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Approximate-Analytical solution to the information measure’s based quanto option pricing model

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  • Batra, Luckshay
  • Taneja, H.C.

Abstract

In this paper, we derive risk-neutral density functions of multi-asset to model the price of European options by incorporating a simple constrained minimization of the Kullback measure of relative information. Based on the theoretical analysis, when the underlying financial asset price follows a geometric Brownian motion, we obtain a two-dimensional quanto-option Black-Scholes equation. In addition, to evaluate the explicit solution of this multi-asset option pricing model, we design a Liouville-Caputo time-fractional derivative and use the Laplace homotopy perturbation method to obtain the explicit scheme in the form of convergent series under suitable regularity conditions.

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  • Batra, Luckshay & Taneja, H.C., 2021. "Approximate-Analytical solution to the information measure’s based quanto option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s096007792100847x
    DOI: 10.1016/j.chaos.2021.111493
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    References listed on IDEAS

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    1. Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
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    3. Batra, Luckshay & Taneja, H.C., 2020. "Evaluating volatile stock markets using information theoretic measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Les Gulko, 1999. "The Entropy Theory Of Stock Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 331-355.
    5. Valenti, Davide & Spagnolo, Bernardo & Bonanno, Giovanni, 2007. "Hitting time distributions in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 311-320.
    6. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.
    7. G. Bonanno & D. Valenti & B. Spagnolo, 2005. "Role of Noise in a Market Model with Stochastic Volatility," Papers cond-mat/0510154, arXiv.org, revised Oct 2006.
    8. G. Bonanno & D. Valenti & B. Spagnolo, 2006. "Role of noise in a market model with stochastic volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 405-409, October.
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    Cited by:

    1. Luckshay Batra & Harish Chander Taneja, 2022. "Comparison between Information Theoretic Measures to Assess Financial Markets," FinTech, MDPI, vol. 1(2), pages 1-18, May.

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