2018/08/01 by Archil Gulisashvili, Gulisashvili, Archil
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Complex Systems and Time Series Analysis
paper · pdf · doi:10.48550/arxiv.1808.00421
In this paper, we establish sample path large and moderate deviation\nprinciples for log-price processes in Gaussian stochastic volatility models,\nand study the asymptotic behavior of exit probabilities, call pricing\nfunctions, and the implied volatility. In addition, we prove that if the\nvolatility function in an uncorrelated Gaussian model grows faster than\nlinearly, then, for the asset price process, all the moments of order greater\nthan one are infinite. Similar moment explosion results are obtained for\ncorrelated models.\n