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Benchmark-Neutral Pricing

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  • Eckhard Platen

Abstract

The paper introduces benchmark-neutral pricing and hedging for long-term contingent claims. It employs the growth optimal portfolio of the stocks as numeraire and the new benchmark-neutral pricing measure for pricing. For a realistic parsimonious model, this pricing measure turns out to be an equivalent probability measure, which is not the case for the risk-neutral pricing measure. Many risk-neutral prices of long-term contracts are more expensive than necessary. Benchmark-neutral pricing identifies the minimal possible prices of contingent claims, which is illustrated with remarkable accuracy for a long-term zero-coupon bond.

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  • Eckhard Platen, 2024. "Benchmark-Neutral Pricing," Papers 2407.01542, arXiv.org.
    • Handle: RePEc:arx:papers:2407.01542
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    File URL: http://arxiv.org/pdf/2407.01542
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    References listed on IDEAS

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    1. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    2. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    4. Ke Du & Eckhard Platen, 2016. "Benchmarked Risk Minimization," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 617-637, July.
    5. Eckhard Platen & Renata Rendek, 2020. "Approximating The Growth Optimal Portfolio And Stock Price Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(07), pages 1-33, November.
    6. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    7. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    8. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
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