the option value itself. For typical applications, this results in computational savings of several order of magnitudes with respect to standard methods.One of the consequences of the current crisis of the Financial Markets is a renewed emphasis on rigorous Risk management practices. In order to quantify the financial exposure of financial firms, and to ensure an efficient capital allocation, and more effective hedging practices, regulators and senior management alike are insisting more and more on a thorough monitoring of Risk. Among all businesses, those dealing with complex, over the counter derivative securities are the ones receiving the most attention.A thorough calculation of the Risk exposure of portfolios of structured derivatives comes with a high operational cost because of the large amount of computer power required. Indeed, highly time consuming Monte Carlo (MC) simulations are very often the only tool available for pricing and hedging complex securities. Calculating the Greeks, or price sensitivities, by 'Bumping' i.e., by perturbing in turn the underlying model parameters, repeating the simulation and forming finite difference approximations results in a computational burden increasing linearly with the number of sensitivities computed. This easily becomes very significant when the models employed depend on a large number of parameters, as it is typically the case.A particularly challenging task is the calculation of correlation Risk, i.e., the calculation of the sensitivites of a security with respect to some measure of the correlations among the random factors it depends on. Indeed, calculating Risk with respect to all the independent pairwise correlations by Bumping requires repeating the MC simulation a large number of times, e.g. increasing quadratically with the number of random factors, and it is often unfeasible because of its high computational cost.Several alternative methods for the calculation of price * Electronic address: luca.capriotti@credit-suisse.com. † Electronic address: mike.giles@maths.ox.ac.uk sensitivities have been proposed in the literature (for a review see e.g., [1]). Among these, the Pathwise Derivative method [2] provides unbiased estimates at a computational cost that may be smaller than the one of Bumping. However, in many problems the standard Pathwise Derivat...

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“…. , n ) is deterministic as in [5], [6], [10], [11], [14], [15], [49], [40] and others. In that case, can be incorporated into the function f , to express the probability that the portfolio loss · N T at T exceeds a level, or an option on · N T , as E[f (N T )].…”

Section: Default Point Processesmentioning

confidence: 99%

Exact and Efficient Simulation of Correlated Defaults

Giesecke¹,

Kakavand²,

Mousavi³

et al. 2010

SIAM J. Finan. Math.

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Abstract. Correlated default risk plays a significant role in financial markets. Dynamic intensity-based models, in which a firm default is governed by a stochastic intensity process, are widely used to model correlated default risk. The computations in these models can be performed by Monte Carlo simulation. The standard simulation method, which requires the discretization of the intensity process, leads to biased simulation estimators. The magnitude of the bias is often hard to quantify. This paper develops an exact simulation method for intensity-based models that leads to unbiased estimators of credit portfolio loss distributions, risk measures, and derivatives prices. In a first step, we construct a Markov chain that matches the marginal distribution of the point process describing the binary default state of each firm. This construction reduces the original estimation problem to one involving a Markov chain expectation. In a second step, we estimate the Markov chain expectation using a simple acceptance/rejection scheme that facilitates exact sampling. To address rare event situations, the acceptance/rejection scheme is embedded in an overarching selection/mutation scheme, in which a selection mechanism adaptively forces the chain into the regime of interest. Numerical experiments demonstrate the effectiveness of the method for a self-exciting model of correlated default risk.

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Sensitivity estimates for portfolio credit derivatives using Monte Carlo

Cited by 18 publications

References 15 publications

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

Fast Correlation Greeks by Adjoint Algorithmic Differentiation

Exact and Efficient Simulation of Correlated Defaults

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