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

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 stochast...

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Bibliographic Details
Published in:Probability in the engineering and informational sciences 2022-04, Vol.36 (2), p.548-563
Main Authors: Kim, Kyong-Hui, Kim, Jong-Kuk, Jo, Ho-Bom
Format: Article
Language:English
Subjects:
Delay
Differential equations
Efficient markets
Formulas (mathematics)
Mathematical models
Prices
Pricing
Random variables
Stochastic models
Volatility
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Summary: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.
ISSN:0269-9648
1469-8951
DOI:10.1017/S0269964820000546