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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 (engelsk)Inngår i: 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, s. 651-665Kapittel i bok, del av antologi (Fagfellevurdert)
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.

sted, utgiver, år, opplag, sider
Springer, 2022. s. 651-665
Serie
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1017, E-ISSN 2194-1009 ; 408
Emneord [en]
European option, Payoff function, Value-at-risk
HSV kategori
Identifikatorer
URN: urn:nbn:se:oru:diva-105091DOI: 10.1007/978-3-031-17820-7_28ISBN: 9783031178207 (digital)ISBN: 9783031178191 (tryckt)OAI: oai:DiVA.org:oru-105091DiVA, id: diva2:1744506
Tilgjengelig fra: 2023-03-20 Laget: 2023-03-20 Sist oppdatert: 2023-03-20bibliografisk kontrollert

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