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Modification terms to the Black-Scholes model in a realistic hedging strategy with discrete temporal steps

Modification terms to the Black-Scholes model in a realistic hedging strategy with discrete temporal steps

Lai, Choi-Hong ORCID: 0000-0002-7558-6398 (2018) Modification terms to the Black-Scholes model in a realistic hedging strategy with discrete temporal steps. International Journal of Computer Mathematics. ISSN 0020-7160 (Print), 1029-0265 (Online) (In Press) (doi:https://doi.org/10.1080/00207160.2018.1542135)

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Abstract

Option pricing models generally require the assumption that stock prices are described by continuous-time stochastic processes. Although the time-continuous trading is easy to conceive theoretically, it is practically impossible to execute in real markets. One reason is because real markets are not perfectly liquid and purchase or sell any amount of an asset would change the asset price drastically. A realistic hedging strategy needs to consider trading that happens at discrete instants of time. This paper focuses on the impact and effect due to temporal discretisation on the pricing partial differential equation (PDE) for European options. Two different aspects of temporal discretisation are considered and used to derive the modification or correction source terms to the continuous pricing PDE. First the finite difference discretisation of the standard Black-Scholes PDE and its modification due to discrete trading. Second the discrete trading leads to a discrete time re-balancing strategy that only cancels risks on average by using a discrete analogy of the stochastic process of the underlying asset. In both cases high order terms in the Taylor series expansion are used and the respective correction source terms are derived.

Item Type: Article
Uncontrolled Keywords: Option pricing, correction source terms, discrete time modification
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 17 May 2019 10:48
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: GREAT 2
URI: http://gala.gre.ac.uk/id/eprint/21554

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