2022/09/21 by Giulia Di Nunno, Di Nunno, Giulia, Yuliya Mishura +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2209.10688
openalex publication_date 2022/09/21 · openalex created_date 2024/09/10 · openalex updated_date 2026/07/28
We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation which ensures the solution to be ``sandwiched'' between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities as well as study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs.