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Option Pricing and Stochastic Optimization
National University of Kyiv-Mohyla Academy, Kyiv, Ukraine.ORCID iD: 0000-0002-7652-8157
National University of Kyiv-Mohyla Academy, Kyiv, Ukraine.
2022 (English)In: Stochastic Processes, Statistical Methods, and Engineering Mathematics: SPAS 2019, Västerås, Sweden, September 30-October 2 / [ed] Anatoliy Malyarenko; Ying Ni; Milica Rančić; Sergei Silvestrov, Springer, 2022, p. 651-665Chapter in book (Refereed)
Abstract [en]

In this  paper we propose an approach to option pricing which is based on the solution of the investor problem. We demonstrate that the link between optimal option pricing from investor’s point of view and risk measuring is especially close, and it is given by stochastic optimization. We consider the optimal option pricing X∗ as the optimal decision of the investor, who should maximize the expected profit. It is possible because the average value-at-risk AV@R is related to the simple stochastic optimization problem with a piecewise linear profit/cost function and as it was proved in [12], maximal value is attained. If we consider investing in a European option, then the profit/cost function is a payoff function Y(S) of a European call or put option and the optimal decision can be found as X∗=V@Rα(Y), where parameter α can be computed using interest rates for borrowing and lending and reflects the level of the real economic environment. We illustrate our results for GBM model and Student-like models with dependence (FAT models) and determine optimal option price as the optimal amount to invest for these cases. Meanwhile we measure and manage risk for these models.

Place, publisher, year, edition, pages
Springer, 2022. p. 651-665
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009 ; 408
Keywords [en]
European option, Payoff function, Value-at-risk
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-105091DOI: 10.1007/978-3-031-17820-7_28ISBN: 9783031178207 (electronic)ISBN: 9783031178191 (print)OAI: oai:DiVA.org:oru-105091DiVA, id: diva2:1744506
Available from: 2023-03-20 Created: 2023-03-20 Last updated: 2023-03-20Bibliographically approved

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Shchestyuk, Nataliya

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CiteExportLink to record
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Citation style
  • apa
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