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Continuously Controlled Options: Derivatives With Added Flexibility

Author

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  • NIKOLAI DOKUCHAEV

    (Department of Mathematics & Statistics, Curtin University, GPO Box U1987, Perth, 6845 Western Australia, Australia)

Abstract

The paper introduces special options such that the holder selects dynamically a continuous time process controlling the distribution of the payments (benefits) over time. For instance, the holder can select dynamically the quantity of a commodity purchased or sold by a fixed price given constraints on the cumulative quantity. In a modification of the Asian option, the control process can represent the averaging kernel describing the distribution of the purchases. The pricing of these options requires to solve special stochastic control problems with constraints for the cumulative control similar to a knapsack problem. Some existence results and pricing rules are obtained via modifications of parabolic Bellman equations.

Suggested Citation

  • Nikolai Dokuchaev, 2013. "Continuously Controlled Options: Derivatives With Added Flexibility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-23.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:01:n:s0219024913500039
    DOI: 10.1142/S0219024913500039
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    Cited by:

    1. Christian Bender & Nikolai Dokuchaev, 2014. "A First-Order BSPDE for Swing Option Pricing: Classical Solutions," Papers 1402.6444, arXiv.org, revised Nov 2014.

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