Model-Free Methods in Valuation and Hedging of Derivative Securities

  • Mark H. A. Davis

Abstract

Were “the quants” to blame for the financial crisis of 2008? In narrow terms the answer appears to be “no” on the argument put forward by Alex Lipton, that the banks that survived were using the same models as those that failed. Be that as it may, it does seem that a contributory factor in the crisis was over-reliance on models that, in retrospect, had insufficient credibility.

Keywords

Hull Arena Volatility Hedging 

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References

  1. Acciaio, B., M. Beiglböck, F. Penkner, and W. Schachermayer (2015). A model-free version of the fundamental theorem of asset pricing and the super-replication theorem. Mathematical Finance. (Published online December 2013).Google Scholar
  2. Bachelier, L. (1900). Théorie de la spéculation. Annales Scientifiques de l’Ecole Normale Supérieure 17, 21–86.Google Scholar
  3. Beiglböck, M., H. Henry-Labordère, and F. Penkner (2013). Model-independent bounds for option prices: A mass transport approach. Finance and Stochastics 17, 477–501.CrossRefGoogle Scholar
  4. Biagini, F. (2010). Second fundamental theorem of asset pricing. In Cont (2010), pp. 1623–1628.Google Scholar
  5. Björk, T. and I. Slinko (2006). Towards a general theory of good-deal bounds. Review of Finance 10, 221–260.CrossRefGoogle Scholar
  6. Black, F. and M. Scholes (1973). The pricing of options and corporate liabilities. The Journal of Political Economy 81(3), 637–654.CrossRefGoogle Scholar
  7. Breeden, D. and R. Litzenberger (1978). Prices of state-contingent claims implicit in option prices. The Journal of Business 51, 621–651.CrossRefGoogle Scholar
  8. Brown, H., D. Hobson, and L. C. G. Rogers (2001). Robust hedging of barrier options. Mathematical Finance 11, 285–314.CrossRefGoogle Scholar
  9. Cochrane, J. and J. Saá-Requejo (2000). Beyond arbitrage: Good deal price bounds in incomplete markets. Journal of Political Economy 108, 79–119.CrossRefGoogle Scholar
  10. Cont, R. (Ed.) (2010). Encyclopedia of Quantitative Finance. John Wiley & Sons Inc.Google Scholar
  11. Cox, A. M. G. and J. Obłój (2011a). Robust hedging of double no-touch barier options. Finance and Stochastics, 15, 573–605.CrossRefGoogle Scholar
  12. Cox, A. M. G. and J. Obłój (2011b). Robust hedging of double touch barrier options. SIAM Journal on Financial Mathematics 2, 141–182.CrossRefGoogle Scholar
  13. Davis, M. H. A. (2010). The Black-Scholes formula. In Cont (2010), pp. 199–207.Google Scholar
  14. Davis, M.H.A. (2016). A Beaufort scale of predictability. In M. Podolskij, R. Stelzer, S. Thorbjrnsen, and A. Veraat (Eds), The Fascination of Probability, Statistics and their Applications. Springer.Google Scholar
  15. Davis, M. H. A. and A. Etheridge (2006). Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Princeton University Press.Google Scholar
  16. Davis, M. H. A. and D. Hobson (2007). The range of traded option prices. Mathematical Finance 17, 1–14.CrossRefGoogle Scholar
  17. Davis, M. H. A., J. Obłój, and V. Raval (2014). Arbitrage bounds for weighted variance swap prices. Mathematical Finance 24, 821–854.CrossRefGoogle Scholar
  18. Delbaen, F. and W. Schachermayer (2008). The Mathematics of Arbitrage. Springer.Google Scholar
  19. Dolinsky, Y. and H. M. Soner (2014). Robust hedging with proportional transaction costs. Finance and Stochastics 18, 327–347.CrossRefGoogle Scholar
  20. Dupire, B. (1994). Pricing with a smile. Risk 7, 18–20.Google Scholar
  21. El Karoui, N., M. Jeanblanc-Picqué, and S. E. Shreve (1998). Robustness of the Black and Scholes formula. Mathematical Finance 8, 93–126.CrossRefGoogle Scholar
  22. Evans, L. C. and W. Gangbo (1999). Differential methods for the the Monge-Kantorovich mass transfer problems. Memoirs of AMS, no. 653, vol. 137.Google Scholar
  23. Föllmer, H. and A. Schied (2011). Stochastic Finance: An Introduction in Discrete Time. De Gruyter.CrossRefGoogle Scholar
  24. Fouque, J.-P., G. Papanicolaou, and K. R. Sircar (2000). Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press.Google Scholar
  25. Galichon, A., H. Henry-Labordère, and N. Touzi (2014). A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options. Annals of Applied Probability 24, 312–336.CrossRefGoogle Scholar
  26. Gatheral, J. (2006). The Volatility Surface: A Practitioner’s Guide. New York: Wiley.Google Scholar
  27. Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer.CrossRefGoogle Scholar
  28. Hilber, N., O. Reichmann, and C. Schwab (2013). Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing. Springer.CrossRefGoogle Scholar
  29. Hobson, D. (2010). The Skorokhod embedding problem and model-independent bounds for option prices. In R. Carmona, E. Cinlar, E. Ekeland, E. Jouini, J. Scheinkman, and N. Touzi (eds), Princeton Lectures on Mathematical Finance 2010, Volume 2003 of Lecture Notes in Math. Springer.Google Scholar
  30. Hobson, D. and M. Klimmek (2015). Robust price bounds for forward-starting straddles. Finance and Stochastics 19, 189–214.CrossRefGoogle Scholar
  31. Hobson, D. and A. Neuberger (2012). Robust bounds for forward start options. Mathematical Finance 22, 31–56.CrossRefGoogle Scholar
  32. Hobson, D. G. (1998). Robust hedging of the lookback option. Finance and Stochastics 2(4), 329–347.CrossRefGoogle Scholar
  33. Hull, J. C. (2011). Options, Futures and Other Derivatives (8th ed.). Pearson Education.Google Scholar
  34. Kantorovich, L. V. (1942). On the transfer of masses. Dokl. Akad. Nauk. SSSR 37, 227–229.Google Scholar
  35. Karlin, S. and W. Studden (1966). Tchebycheff Systems, with Applications in Analysis and Statistics. Wiley Interscience.Google Scholar
  36. Monge, G. (1781). Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie royale des sciences avec les mémoires de mathématique et de physique tirés des registres de cette Académie, 666–705.Google Scholar
  37. Obłój, J. (2004). The Skorokhod embedding problem and its offspring. Probab. Surveys 1, 321–390.CrossRefGoogle Scholar
  38. Obłój, J. (2010). The Skorokhod embedding problem. In Cont (2010), pp. 1653–1657.Google Scholar
  39. Samuelson, P. (1965). Rational theory of warrant pricing. Industrial Management Review 6, 13–39.Google Scholar
  40. Schachermayer, W. (2010). The fundamental theorem of asset pricing. In Cont (2010), pp. 792–801.Google Scholar
  41. Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423–439.CrossRefGoogle Scholar
  42. Villani, C. (2009). Optimal Transport, Old and New. Springer.CrossRefGoogle Scholar

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© Mark H. A. Davis 2016

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  • Mark H. A. Davis

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