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Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment

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  • Maxim Bichuch

Abstract

We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost ε>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307–324, 1997 ), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of $\varepsilon^{\frac{1}{3}}$ in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of $\varepsilon^{\frac{2}{3}}$ . In both cases, we also obtain a “nearly optimal” strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Maxim Bichuch, 2014. "Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment," Finance and Stochastics, Springer, vol. 18(3), pages 651-694, July.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:3:p:651-694
    DOI: 10.1007/s00780-014-0233-z
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    References listed on IDEAS

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    Cited by:

    1. Bouchard, Bruno & Muhle-Karbe, Johannes, 2022. "Simple bounds for utility maximization with small transaction costs," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 98-113.
    2. Lu, Xiaoping & Yan, Dong & Zhu, Song-Ping, 2022. "Optimal exercise of American puts with transaction costs under utility maximization," Applied Mathematics and Computation, Elsevier, vol. 415(C).

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    More about this item

    Keywords

    Transaction costs; Optimal control; Asymptotic analysis; Utility maximization; Option pricing; 91G80; 60H30; G13;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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