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A Quantization Approach to the Counterparty Credit Exposure Estimation

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  • M. Bonollo
  • L. Di Persio
  • I. Oliva
  • A. Semmoloni

Abstract

During recent years the counterparty risk subject has received a growing attention because of the so called Basel Accord. In particular the Basel III Accord asks the banks to fulfill finer conditions concerning counterparty credit exposures arising from banks' derivatives, securities financing transactions, default and downgrade risks characterizing the Over The Counter (OTC) derivatives market, etc. Consequently the development of effective and more accurate measures of risk have been pushed, particularly focusing on the estimate of the future fair value of derivatives with respect to prescribed time horizon and fixed grid of time buckets. Standard methods used to treat the latter scenario are mainly based on ad hoc implementations of the classic Monte Carlo (MC) approach, which is characterized by a high computational time, strongly dependent on the number of considered assets. This is why many financial players moved to more enhanced Technologies, e.g., grid computing and Graphics Processing Units (GPUs) capabilities. In this paper we show how to implement the quantization technique, in order to accurately estimate both pricing and volatility values. Our approach is tested to produce effective results for the counterparty risk evaluation, with a big improvement concerning required time to run when compared to MC approach.

Suggested Citation

  • M. Bonollo & L. Di Persio & I. Oliva & A. Semmoloni, 2015. "A Quantization Approach to the Counterparty Credit Exposure Estimation," Papers 1503.01754, arXiv.org.
    • Handle: RePEc:arx:papers:1503.01754
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    References listed on IDEAS

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    1. Luschgy, Harald & Pagès, Gilles, 2006. "Functional quantization of a class of Brownian diffusions: A constructive approach," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 310-336, February.
    2. Walter Schachermayer & Josef Teichmann, 2008. "How Close Are The Option Pricing Formulas Of Bachelier And Black–Merton–Scholes?," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 155-170, January.
    3. Gilles Pagès & Abass Sagna, 2015. "Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(5), pages 463-498, November.
    4. T. A. McWalter & R. Rudd & J. Kienitz & E. Platen, 2018. "Recursive marginal quantization of higher-order schemes," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 693-706, April.
    5. Gilles Pag`es & Benedikt Wilbertz, 2011. "GPGPUs in computational finance: Massive parallel computing for American style options," Papers 1101.3228, arXiv.org.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Cited by:

    1. Michele Bonollo & Luca Di Persio & Luca Mammi & Immacolata Oliva, 2017. "Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time," Papers 1704.03244, arXiv.org.
    2. Erdinc Akyildirim & Alper A. Hekimoglu & Ahmet Sensoy & Frank J. Fabozzi, 2023. "Extending the Merton model with applications to credit value adjustment," Annals of Operations Research, Springer, vol. 326(1), pages 27-65, July.

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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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