Benjamin Joseph

MMath

Status

Postgraduate Student

Research groups

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

Calibration of Local Volatility Models with Stochastic Interest Rates using Optimal Transport, with Gregoire Loeper and Jan Obloj.
Available on arXiv at: https://arxiv.org/abs/2305.00200
Joint Calibration of Local Volatility Models with Stochastic Interest Rates using Semimartingale Optimal Transport, with Gregoire Loeper and Jan Obloj.
Available on arXiv at: https://arxiv.org/abs/2308.14473
The Measure Preserving Martingale Sinkhorn Algorithm, with Gregoire Loeper and Jan Obloj.
Available on arXiv at: https://arxiv.org/abs/2310.13797

Research interests

I am a fourth year DPhil student supervised by Gregoire Loeper and Jan Obloj, at the CDT Random Systems, and funded by BNP Paribas. My research has so far been focussed on non-parametric model calibration using optimal transport. My first two papers study the calibration of a stochastic interest rate and underlying stock to observed European option prices. We present results for different calibration approaches, namely a "sequential" calibration where the interest rate is assumed to perfectly match the market conditions and a "joint" calibration where both state variables are calibrated together. The joint calibration is tested on market data against a "parametrically calibrated" reference model to demonstrate a use case of the method improving the accuracy of model calibration.

Teaching

MT 2020: B8.1 Probability, Measure and Martingales (TA)

HT 2021: B8.2 Continuous Martingales and Stochastic Calculus (TA)

MT 2021: B8.1 Probability, Measure and Martingales (TA)

HT 2022: MCF Fixed Income & Credit (Tutor)

MT 2022: B8.1 Probability, Measure and Martingales (Tutor)

MT 2023: B8.1 Probability, Measure and Martingales (Tutor)