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Research Papers

A static replication approach for callable interest rate derivatives: mathematical foundations and efficient estimation of SIMM–MVA

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Pages 409-432 | Received 16 Jun 2023, Accepted 20 Jan 2024, Published online: 26 Feb 2024

References

  • Andersen, L.B.G. and Piterbarg, V.V., Interest Rate Modeling, Volume II: Term Structure Models, 2010 (Atlantic Financial Press: London, UK).
  • Andersson, K. and Oosterlee, C.W., A deep learning approach for computations of exposure profiles for high-dimensional bermudan options. Appl. Math. Comput., 2021, 408, 126332.
  • Antonov, A., Issakov, S. and McClelland, A., Efficient SIMM-MVA calculations for callable exotics. Available at SSRN 3040061, 2017.
  • Bank for International Settlements, Counterparty credit risk definitions and terminology, 2019.
  • Burgard, C. and Kjaer, M., Funding strategies, funding costs. Risk, 2013, 26, 82.
  • Capriotti, L., Fast Greeks by algorithmic differentiation. J. Comput. Finance, 2011, 14, 3.
  • Capriotti, L., Jiang, Y. and Macrina, A., AAD and least-square Monte Carlo: Fast bermudan-style options and xVA Greeks. Algorithmic Finance, 2017, 6, 35–49.
  • Carriere, J.F., Valuation of the early-exercise price for options using simulations and nonparametric regression. Insur. Math. Econ., 1996, 19, 19–30.
  • Caspers, P. and Lichters, R., Initial margin forecast-bermudan swaption methodology and case study. Available at SSRN 3132008, 2018.
  • De Graaf, C.S., Feng, Q., Kandhai, D. and Oosterlee, C.W., Efficient computation of exposure profiles for counterparty credit risk. Int. J. Theor. Appl. Finance, 2014, 17, 1450024.
  • Duffie, D. and Kan, R., A yield-factor model of interest rates. Math. Financ., 1996, 6, 379–406.
  • Feng, Q., Jain, S., Karlsson, P., Kandhai, D. and Oosterlee, C.W., Efficient computation of exposure profiles on real-world and risk-neutral scenarios for bermudan swaptions. Available at SSRN 2790874, 2016.
  • Filipovic, D., Term-Structure Models. A Graduate Course, 2009 (Springer: Berlin, Heidelberg).
  • Fries, C.P., Fast stochastic forward sensitivities in Monte Carlo simulations using stochastic automatic differentiation (with applications to initial margin valuation adjustments). J. Comput. Finance, 2019, 22, 103–125.
  • Giles, M. and Glasserman, P., Smoking adjoints: Fast Monte Carlo Greeks. Risk, 2006, 19, 88–92.
  • Glasserman, P., Monte Carlo Methods in Financial Engineering, Vol. 53, 2004 (Springer: Berlin, Heidelberg).
  • Glasserman, P. and Yu, B., Simulation for American options: Regression now or regression later? In Monte Carlo and Quasi-Monte Carlo Methods 2002: Proceedings of a Conference held at the National University of Singapore, Republic of Singapore, 25–28 November, 2002, pp. 213–226, 2004, (Springer: Berlin, Heidelberg).
  • Glau, K., Pachon, R. and Pötz, C., Speed-up credit exposure calculations for pricing and risk management. Quant. Finance, 2021, 21, 481–499.
  • Green, A., XVA: Credit, Funding and Capital Valuation Adjustments, 2015 (John Wiley & Sons: Hoboken, NJ).
  • Green, A.D. and Kenyon, C., Mva: Initial margin valuation adjustment by replication and regression. Available at SSRN 2432281, 2015.
  • Gregory, J., The XVA Challenge: Counterparty Risk, Funding, Collateral, Capital and Initial Margin, 2020 (John Wiley & Sons: Chichester, UK).
  • Griewank, A. and Walther, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2008 (SIAM: Philadelphia, USA).
