2022/03/04 by Fei Gao, Shuaiqiang Liu, Gao, Fei +5
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2203.02323
openalex publication_date 2022/03/04 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all relevant Hurst indices, i.e. H ∈ (0,1). The fractional Ornstein-Uhlenbeck (fOU) process, for example, gives rise to highly nontrivial integration formulas that need careful analysis when considering the whole range of Hurst indices. We will show that the classical technique of analytic continuation, from complex analysis, provides a way of extending the domain of validity of an integral, from H∈(1/2,1), to the larger domain, H∈(0,1). Numerical experiments for different Hurst indices confirm the robustness and efficiency of the integral formulations presented here. Moreover, we provide accurate and highly efficient financial option pricing results for processes that are related to the fOU process, with the help of Fourier cosine expansions.