The next meeting of the seminar of the Information Modelling Department

will be held on May 17, 2022, Tuesday, at 2:00 pm (UCT+3) in the Meeting Room of the Institute of Mathematics and Informatics.

Slavi Georgiev will deliver a talk on

Numerical reconstruction of time-dependent volatility in the Black-Scholes market model. 

Abstract: In this report, numerical algorithms to solve the inverse problem of time-dependent volatility reconstruction from European option quotes are proposed. Following the Black–Scholes framework, we calibrate the models to obtain the volatility term structure. The first algorithm is based on solving auxiliary problems that help to reconstruct the unknown volatility function in step-by-step manner over each temporal node. The option price is decomposed with respect to the volatility. The algorithm requires point or integral observations at each temporal node. It is developed for one- and two-dimensional cases and is tested with real data from CBOE. What is more, this algorithm is adapted to work in the framework of regime-switching. The second algorithm relies on squared cost functional minimization. It iterates over the maturities of the options. The required observations are of market type, i. e. option quotes for different pairs (T,K). The algorithm is also tailored to solve 1D and 2D problems and tested with real market data. For each algorithm informational models are designed and implemented.

Participation via Zoom will also be possible at:
https://us02web.zoom.us/j/89181905247?pwd=bUtKYkRwamRZZXJHU1I4SHRYUGNjQT09
Meeting ID: 891 8190 5247
Passcode: 528714