Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

Stephane Crepey; Andrea Macrina; Tuyet Mai Nguyen; David Skovmand

Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

Stephane Crepey, Andrea Macrina, Tuyet Mai Nguyen, David Skovmand

8 Citationer (Scopus)

59 Downloads (Pure)

Abstract

We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure Q and their consistent equivalence class under the real-world probability measure P. The consistent P-pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as CVA, we show how positive default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.

Originalsprog	Engelsk
Tidsskrift	Quantitative Finance
Vol/bind	16
Udgave nummer	6
ISSN	1469-7688
Status	Udgivet - 2 jun. 2016
Udgivet eksternt	Ja

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1502.07397v1

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title = "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments",

abstract = "We develop a multi-curve term structure set-up in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to London Interbank Offer Rate swaptions data and show that a rational two-factor log-normal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure ℚ and their consistent equivalence class under the real-world probability measure ℙ. The consistent ℙ -pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as credit valuation adjustment, we show how default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.",

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author = "Stephane Crepey and Andrea Macrina and Nguyen, {Tuyet Mai} and David Skovmand",

note = "34 pages, 9 figures",

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T1 - Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

AU - Crepey, Stephane

AU - Macrina, Andrea

AU - Nguyen, Tuyet Mai

AU - Skovmand, David

N1 - 34 pages, 9 figures

PY - 2016/6/2

Y1 - 2016/6/2

N2 - We develop a multi-curve term structure set-up in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to London Interbank Offer Rate swaptions data and show that a rational two-factor log-normal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure ℚ and their consistent equivalence class under the real-world probability measure ℙ. The consistent ℙ -pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as credit valuation adjustment, we show how default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.

AB - We develop a multi-curve term structure set-up in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to London Interbank Offer Rate swaptions data and show that a rational two-factor log-normal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship between the models developed and calibrated under a risk-neutral measure ℚ and their consistent equivalence class under the real-world probability measure ℙ. The consistent ℙ -pricing models are applied to compute the risk exposures which may be required to comply with regulatory obligations. In order to compute counterparty-risk valuation adjustments, such as credit valuation adjustment, we show how default intensity processes with rational form can be derived. We flesh out our study by applying the results to a basis swap contract.

KW - q-fin.MF

M3 - Journal article

SN - 1469-7688

VL - 16

JO - Quantitative Finance

JF - Quantitative Finance

IS - 6

ER -

Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments

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