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Real World Pricing of Long Term Contracts

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Abstract

Long dated contingent claims are relevant in insurance, pension fund management and derivative pricing. This paper proposes a paradigm shift in the valuation of long term contracts, away from classical no-arbitrage pricing towards pricing under the real world probability measure. In contrast to risk neutral pricing, the long term excess return of the equity market, known as the equity premium, is taken into account. Further, instead of the savings account, the numeraire portfolio isused, as the fundamental unit of value in the analysis. The numeraire portfolio is the strictly positive, tradable portfolio that when used as benchmark makes all benchmarked non negative portfolios supermartingales, which means intuitively that these are downward trending or at least trendless. Furthermore, the benchmarked real world price of a benchmarked claimis defined to be its real world conditional expectation. This yields the minimal possible price for its hedgable part and minimizes the variance of the benchmarked hedge error. The pooled total benchmarked replication error of a large insurance company or bank essentially vanishes due to diversification. Interestingly, in long terml iability and asset valuation, real world pricing can lead to significantly lower prices than suggested by classical no-arbitragea rguments. Moreover, since the existence of some equivalent risk neutral probability measure is no longer required, a wider and more realistic modeling framework is available for exploration. Classical actuarial and risk neutral pricing emerge as special cases of real world pricing.

Suggested Citation

  • Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:262
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    Cited by:

    1. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2.
    2. Eckhard Platen, 2011. "A Benchmark Approach to Investing and Pricing," World Scientific Book Chapters,in: THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 28, pages 409-426 World Scientific Publishing Co. Pte. Ltd..
    3. Jan Baldeaux & Eckhard Platen, 2013. "Liability Driven Investments under a Benchmark Based Approach," Research Paper Series 325, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Mathias Barkhagen & Jörgen Blomvall & Eckhard Platen, 2015. "Recovering the Real-World Density and Liquidity Premia From Option Data," Research Paper Series 363, Quantitative Finance Research Centre, University of Technology, Sydney.

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    Keywords

    long term pricing; real world pricing; risk neutral pricing; numeraire portfolio; law of the minimal price; strong arbitrage; hedges imulation; diversification; liquidity premium;

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