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Efficient Approximations for Utility-Based Pricing

Author

Listed:
  • Laurence Carassus

    (Laboratoire de Mathématiques de Reims, UMR9008 CNRS et Université de Reims Champagne-Ardenne)

  • Massinissa Ferhoune

    (Laboratoire de Mathématiques de Reims, UMR9008 CNRS et Université de Reims Champagne-Ardenne
    Léonard de Vinci Pôle Universitaire, Research Center)

Abstract

In a context of illiquidity, the reservation price is a well-accepted alternative to the usual martingale approach which does not apply. However, this price is not available in closed form and requires numerical methods such as Monte Carlo or polynomial approximations to evaluate it. We show that these methods can be inaccurate and propose a deterministic decomposition of the reservation price using the Lambert function. This decomposition allows us to perform an improved Monte Carlo method, which we name Lambert Monte Carlo (LMC) and to give deterministic approximations of the reservation price and of the optimal strategies based on the Lambert function. We also give an answer to the problem of selecting a hedging asset that minimizes the reservation price and also the cash invested. Our theoretical results are illustrated by numerical simulations.

Suggested Citation

  • Laurence Carassus & Massinissa Ferhoune, 2024. "Efficient Approximations for Utility-Based Pricing," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-38, June.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:2:d:10.1007_s11009-024-10076-z
    DOI: 10.1007/s11009-024-10076-z
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    References listed on IDEAS

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    1. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    2. Longstaff, Francis A, 1995. "How Much Can Marketability Affect Security Values?," Journal of Finance, American Finance Association, vol. 50(5), pages 1767-1774, December.
    3. Kahl, Matthias & Liu, Jun & Longstaff, Francis A., 2003. "Paper millionaires: how valuable is stock to a stockholder who is restricted from selling it?," Journal of Financial Economics, Elsevier, vol. 67(3), pages 385-410, March.
    4. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373, October.
    5. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
    6. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    7. Tehranchi, Michael, 2004. "Explicit solutions of some utility maximization problems in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 109-125, November.
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