2017/06/14 by Robert Azencott, Peng Ren, Azencott, Robert +3 · 1 citation
Economics, Econometrics and Finance · #60F99 #62M05 #91G80 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1706.04566
openalex publication_date 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a detailed analysis of observable moments based parameter estimators for the Heston SDEs jointly driving the rate of returns Rt and the squared volatilities Vt. Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realized volatilities Yt, which are of course observable. Realized volatilities are computed over sliding windows of size ε, partitioned into J(ε) intervals. We establish criteria for the joint selection of J(ε) and of the sub-sampling frequency of return rates data. We obtain explicit bounds for the Lq speed of convergence of realized volatilities to true volatilities as ε → 0. In turn, these bounds provide also Lq speeds of convergence of our observable estimators for the parameters of the Heston volatility SDE. Our theoretical analysis is supplemented by extensive numerical simulations of joint Heston SDEs to investigate the actual performances of our moments based parameter estimators. Our results provide practical guidelines for adequately fitting Heston SDEs parameters to observed stock prices series.