When memory matters: exploring new approaches to pricing and hedging in financial markets

Financial markets have a memory. Volatility, interest rates and other financial quantities can be influenced by their past, while some financial products depend on the entire trajectory of an asset price. In his PhD research at LIDAM, Edouard Motte develops new mathematical tools to address the challenges raised by these memory effects and improve the way financial risks are modelled, priced and hedged.


In financial mathematics, two fundamental questions are pricing and hedging: determining the fair value of a financial product and designing investment strategies to manage the associated risks.

These questions become significantly more challenging when financial markets exhibit memory effects. Unlike in classical models, where decisions can often be based primarily on the current state of the market, memory-dependent models require taking into account the history of market movements. Mathematically, this leads to what is known as a non-Markovian framework.

In his PhD research in mathematical finance at LIDAM, Edouard Motte investigates pricing and hedging problems in financial markets with memory. His work develops mathematical tools that can better capture the path-dependent nature of financial markets and the impact of their past dynamics.

A key element of his research is the use of Volterra processes to model financial risk factors exhibiting memory. He also explores path-signatures to develop efficient hedging strategies while accounting for market impact – the fact that trading decisions themselves can influence asset prices.

By combining these mathematical approaches, Edouard’s research contributes to a better understanding of financial markets in which memory, path dependence and market impact interact. Such models can help improve risk management and the robustness of financial decision-making, particularly as financial markets become increasingly complex.

In this video, Edouard presents the main challenges of his research and explains how advanced mathematical tools can contribute to addressing them.

https://youtube.com/shorts/OXdwgIQiS7k?feature=share

Congratulations to Edouard Motte on the successful completion of his PhD! We wish him every success as he continues exploring the fascinating questions raised by memory in financial markets.

PhD supervisor: Donatien Hainaut