The PhD course "Dottorato in Economia e Management" (DEM) organizes an intense workshop, where leading experts meet in Verona to discuss recent advances in financial mathematics. Join us!
09 : 45 AM - 10 : 00 AM
10 : 00 AM - 10 : 40 AM
Motivated by financial applications, we solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients. These equations arise, e.g., in fractional Heston stochastic volatility models when computing the characteristic function of the log-spot price. We first consider the case of a zero initial value corresponding to the characteristic function of the log-price. Then we investigate the case of a general starting value associated to a transform also involving the volatility process. The solution to the fractional Riccati equation takes the form of power series, whose coefficients satisfy a convolution equation. We show that this solution has a positive convergence domain, which is typically finite. This naturally suggests a hybrid numerical algorithm to explicitly obtain the solution also beyond the convergence domain of the power series representation. Our numerical tests show that the hybrid algorithm turns out to be extremely fast and stable. When applied to option pricing, our method largely outperforms the only available alternative in the literature, based on the Adams method.
10 : 40 AM - 11 : 20 AM
In this talk, we propose an integrated pricing framework for Credit Value Adjustment of equity and commoditiy products. The given framework, in fact, generates dependence endogenously, allows for calibration and pricing to be based on the same numerical schemes (up to Monte Carlo simulation), and also allows the inclusion of risk mitigation clauses such as netting, collateral and initial margin provisions. The model is based on a structural approach which uses correlated Lévy processes with idiosyncratic and systematic components; the pricing numerical scheme, instead, efficiently combines Monte Carlo simulation and Fourier transform based methods. The work is in collaboration with L.Ballotta (Cass Business School) and G.Fusai (Università del Piemonte Orientale).
11 : 50 AM - 12 : 30 AM
We present a stochastic-local volatility model for derivative contracts on commodity futures able to describe forward-curve and smile dynamics with a fast calibration to liquid market quotes. A parsimonious parametrization is introduced to deal with the limited number of options quoted in the market. Cleared commodity markets for futures and options are analyzed to include in the pricing framework specific trading clauses and margining procedures. Numerical examples for calibration and pricing are provided for different commodity products.
12 : 30 AM - 13 : 30 AM
A central task in modeling, which has to be performed each day in banks and financial institutions, is to calibrate models to market and historical data. So far the choice which models should be used was not only driven by their capacity of capturing empirically observed market features well, but rather by computational tractability considerations. This is now undergoing a big change since neural network approaches offer the possibility to transform a daily online calibration into an offline learning phase and an online evaluation phase where the latter will be – thanks to the learning phase – extremely fast no matter what complex type of model needs to be calibrated. Inspired by the work of Andrez Hernandez, we consider two examples of calibration with neural networks: first a mixture model for interest rate dynamics in the spirit of Brigo and Mercurio and second a local stochastic volatility model where the local volatility function is parametrized via neural nets. The talk is based on joint work with Andres Hernandez, Wahid Khosrawi and Josef Teichmann.