PRICING FORMULA FOR EXCHANGE OPTION BASED ON STOCHASTIC DELAY DIFFERENTIAL EQUATION WITH JUMPS
2020 ◽
pp. 1-16
Keyword(s):
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.
2007 ◽
Vol 137
(9)
◽
pp. 3007-3023
Almost sure exponential stability of numerical solutions for stochastic delay differential equations
2010 ◽
Vol 115
(4)
◽
pp. 681-697
◽
2014 ◽
Vol 29
(1)
◽
pp. 205-212
◽
2021 ◽
Vol 0
(0)
◽
pp. 0
2006 ◽
Vol 197
(1)
◽
pp. 89-121
◽