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On the Pricing and Hedging of Long Dated Zero Coupon Bonds

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The pricing and hedging of long dated derivative contracts is a challenging area of research. As a result of utility indifference pricing for general payoffs the growth optimal portfolio turns out to be the appropriate numeraire or benchmark with the real world probability measure as corresponding pricing measure. This concept of real world pricing can be applied for valuing long dated derivatives. An equivalent risk neutral probability measure does not need to exist under this benchmark approach. This paper develops a parsimonious model for a stock index dynamics, which is based on a time transformed squared Bessel process. It uses a diversified world stock index as proxy for the growth optimal portfolio. Surprisingly low prices result for long dated zero coupon bonds that can be replicated using historical data. Such prices and hedges are difficult to explain under the prevailing risk neutral approach.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 185.

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Length: 18
Date of creation: 01 Sep 2006
Date of revision:
Handle: RePEc:uts:rpaper:185

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Keywords: growth optimal portfolio; benckmark approach; real world pricing; expected utility maximization; utility indifference pricing; long dated zero coupon bonds; minimal market model;

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  1. Kevin Fergusson & Eckhard Platen, 2005. "On the Distributional Characterization of Log-returns of a World Stock Index," Research Paper Series 153, Quantitative Finance Research Centre, University of Technology, Sydney.
  2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  3. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  4. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  5. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
  6. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  8. Eckhard Platen, 2004. "A Benchmark Approach to Finance," Research Paper Series 138, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  11. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
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