  • Harrison, J.M. and Pliska, S.R., Martingales and stochastic integrals in the theory of continuous trading. Processes and Their Applications¡/DIFdel¿Stoch. Process. Their. Appl., 1981, 11, 215–260.
  • Hoencamp, J., Jain, S. and Kandhai, D., A semi-static replication method for bermudan swaptions under an affine multi-factor model. Risks, 2023, 11, 168.
  • International Swaps and Derivatives Association, Inc, Isda SIMM: From principles to model specification, 2016.
  • International Swaps and Derivatives Association, Inc, Isda SIMM: Methodology, version 2.3, 2020.
  • International Swaps and Derivatives Association, Inc, Isda margin survey year-end 2021, 2021.
  • Jain, S. and Oosterlee, C.W., The stochastic grid bundling method: Efficient pricing of bermudan options and their Greeks. Appl. Math. Comput., 2015, 269, 412–431.
  • Jain, S., Leitao, Á. and Oosterlee, C.W., Rolling adjoints: Fast Greeks along monte carlo scenarios for early-exercise options. J. Comput. Sci., 2019, 33, 95–112.
  • Jamshidian, F., Libor and swap market models and measures. Finance Stoch., 1997, 1, 293–330.
  • Jeanblanc, M. and Li, L., Characteristics and constructions of default times. SIAM J. Financ. Math., 2020, 11, 720–749.
  • Joshi, M. and Kwon, O.K., Least squares monte carlo credit value adjustment with small and unidirectional bias. Int. J. Theor. Appl. Finance, 2016, 19, 1650048.
  • Kappen, C., Computing MVA via regression and principal component analysis, SSRN, 2017.
  • Karlsson, P., Jain, S. and Oosterlee, C.W., Counterparty credit exposures for interest rate derivatives using the stochastic grid bundling method. Appl. Math. Finance, 2016, 23, 175–196.
  • Kingma, D.P. and Ba, J., Adam: A method for stochastic optimization, 2014, arXiv preprint arXiv:1412.6980.
  • Lakhany, A. and Zhang, A., Efficient ISDA initial margin calculations using least squares monte-carlo, 2021, arXiv preprint arXiv:2110.13296.
  • Lokeshwar, V., Bharadwaj, V. and Jain, S., Explainable neural network for pricing and universal static hedging of contingent claims. Appl. Math. Comput., 2022, 417, 126775.
  • Longstaff, F.A. and Schwartz, E.S., Valuing American options by simulation: A simple least-squares approach. Rev. Financ. Stud., 2001, 14, 113–147.
  • Lyashenko, A. and Mercurio, F., Looking forward to backward-looking rates: A modeling framework for term rates replacing LIBOR. Available at SSRN 3330240, 2019.
  • Musiela, M. and Rutkowski, M., Martingale Methods in Financial Modeling, 2nd ed., 1997 (Springer: Berlin, Heidelberg).
  • Schrager, D.F. and Pelsser, A.A., Pricing swaptions and coupon bond options in affine term structure models. Math. Financ., 2006, 16, 673–694.
  • Shen, Y., Van Der Weide, J.A. and Anderluh, J.H., A benchmark approach of counterparty credit exposure of bermudan option under Lévy process: The Monte Carlo-cos method. Procedia. Comput. Sci., 2013, 18, 1163–1171.
  • Simaitis, S., de Graaf, C., Hari, N. and Kandhai, D., Smile and default: The role of stochastic volatility and interest rates in counterparty credit risk. Quant. Finance, 2016, 16, 1725–1740.
  • Tsitsiklis, J.N. and Van Roy, B., Regression methods for pricing complex American-style options. IEEE Trans. Neural Netw., 2001, 12, 694–703.
  • Zeron, M. and Ruiz, I., Dynamic initial margin via Chebyshev spectral decomposition, Tech. Rep., Working paper (24 August), 2018.
  • Zhu, S.H. and Pykhtin, M., A guide to modeling counterparty credit risk, GARP Risk Review, July/August 2007.