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Real World Pricing for a Modified Constant Elasticity of Variance Model

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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 M Miller & Eckhard Platen, 2008. "Real World Pricing for a Modified Constant Elasticity of Variance Model," Research Paper Series 237, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:237
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
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    3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
    4. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    5. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. MacBeth, James D & Merville, Larry J, 1980. " Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
    7. Shane Miller & Eckhard Platen, 2004. "A Two-Factor Model for Low Interest Rate Regimes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 107-133, March.
    8. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    9. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
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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. 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.
    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.

    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;

    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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