Pricing derivatives with counterparty risk and collateralization: A fixed point approach

Kim, Jinbeom; Leung, Tim

doi:10.1016/j.ejor.2015.06.055

Cited by 17 publications

(4 citation statements)

References 27 publications

(37 reference statements)

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“…However, the independent case ρ = 0 is unrealistic, and may lead to severe over or underestimations of CVA Kim and Leung (2016); Brigo and Vrins (2018); Breton and Marzouk (2018).…”

Section: Wrong-way Risk Impact In Credit Valuation Adjustmentsmentioning

confidence: 99%

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Mbaye

Vrins²

2019

SSRN Journal

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We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield, prepayment or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compound Poisson jumps, JCIR, a.k.a. SRJD), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter, Hull-White or JCIR++ (a.k.a. SSRJD) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach may not be appropriate when positivity is required, a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach, leading to the TC-JCIR model. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of variance. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The TC-JCIR model is able to generate much larger implied volatilities and covariance effects than JCIR++ under positivity constraint, and therefore offers an appealing alternative to the shift extension in such cases.Model calibration is a standard problem in many areas of finance Brigo and Mercurio (2006);Joshi (2003); Veronesi (2010). It consists of tuning a model such that it "best fits" market quotes at a given time. As an example, financial markets provide a set of prices associated with liquid instruments, that openly trade on the market. Alongside with risk management (hedging), the main purpose of a model here is to act as an "interpolation/extrapolation" tool, i.e., to obtain the value of products at a given time t for which the market does not disclose prices in a transparent way. This could happen because either the product to be priced is "exotic" (i.e., is too "special", it does not quote openly on a platform, only on a bilateral basis) or because its cashflow schedule is not in line with the products that currently trade openly at t (a situation that commonly happens since products that were "standard" at inception, may have time-to-expiry or moneyness levels that are no longer "standard" afterwards).Mathematically, model calibration is nothing but an optimization problem. Starting from a set of prices quoted on the market (called "market prices") for a set of specific financial products (called "calibration instruments"), model calibration consists of computing the model parameters such that the prices generated by the model (called "model prices") best fit to the market prices, according to some error function. Model calibration is crucial in finance;it is strongly related to arbitrage opportunities. In practice, only models that are able to reproduce the market prices of "simple instruments" ...

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“…However, the independent case ρ = 0 is unrealistic, and may lead to severe over or underestimations of CVA Kim and Leung (2016); Brigo and Vrins (2018); Breton and Marzouk (2018).…”

Section: Wrong-way Risk Impact In Credit Valuation Adjustmentsmentioning

confidence: 99%

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Mbaye

Vrins²

2019

SSRN Journal

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“…An algorithm using a fixed-point approach has been recently proposed to calculate CVA in Kim and Leung [2016].…”

Section: Previous Literaturementioning

confidence: 99%

Multi Currency Credit Default Swaps: Quanto Effects and FX Devaluation Jumps

2015

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Credit Default Swaps (CDS) on a reference entity may be traded in multiple currencies, in that protection upon default may be offered either in the currency where the entity resides, or in a more liquid and global foreign currency. In this situation currency fluctuations clearly introduce a source of risk on CDS spreads. For emerging markets, but in some cases even in well developed markets, the risk of dramatic Foreign Exchange (FX) rate devaluation in conjunction with default events is relevant. We address this issue by proposing and implementing a model that considers the risk of foreign currency devaluation that is synchronous with default of the reference entity. As a fundamental case we consider the sovereign CDSs on Italy, quoted both in EUR and USD. We explain in detail the sources for such discrepancies. Our modeling approach is based on the reduced form framework for credit risk, where the default time is modeled in a Cox process setting with explicit diffusion dynamics for default intensity/hazard rate and exponential jump to default. For the FX part, we include an explicit default-driven jump in the FX dynamics. As * Imperial College, London, U.K. our results show, such a mechanism provides a further and more effective way to model credit / FX dependency than the instantaneous correlation that can be imposed among the driving Brownian motions of default intensity and FX rates, as it is not possible to explain the observed basis spreads during the Euro-debt crisis by using the latter mechanism alone.

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“…In particular see [4,39] for an analysis of the shareholder/bondholder problem in assessing the costs of financing (this aspect is treated in Section 5.1) and [1,26] for a preliminary analysis of how to deal with netting sets (this subject will be treated in Section 5.2). Finally, for what concerns the numerical aspects of the problem see for example [42].…”

Section: A Concise Introduction To Valuation Adjustmentsmentioning

confidence: 99%

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

Brigo

Francischello

Pallavicini

2019

European Journal of Operational Research

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2 The opinions here expressed are solely those of the authors and do not represent in any way those of their employers. Acknowledgments: we are grateful to Cristin Buescu, Jean-François Chassagneux, François Delarue, Federico Graceffa, and Marek Rutkowski for helfpul discussion and suggestions that helped us improve the paper. Marek Rutkowski and Andrea Pallavicini visits were funded via the EPSRC Mathematics Platform grant EP/I019111/1.

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Pricing derivatives with counterparty risk and collateralization: A fixed point approach

Cited by 17 publications

References 27 publications

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Affine Term-Structure Models: A Time-Changed Approach with Perfect Fit to Market Curves

Multi Currency Credit Default Swaps: Quanto Effects and FX Devaluation Jumps

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

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