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Pricing European Passport Option with Radial Basis Function

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Abstract

Passport option is a financial derivative with the value of a trading account as the underlying security. The valuation of this option can be obtained through the solution of a backward partial differential equation. A closed form solution for this valuation problem exists for the symmetric case when the risk-free rate is identical to the cost of carry. We obtain the value of the European passport option in this case, by using radial basis function and extend it to the asymmetric case when the risk-free rate is distinct from the cost of carry. The numerical schemes and algorithm are presented along with illustrative examples.

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References

  1. Hyer, T., Lipton-Lifschitz, A., Pugachevsky, D.: Passport to success. Risk 10(9), 127–131 (1997)

    Google Scholar 

  2. Topper, J.: A finite element implementation of passport options. M.Sc. Thesis, University of Oxford (2003)

  3. Andersen, L., Andreasen, J., Brotherton-Ratcliffe, R.: The passport option. J. Comput. Finance 1(3), 15–36 (1998)

    Article  Google Scholar 

  4. Nagayama, I.: Pricing of passport option. J. Math. Sci. Univ. Tokyo 5(4), 747–785 (1998)

    MathSciNet  MATH  Google Scholar 

  5. Chan, S.-S.: The valuation of American passport options. University of Wisconsin-Madison, Working Paper (1999)

  6. Dirkse, S.P., Ferris, M.C.: The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems. Optim. Methods Softw. 5, 123–156 (1995)

    Article  Google Scholar 

  7. Ahn, H., Penaud, A., Wilmott, P.: Various passport options and their valuation. Appl. Math. Finance 6(4), 275–292 (1999)

    Article  MATH  Google Scholar 

  8. Penaud, A., Wilmott, P., Ahn, H.: Exotic passport options. Asia Pacific Financ. Mark. 6(2), 171–182 (1999)

    Article  MATH  Google Scholar 

  9. Henderson, V., Hobson, D.: Local time, coupling and the passport option. Finance Stoch. 4(1), 69–80 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Henderson, V., Hobson, D.: Passport options with stochastic volatility. Appl. Math. Finance 8(2), 97–118 (2001)

    Article  MATH  Google Scholar 

  11. Hull, J., White, A.: The pricing of options on assets with stochastic volatilities. J. Finance 42(2), 281–300 (1987)

    Article  MATH  Google Scholar 

  12. Stein, E.M., Stein, J.C.: Stock price distributions with stochastic volatility: an analytic approach. Rev. Financ. Stud. 4(4), 727–752 (1991)

    Article  Google Scholar 

  13. Shreve, S.E., Vecer, J.: Options on a traded account: vacation calls, vacation puts and passport options. Finance Stoch. 4(3), 255–274 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hajek, B.: Mean stochastic comparison of diffusions. Zeitschrift fr Wahrscheinlichkeitstheorie und Verwandte Gebiete 68(3), 315–329 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pooley, D.: Numerical methods for nonlinear equations in option pricing. Ph.D. Thesis, University of Waterloo (2003)

  16. Baojun, B., Yang, W.: A viscosity solution approach to valuation of passport options in a jump-diffusion model. In: Proceedings of the 27th Chinese Control Conference, Kunming, Yunnan, China, pp. 606–608 (2008)

  17. Baojun, B., Yang, W., Jizhou, Z.: Viscosity solutions of HJB equations arising from the valuation of European passport options. Acta Math. Sci. 30(1), 187–202 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kampen, J.: Optimal strategies of passport options. Math. Ind. 12, 666–670 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Malloch, H., Buchen, P.W.: Passport option: continuous and binomial models. Finance and Corporate Governance Conference (2011)

  20. Chen, W., Fu, Z.-J., Chen, C.S.: Recent Advances in Radial Basis Function Collocation Methods. Springer Briefs in Applied Sciences and Technology. Springer-Verlag, Berlin, Heidelberg (2014)

    Book  Google Scholar 

  21. Iske, A.: Scattered Data Modelling Using Radial Basis Functions, Tutorials on Multiresolution in Geometric Modelling. Springer, Berlin, Heidelberg, pp. 205–242 (2002)

  22. Chen, S., Cowan, C.F.N., Grant, P.M.: Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans. Neural Netw. 2(2), 302–309 (1991)

    Article  Google Scholar 

  23. Liu, G.R., Gu, Y.T.: A point interpolation method for two-dimensional solids. Int. J. Numer. Methods Eng. 50(4), 937–951 (2001)

    Article  MATH  Google Scholar 

  24. Liu, G.R., Yan, L., Wang, J.G., Gu, Y.T.: Point interpolation method based on local residual formulation using radial basis functions. Struct. Eng. Mech. 14(6), 713–732 (2002)

    Article  Google Scholar 

  25. Liu, G.R., Gu, Y.T.: An Introduction to Meshfree Methods and Their Programming. Springer, Netherlands (2005)

    Google Scholar 

  26. Rad, J.A., Parand, K., Ballestra, L.V.: Pricing European and American options by radial basis point interpolation. Appl. Math. Comput. 251, 363–377 (2015)

    MathSciNet  MATH  Google Scholar 

  27. Kumar, A., Tripathi, L.P., Kadalbajoo, M.K.: A numerical study of Asian option with radial basis functions based finite differences method. Eng. Anal. Bound. Elem. 50, 1–7 (2015)

    Article  MathSciNet  Google Scholar 

  28. Buhmann, M.D.: Radial basis functions: theory and implementations. Camb. Monogr. Appl. Comput. Math. 12, 147–165 (2004)

    Google Scholar 

  29. Fasshauer, G.E.: Meshfree Approximation Methods with Matlab, vol. 6. World Scientific, Singapore (2007)

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Acknowledgments

The first author is grateful to Indian Institute of Technology Guwahati for the financial support provided to pursue his Ph.D. The authors express their gratitude to the learned reviewers for the suggestions which resulted in an improved manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Ankur Kanaujiya & Siddhartha P. Chakrabarty

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  1. Ankur Kanaujiya
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  2. Siddhartha P. Chakrabarty
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Correspondence to Siddhartha P. Chakrabarty.

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Kanaujiya, A., Chakrabarty, S.P. Pricing European Passport Option with Radial Basis Function. Int. J. Appl. Comput. Math 3, 1589–1604 (2017). https://doi.org/10.1007/s40819-016-0240-1

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  • DOI: https://doi.org/10.1007/s40819-016-0240-1

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