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Model-Free Methods in Valuation and Hedging of Derivative Securities

  • Chapter
The Handbook of Post Crisis Financial Modeling

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.

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References

  • 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 

  • Bachelier, L. (1900). Théorie de la spéculation. Annales Scientifiques de l’Ecole Normale Supérieure 17, 21–86.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Biagini, F. (2010). Second fundamental theorem of asset pricing. In Cont (2010), pp. 1623–1628.

    Google Scholar 

  • Björk, T. and I. Slinko (2006). Towards a general theory of good-deal bounds. Review of Finance 10, 221–260.

    Article  Google Scholar 

  • Black, F. and M. Scholes (1973). The pricing of options and corporate liabilities. The Journal of Political Economy 81(3), 637–654.

    Article  Google Scholar 

  • Breeden, D. and R. Litzenberger (1978). Prices of state-contingent claims implicit in option prices. The Journal of Business 51, 621–651.

    Article  Google Scholar 

  • Brown, H., D. Hobson, and L. C. G. Rogers (2001). Robust hedging of barrier options. Mathematical Finance 11, 285–314.

    Article  Google Scholar 

  • Cochrane, J. and J. Saá-Requejo (2000). Beyond arbitrage: Good deal price bounds in incomplete markets. Journal of Political Economy 108, 79–119.

    Article  Google Scholar 

  • Cont, R. (Ed.) (2010). Encyclopedia of Quantitative Finance. John Wiley & Sons Inc.

    Google Scholar 

  • Cox, A. M. G. and J. Obłój (2011a). Robust hedging of double no-touch barier options. Finance and Stochastics, 15, 573–605.

    Article  Google Scholar 

  • Cox, A. M. G. and J. Obłój (2011b). Robust hedging of double touch barrier options. SIAM Journal on Financial Mathematics 2, 141–182.

    Article  Google Scholar 

  • Davis, M. H. A. (2010). The Black-Scholes formula. In Cont (2010), pp. 199–207.

    Google Scholar 

  • 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 

  • Davis, M. H. A. and A. Etheridge (2006). Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Princeton University Press.

    Google Scholar 

  • Davis, M. H. A. and D. Hobson (2007). The range of traded option prices. Mathematical Finance 17, 1–14.

    Article  Google Scholar 

  • Davis, M. H. A., J. Obłój, and V. Raval (2014). Arbitrage bounds for weighted variance swap prices. Mathematical Finance 24, 821–854.

    Article  Google Scholar 

  • Delbaen, F. and W. Schachermayer (2008). The Mathematics of Arbitrage. Springer.

    Google Scholar 

  • Dolinsky, Y. and H. M. Soner (2014). Robust hedging with proportional transaction costs. Finance and Stochastics 18, 327–347.

    Article  Google Scholar 

  • Dupire, B. (1994). Pricing with a smile. Risk 7, 18–20.

    Google Scholar 

  • El Karoui, N., M. Jeanblanc-Picqué, and S. E. Shreve (1998). Robustness of the Black and Scholes formula. Mathematical Finance 8, 93–126.

    Article  Google Scholar 

  • 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 

  • Föllmer, H. and A. Schied (2011). Stochastic Finance: An Introduction in Discrete Time. De Gruyter.

    Book  Google Scholar 

  • Fouque, J.-P., G. Papanicolaou, and K. R. Sircar (2000). Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gatheral, J. (2006). The Volatility Surface: A Practitioner’s Guide. New York: Wiley.

    Google Scholar 

  • Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer.

    Book  Google Scholar 

  • Hilber, N., O. Reichmann, and C. Schwab (2013). Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing. Springer.

    Book  Google Scholar 

  • 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 

  • Hobson, D. and M. Klimmek (2015). Robust price bounds for forward-starting straddles. Finance and Stochastics 19, 189–214.

    Article  Google Scholar 

  • Hobson, D. and A. Neuberger (2012). Robust bounds for forward start options. Mathematical Finance 22, 31–56.

    Article  Google Scholar 

  • Hobson, D. G. (1998). Robust hedging of the lookback option. Finance and Stochastics 2(4), 329–347.

    Article  Google Scholar 

  • Hull, J. C. (2011). Options, Futures and Other Derivatives (8th ed.). Pearson Education.

    Google Scholar 

  • Kantorovich, L. V. (1942). On the transfer of masses. Dokl. Akad. Nauk. SSSR 37, 227–229.

    Google Scholar 

  • Karlin, S. and W. Studden (1966). Tchebycheff Systems, with Applications in Analysis and Statistics. Wiley Interscience.

    Google Scholar 

  • 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 

  • Obłój, J. (2004). The Skorokhod embedding problem and its offspring. Probab. Surveys 1, 321–390.

    Article  Google Scholar 

  • Obłój, J. (2010). The Skorokhod embedding problem. In Cont (2010), pp. 1653–1657.

    Google Scholar 

  • Samuelson, P. (1965). Rational theory of warrant pricing. Industrial Management Review 6, 13–39.

    Google Scholar 

  • Schachermayer, W. (2010). The fundamental theorem of asset pricing. In Cont (2010), pp. 792–801.

    Google Scholar 

  • Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423–439.

    Article  Google Scholar 

  • Villani, C. (2009). Optimal Transport, Old and New. Springer.

    Book  Google Scholar 

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Authors
  1. Mark H. A. Davis
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Editor information

Editors and Affiliations

  1. School of Management and Institute of Finance, University of Leicester, UK

    Emmanuel Haven (Professor) (Professor)

  2. College of Business, Law, Education and Social Science, Bangor University, UK

    Philip Molyneux (Dean) (Dean)

  3. University of St Andrews, UK

    John O. S. Wilson (Professor of Banking and Finance) (Professor of Banking and Finance)

  4. University of Manchester, UK

    Sergei Fedotov (Professor of Applied Mathematics) (Professor of Applied Mathematics)

  5. Hull University Business School, UK

    Meryem Duygun (Professor of Banking and Finance) (Professor of Banking and Finance)

Copyright information

© 2016 Mark H. A. Davis

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Davis, M.H.A. (2016). Model-Free Methods in Valuation and Hedging of Derivative Securities. In: Haven, E., Molyneux, P., Wilson, J.O.S., Fedotov, S., Duygun, M. (eds) The Handbook of Post Crisis Financial Modeling. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-137-49449-8_7

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