The Team:​ 

You will become a part of the Front Office (FO) Trading Product Development Domain (PDD) which is at heart of MX.3 software evolution, where you will integrate the Financial Engineering team. Our multi-cultural team designs, validates and delivers Murex Advanced Analytics (MACS) which is a combination of rich catalogue of derivative products covering all asset classes, a large set of models for evaluation and risk management of derivatives. 

We work closely with the quant development and integration teams to enhance our products and models. We provide our quantitative expertise and collaborate with FO Trading PDD teams like Equity Derivatives, Non-Linear Rates, Foreign Exchange Derivatives, Commodity Derivatives, etc. to build trading solutions. Similarly, we assist Client Services and regional offices across the globe to provide cutting-edge solutions to our clients. 

The Mission: 

The goal of this internship is to develop a robust validation framework for pricing models of exotic interest rate derivatives, with a focus on benchmarking their financial performance. 

Pricing exotic financial products typically begins with selecting a suitable mathematical model, often defined by a stochastic differential equation. The model parameters are calibrated to replicate the prices of liquid market instruments as closely as possible. Once calibrated, numerical methods – such as Monte Carlo simulations or partial differential equation (PDE) solvers – are used to compute the price of the exotic product. 

In essence, the model serves as an interpolator, enabling the valuation of complex instruments based on the prices of simpler, liquid ones. To evaluate the quality of the pricing model, two key tests are employed, namely daily Profit-and-Loss (PnL) explanation and hedging efficiency. 

PnL explanation decomposes the daily change in the value of security using a Taylor expansion into Delta (sensitivity to changes in the underlying asset) and Vega (sensitivity to changes in volatility): 

Vt+1−Vt=∂Vt∂St×(St+1−St)+ ∂Vt∂σt×(σt+1−σt)+ϵ Vt+1−Vt=𝜕Vt𝜕St×(St+1−St)+ 𝜕Vt𝜕𝜎t×(𝜎t+1−𝜎t)+𝜖 

where

ϵ𝜖

is the residual term. The quality of the model is assessed by analyzing the magnitude and behavior of this residual. 

Hedging efficiency test involves simulating a strategy where the exotic product is sold and its risk is hedged daily using Delta and Vega hedging. The resulting PnL of this strategy provides insight into the model’s effectiveness in managing risk. 

Your Role: 

Under the supervision of the Front Office Financial Engineering team, you will: 

• Build a test framework using market data and pricing REST APIs. 

• Benchmark widely used IRD models such as Hull-White and Forward Market Model, specifically applied to Bermuda swaptions. 

• Analyze model performance through PnL explanation and hedging efficiency tests. 

The deliverables of your mission are a documented python module and a model validation document summarizing the tests results, as well as a list of gaps, and enhancement proposals.

Your Profile/Who you are? 

• You are in the last year of a master’s degree looking for a 6-months internship 

• You master python including numpy, pandas, matplotlib 

• You are passionate about technology and financial mathematics 

• Strong academic background in a quantitative field (Quantitative Finance, Computer Science, Engineering, Physics, Mathematics) 

• Understanding of stochastic processes and financial mathematics 

• You can efficiently communicate in multicultural environment: English is a must 

• You have strong analytical and problem-solving skills 

Duration: 6 months