# Mathematical Finance & Financial Data Science Seminar

#### Learning The Pricing Kernel: Applications To Option Pricing

**Speaker:**
Daniel Bloch, Head of Quant at Blu Analytics

**Location:**
Online Zoom access provided to registrants

**Date:**
Tuesday, May 9, 2023, 5:30 p.m.

**Synopsis:**

We propose to identify the pricing kernel from option prices on both the natural probability measure

and the risk-neutral one. We use Machine Learning to generate consistent synthetic data closely related to

the original time series, and use it for computing conditional expectations, under the historical measure,

with Reinforcement Learning in a model independent way. We are interested in estimating a portfolio of

option prices at any future time for trading and risk management purposes. However, we do not know the

model driving the dynamics of the actual stock prices, but only observe discretely their evolution.

We use these subjective option prices, under the historical measure, to compute the adjusted pricing kernel,

which maps the option prices from the historical measure to the risk-neutral measure. We use it to modify the

discretely observed stock prices into a risk-adjusted process, which we use for computing the expected value

of the contingent claims in the risk-neutral measure. Finally, we illustrate our approach in a simple model

where the market price of risk is driven by an Ornstein-Uhlenbeck process.

**Speaker Bio:**

Daniel Bloch is head of quantitative strategies at Blu, a systematic event trading fund using NLP to anticipate large market moves

based on news. Prior to working at Blu, Daniel managed teams of quant researchers in top tier banks, developing and

implementing option pricing and risk models. He was also a portfolio manager on multi-strategies systematic trading

across continents, using multifractal analysis and machine learning. Daniel conducts research on mathematical finance

and AI, focusing on dynamical models applied to forecasting the stock and option market in order to maximise return

and minimise risk.

**Notes:**