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A Quantum Algorithm for Pricing Asian Options on Valuation Trees

Author

Listed:
  • Mark-Oliver Wolf

    (Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • Roman Horsky

    (Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

  • Jonas Koppe

    (Department of Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany)

Abstract

We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load the corresponding distribution onto the states. We implement the expectation value of the option pricing formula as a composition of the price probabilities, the payout and an indicator function, mapping their respective values to amplitudes of additional qubits. Thus, the underlying no longer has to be discretized into the same bit values for different times, resulting in smaller quantum circuits. The algorithm may be used with quantum amplitude estimation, enabling a quadratic speed-up over classical Monte Carlo methods.

Suggested Citation

  • Mark-Oliver Wolf & Roman Horsky & Jonas Koppe, 2022. "A Quantum Algorithm for Pricing Asian Options on Valuation Trees," Risks, MDPI, vol. 10(12), pages 1-14, November.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:12:p:221-:d:980377
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    References listed on IDEAS

    as
    1. Kenji Kubo & Koichi Miyamoto & Kosuke Mitarai & Keisuke Fujii, 2022. "Pricing multi-asset derivatives by variational quantum algorithms," Papers 2207.01277, arXiv.org.
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