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The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problem

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  • Jherek Healy

Abstract

In the standard Black-Scholes-Merton framework, dividends are represented as a continuous dividend yield and the pricing of Vanilla options on a stock is achieved through the well-known Black-Scholes formula. In reality however, stocks pay a discrete fixed cash dividend at each dividend ex-date. This leads to the so-called piecewise lognormal model, where the asset jumps from a fixed known amount at each dividend date. There is however no exact closed-form formula for the pricing of Vanilla options under this model. Approximations must be used. While there exists many approximations taylored to this specific problem in the litterature, this paper explores the use of existing well-known basket option formulas for the pricing of European options on a single asset with cash dividends in the piecewise lognormal model.

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  • Jherek Healy, 2021. "The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problem," Papers 2106.12971, arXiv.org.
    • Handle: RePEc:arx:papers:2106.12971
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    Cited by:

    1. Fabien Le Floc'h, 2024. "Stochastic Expansion for the Pricing of Asian and Basket Options," Papers 2402.17684, arXiv.org, revised Aug 2024.
    2. Michael Samet & Christian Bayer & Chiheb Ben Hammouda & Antonis Papapantoleon & Ra'ul Tempone, 2022. "Optimal Damping with Hierarchical Adaptive Quadrature for Efficient Fourier Pricing of Multi-Asset Options in L\'evy Models," Papers 2203.08196, arXiv.org, revised Oct 2023.

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