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Research Papers

Effective Markovian projection: application to CMS spread options and mid-curve swaptions

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Pages 1169-1192 | Received 10 Mar 2021, Accepted 28 Jan 2022, Published online: 18 Mar 2022

References

  • Alexander, C. and Nogueira, L.M., Stochastic local volatility. In Proceedings of the 2nd IASTED International Conference: Financial Engineering and Applications, edited by M.H. Hamza, pp. 136–141, 2004 (Cambridge).
  • Andersen, L.B.G. and Piterbarg, V., Interest Rate Modeling – Volume I: Foundations and Vanilla Models, 2010a (Atlantic Financial Press: London).
  • Andersen, L.B.G. and Piterbarg, V., Interest Rate Modeling – Volume II: Term Structure Models, 2010b (Atlantic Financial Press: London).
  • Andersen, L.B.G. and Piterbarg, V., Interest Rate Modeling – Volume III: Products and Risk Management, 2010c (Atlantic Financial Press: London).
  • Andreasen, J. and Huge, B., ZABR–expansions for the masses. Available at SSRN, 2011.
  • Antonov, A., Black basket analytics for mid-curves and spread-options. Available at SSRN, 2020.
  • Antonov, A., Arneguy, M. and Audet, N., Markovian projection to a displaced volatility heston model. Available at SSRN, 2008.
  • Antonov, A. and Misirpashaev, T., Markovian projection onto a displaced diffusion. Int. J. Theoretical Appl. Finance, 2009, 12, 507–522.
  • Carr, P. and Madan, D.B., Option valuation using the fast fourier transform. J. Comput. Finance, 1999, 2, 61–73.
  • Charvet, X. and Ticot, Y., Pricing with a smile: An approach using normal inverse Gaussian distributions with a SABR-like parameterisation. Available at SSRN, 2011.
  • Choi, J., Liu, C. and Seo, B.K., Hyperbolic normal stochastic volatility model. J. Futures Markets, 2018, 39, 186–204.
  • Chuni, V., On SDE systems with non-Lipschitz diffusion coeffcients, 2020.
  • Derman, E. and Kani, I., Riding on a smile. Risk, 1994, 7, 32–39.
  • Dupire, B., Pricing with a smile. Risk, 1994, 7, 18–20.
  • Durrett, R., Probability: Theory and Examples, 4th ed., Cambridge Series in Statistical and Probabilistic Mathematics, 2010 (Cambridge University Press: Cambridge).
  • Eriksson, A., Ghysels, E. and Wang, F., The normal inverse Gaussian distribution and the pricing of derivatives. J. Derivatives, 2009, 16, 23–37.
  • Feldman, K., Change of measure in midcurve pricing. Wilmott, 2020, 106, 76–81.
  • Felpel, M., Kienitz, J. and McWalter, T.A., Effective stochastic volatility: Applications to ZABR-type models. Quant. Finance, 2021, 21, 837–852.
  • Göttker-Schnetmann, J. and Spanderen, K., Heston stochastic local volatility. Quantlib Report, 2015.
  • Gyoengy, I., Mimicking the one-dimensional marginal distributions of processes having an ito differential. Probab. Theory. Relat. Fields., 1986, 71, 501–516.
  • Hagan, P.S., Kumar, D., Lesniewski, A.S. and Woodward, D.E., Arbitrage-Free SABR. Wilmott Magazine, 2014, 1, 60–75.
  • Hagan, P.S., Lesniewski, A.S., Skoufis, G.E. and Woodward, D.E., SABR for baskets. Wilmott, 2021, 112, 50–61.
  • Hagan, P.S., Lesniewski, A.S., Skoufis, G.E. and Woodward, D.E., CMS spread options. Available at Researchgate, 2020.
  • Hagan, P.S., Lesniewski, A.S. and Woodward, D.E., Implied volatility formulas for Heston models. Wilmott Magazine, 2018, 98, 44–57.
  • Hagan, P.S., Conservative schemes for solving 1D PDEs. Available at Researchgate, 2015.
  • Horvath, B. and Reichmann, O., Dirichlet forms and finite element methods for the SABR model, 2018.
  • Johnson, N., Systems of frequency curves generated by methods of translation. Biometrika, 1949, 36, 149–176.
  • Karlsmark, M., Four essays in quantitative finance. PhD Thesis, University of Copenhagen, 2013.
  • Kienitz, J. and Wetterau, D., Financial Modeling – Theory, Implementation and Practice – (with Matlab Source), 2012 (Wiley: Chichester).
  • Kumar, K.S., A Class of degenerate Stochastic differential equations with non-Lipschitz coefficients. Indian Academy of Sciences, 2013.
  • Lambert, J.H., Observations variae in mathesin puram. Acta Helvitica, Physico-Mathematico-Anatomico-Botanico-Medica, 1758, 3, 128–168.
  • Lindsay, A. and Brecher, D., Simulation of the CEV process and the local martingale property. Math. Comput. Simul., 2012, 82, 868–878.
  • Øksendal, B., Stochastic Differential Equations, 6th ed., 2003 (Springer: Berlin).
  • Piterbarg, V., Markovian projection method for volatility calibration. Available at SSRN, 2006.
  • Saporito, Y.F., Yang, X. and Zubelli, J.P., The calibration of stochastic local-volatility models: An inverse problem perspective. Comput. Math. Appl., 2019, 77, 3054–3067.
  • Tavin, B., Implied distribution as a function of the volatility smile. European Finance eJ., 2011.
  • Taylor, S., Perturbation and symmetry techniques applied to finance, 2010.
  • Tsuchiya, O., Markovian projection for the local stochastic volatility LIBOR market model. Available at SSRN, 2015.
  • Tuenter, H.J.H., An algorithm to determine the parameters of SU-curves in the Johnson system of probability distributions by moment matching. J. Stat. Comput. Simul., 2001, 70, 325–347.

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