2015/05/20 by Archil Gulisashvili, Gulisashvili, Archil, Frédéri Viens +3 · 1 citation
Economics, Econometrics and Finance · #40E05 #60G15 #91G20 #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1505.05256
openalex publication_date 2015/05/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small-time behaviors of the above depend heavily on the model, and require a control of the asset price density which is uniform with respect to the asset price variable, in order to translate into results for call prices and implied volatilities. Away from the money, we express the asymptotics explicitly using the volatility process' self-similarity parameter H, its first Karhunen-Loeve eigenvalue at time 1, and the latter's multiplicity. Several model-free estimators for H result. At the money, a separate study is required: the asymptotics for small time depend instead on the integrated variance's moments of orders 1/2 and 3/2, and the estimator for H sees an affine adjustment, while remaining model-free.