2015/10/05 by Wei Lin, Shenghong Li, Lin, Wei +5
Economics, Econometrics and Finance · Mathematics · #91G20 #Computational Finance (q-fin.CP) #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Biology Tumor Growth #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1510.01172
openalex publication_date 2015/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we develop a 4/2 stochastic volatility plus jumps model, namely, a new stochastic volatility model including the Heston model and 3/2 model as special cases. Our model is highly tractable by applying the Lie symmetries theory for PDEs, which means that the pricing procedure can be performed efficiently. In fact, we obtain a closed-form solution for the joint Fourier-Laplace transform so that equity and realized-variance derivatives can be priced. We also employ our model to consistently price equity and VIX derivatives. In this process, the quasi-closed-form solutions for future and option prices are derived. Furthermore, through adopting data on daily VIX future and option prices, we investigate our model along with the Heston model and 3/2 model and compare their different performance in practice. Our result illustrates that the 4/2 model with an instantaneous volatility of the form (a√(Vt)+b/√(Vt)) for some constants a, b presents considerable advantages in pricing VIX derivatives.