Asset pricing and simulation under the environment of jumping and mixed Gaussian process
- PENG Bo, GUO Jing-jun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(5):
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The European option pricing model is established by based on mixed sub-fractional Brownian motion in jump environment. Firstly, the partial differential equation satisfying European option can be obtained through the Delta hedging principle. Secondly, the call option, the put option pricing formula and the call-put parity formula are respectively obtained by using the quasi-conditional expectation. Then, the asset risk is further quantified by Greeks Δ, Δ, ρ, Θ, Γ, ν and the partial derivative formula forthe Hurst index H. Finally, numerical simulation show that the Hurst index H and jump intensity λ in pricing parameters have a significant impact on the value of option.