Diversity of Financial Risk 2024
29 November, 2024
ELTE TTK, Budapest
Speaker's bio
Dalma
Tóth-Lakits
(Eötvös University)
Dalma holds an MSc in Financial Mathematics and is currently a Ph.D. candidate in Applied Mathematics. Her research focuses on parameter estimation and model calibration in negative interest rate frameworks, utilizing artificial intelligence techniques. She is also a risk management intern at Morgan Stanley, where she bridges theoretical knowledge with practical application. Dalma has been teaching various probability theory, statistics, and financial mathematics courses at the university for four years, and she is also a member of the ELTE AI Research Group and RiskLab.
Calibration of the Kennedy model
The Kennedy model uses Gaussian random fields to model forward rates, providing a natural solution for handling negative interest rates. In our research, we provided probability 1 and maximum likelihood estimations for the parameters of the Kennedy field using Radon-Nikodym derivatives. Additionally, we present an efficient method for simulating the Kennedy field. We derive Black-Scholes-like pricing formulas for various financial products (caplets, floorlets, and swaps). Furthermore, we introduce a parameter estimation algorithm based on numerical extreme value analysis (specifically stochastic gradient descent), which we test on different financial products, first using simulated data and then assessing the Kennedy field's fit to real par swap rates. Finally, we present a neural network built for calibration, with ongoing work to improve its accuracy.