Abstract
In this paper we studied stochastic delayed differential equations driven by Le’vy noise. The analogue of Ito formula is considered. The Black-Scholes formula analogue for Vanilla call option price formula is derived.
Highlights
In this paper we studied stochastic delayed differential equations driven by Le’vy noise
In this paper we studied the Stochastic Delay Differential Equations driven by Le’vy noise which arise in many applications of stochastic analysis in finance in pricing of options security markets
As known such systems are quite hard to study due to their lack of Markovianity which is a key property for the study of option prices
Summary
In this paper we studied the Stochastic Delay Differential Equations driven by Le’vy noise which arise in many applications of stochastic analysis in finance in pricing of options security markets. As known such systems are quite hard to study due to their lack of Markovianity which is a key property for the study of option prices. The model for the stock price ζ(t) that we consider satisfies a stochastic delay differential equation driven by Le’vy noise with volatility σ depending on time t and the path ζt = {ζ(t + θ), θ ∈ [−τ, 0]} called a level and past-dependent volatility. Stochastic delay equations; Black-Scholes formula; (B,S)-securities market. −τ when g1(ζ(t), t) is a classical Black-Scholes call option is studied.
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