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PRICING FORMULA FOR EXCHANGE OPTION BASED ON STOCHASTIC DELAY DIFFERENTIAL EQUATION WITH JUMPS

Published online by Cambridge University Press:  20 November 2020

Kyong-Hui Kim Open the ORCID record for Kyong-Hui Kim [Opens in a new window] ,
Jong-Kuk Kim  and
Ho-Bom Jo
Kyong-Hui Kim
Affiliation:
Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea E-mail: [email protected]
Jong-Kuk Kim
Affiliation:
Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea E-mail: [email protected]
Ho-Bom Jo
Affiliation:
Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea E-mail: [email protected]
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Abstract

This paper deals with pricing formulae for a European call option and an exchange option in the case where underlying asset price processes are represented by stochastic delay differential equations with jumps (hereafter “SDDEJ”). We introduce a new model in which Poisson jumps are added in stochastic delay differential equations to capture behaviors of an underlying asset process more precisely. We derive explicit pricing formulae for the European call option and the exchange option by proving a Lemma on the conditional expectation. Finally, we show that our “SDDEJ” model is meaningful through some numerical experiments and discussions.

Keywords

Black–Scholes modeldelay differential equations with jumpsEuropean call optionexchange optionpricing formula
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 548 - 563
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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