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Real-World Pricing for a Modified Constant Elasticity of Variance Model

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  • Shane Miller
  • Eckhard Platen

Abstract

This paper considers a modified constant elasticity of variance (MCEV) model. This model uses the familiar constant elasticity of variance form for the volatility of the growth optimal portfolio (GOP) in a continuous market. It leads to a GOP that follows the power of a time-transformed squared Bessel process. This paper derives analytic real-world prices for zero-coupon bonds, instantaneous forward rates and options on the GOP that are both theoretically revealing and computationally efficient. In addition, the paper examines options on exchange prices and options on zero-coupon bonds under the MCEV model. The semi-analytic prices derived for options on zero-coupon bonds can subsequently be used to price interest rate caps and floors.

Suggested Citation

  • Shane Miller & Eckhard Platen, 2010. "Real-World Pricing for a Modified Constant Elasticity of Variance Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(2), pages 147-175.
    • Handle: RePEc:taf:apmtfi:v:17:y:2010:i:2:p:147-175
    DOI: 10.1080/13504860903155035
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    8. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Leunglung Chan & Eckhard Platen, 2015. "Pricing Volatility Derivatives Under the Modified Constant Elasticity of Variance Model," Research Paper Series 360, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Wang, Xingchun, 2021. "Pricing volatility-equity options under the modified constant elasticity of variance model," Finance Research Letters, Elsevier, vol. 38(C).
    3. Ralph Rudd & Thomas A. McWalter & Joerg Kienitz & Eckhard Platen, 2018. "Quantization Under the Real-world Measure: Fast and Accurate Valuation of Long-dated Contracts," Papers 1801.07044, arXiv.org, revised Jan 2018.
    4. Chin Yang & Anthony Loviscek & Hui Cheng & Ken Hung, 2012. "A Note on Allen’s Arc Elasticity with Arithmetic, Geometric and Harmonic Means," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 40(2), pages 161-171, June.

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    More about this item

    Keywords

    Benchmark approach; real-world pricing; growth optimal portfolio; constant elasticity of variance; zero-coupon bonds; exchange prices; interest rate caps and floors;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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