CVA and vulnerable options pricing by correlation expansions

We consider the problem of computing the credit value adjustment (CVA) of a European option in presence of the wrong way risk in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an...

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Bibliographic Details
Published in:Annals of operations research Vol. 299; no. 1-2; pp. 401 - 427
Main Authors: Antonelli, F., Ramponi, A., Scarlatti, S.
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2021
Springer
Springer Nature B.V
Subjects:
Adjusting entries
Asset management
Business and Management
Combinatorics
Correlation
Correlation (Statistics)
Credit
Credit risk
Default
Funding
Interest rates
Linear equations
Linear programming
Liquidity
Market prices
Methods
Operations research
Operations Research/Decision Theory
Options (Finance)
Prices and rates
S.I.: Recent Developments in Financial Modeling and Risk Management
Securities prices
Theory of Computation
Valuation
Italy
Rome Italy
XVA
Affine processes
91G60
Vulnerable options
60J70
Counterparty credit risk
91G20
Wrong way risk
Credit value adjustment
Duhamel principle
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:We consider the problem of computing the credit value adjustment (CVA) of a European option in presence of the wrong way risk in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option’s price, by exploiting a correlation expansion approach, introduced in Antonelli and Scarlatti (Finance Stoch 13:269–303, 2009). We also extend our theoretical analysis to include some further value adjustments, for instance due to collateralization and funding costs. Finally, in the CVA case, we compare the numerical performance of our method with the one recently proposed by Brigo and Vrins (Eur J Oper Res 269:1154–1164, 2018) and Brigo et al. (Innovations in insurance, risk and asset management, WSPC proceedings, 2018), in the case of a call option driven by a GBM correlated with a CIR default intensity. We additionally compare with the numerical evaluations obtained by other methods.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-019-03367-z