The pricing of European options on two underlying assets with delays

Pricing Formula for Exchange Option Based on Stochastic Delay Differential Equation With Jumps

“…Then, the price of the exchange option in this model is obtained from Theorem 3.3 and Theorem 3.4 as mentioned in Remark 3.1. This is the just result of Lin et al [7].…”

“…Table 1 shows jump parameters. Also, we assume that the volatility function with delay response is g(u) = u 0.05 , b = 1 as in Lin et al [7].…”

“…In the case where the underlying asset process is represented by the "SDDE" model, pricing formulae for various options have been derived by Lin et al [7], Arriojas et al [1], Kazmerchuk et al [4], McWilliams [9], and Swishchuk [15].…”

“…In Arriojas et al [1], authors have derived an explicit delayed Black-Scholes formula for a European call option and proved that the corresponding market is complete by using a martingale method, where the underlying asset prices were assumed to follow the "SDDE" model. Lin et al [7] derived the pricing formula for an exchange option on two underlying assets with such volatility as a function of past asset prices. McWilliams [9] studied pricing for an Asian option and a basket option in the "SDDE" model; however, no explicit formula but only the lower and upper bounds were researched.…”

Drawbacks and Limitations of Black-Scholes Model for Options Pricing

“…Li et al (2014) examined the effects of delay on the stochastic resonance of the stock prices in the financial market with the Heston model driven by the extrinsic and intrinsic periodic information. Lin et al (2018) discussed the pricing of European options on two underlying assets with delays whose price processes satisfy geometric Brownian motions with delays. Cordoni et al (2017) discussed stochastic functional delay differential equation, whose evolution depends on its past history as well as on its present state.…”