Murex
END-OF-STUDIES INTERNSHIP / Stage - Consultant Financial Engineering H/F: Validation of the Heath-Jarrow-Morton (HJM) 2 Factor Model for Interest Rates Derivatives
Job Location
Paris, France
Job Description
Murex is a global fintech leader in trading, risk management and processing solutions for capital markets.
Operating from our 19 offices, 3 000 Murexians from over 60 different nationalities ensure the development, implementation and support of our platform which is used by banks, asset managers, corporations and utilities, across the world.
Join Murex and work on the challenges of an industry at the forefront of innovation and thrive in a people-centric environment.
You'll be part of one global team where you can learn fast and stay true to yourself.
The team
You will become a part of the Front Office 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 EQD, Non-Linear Rates, FXD, COM, 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
European swaption is a popular vanilla interest rate option, which gives a right to enter in a spot starting swap upon exercise and co mmonly evaluated with Black/Bachelier formula. Bermuda swaption is a very similar product that allows to choose one of possible exercise dates. European swaptions can be priced analytically i.e. using a simple formula; Bermuda swaptions depend on the dynamics of rate curve and, thus, require usage of more advanced models and numerical methods for pricing.
Practitioners often rely on Hull-White 1-factor model for pricing of Bermuda swaption. The model was invented by John C. Hull and Alan White in 1990 who offered to describe the dynamics of instantaneous spot (short) interest rate as a mean-reverting process. The model gained popularity due to its robustness, fast calibration, and possibility to cope with negative rates. But due to the single source of randomness (1-factor), the model simulates predominantly parallel shifts of the rate curve .
T he recent s urge of inflation and subsequent interest rate hikes by central banks resulted in a rare phenomenon known as an inverted yield curve i.e. a situation where short-term rates are higher than long-term rates. Under such market conditions, more and more practitioners are willing to use a 2-factor model to achieve de-correlation between the short- and long-term rates. Murex 's Gaussian Heath-Jarrow-Morton (HJM) 2-factor model is a perfect candidate to address this client requirement!
Under supervision of the Front Office Financial Engineering team, you will conduct the validation of HJM 2F model for Bermuda swaptions under the new market conditions . More precisely, you will elaborate and execute a test strategy to
The ultimate deliverable of your mission is a model validation document summarizing the tests results, as well as a list of model gaps and limitations.
Validation activity will be mostly conducted via Murex Pricing API using python for tests execution and visualization of results.
Who you ar e?
Location: Paris, FR
Posted Date: 11/5/2024
Operating from our 19 offices, 3 000 Murexians from over 60 different nationalities ensure the development, implementation and support of our platform which is used by banks, asset managers, corporations and utilities, across the world.
Join Murex and work on the challenges of an industry at the forefront of innovation and thrive in a people-centric environment.
You'll be part of one global team where you can learn fast and stay true to yourself.
The team
You will become a part of the Front Office 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 EQD, Non-Linear Rates, FXD, COM, 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
European swaption is a popular vanilla interest rate option, which gives a right to enter in a spot starting swap upon exercise and co mmonly evaluated with Black/Bachelier formula. Bermuda swaption is a very similar product that allows to choose one of possible exercise dates. European swaptions can be priced analytically i.e. using a simple formula; Bermuda swaptions depend on the dynamics of rate curve and, thus, require usage of more advanced models and numerical methods for pricing.
Practitioners often rely on Hull-White 1-factor model for pricing of Bermuda swaption. The model was invented by John C. Hull and Alan White in 1990 who offered to describe the dynamics of instantaneous spot (short) interest rate as a mean-reverting process. The model gained popularity due to its robustness, fast calibration, and possibility to cope with negative rates. But due to the single source of randomness (1-factor), the model simulates predominantly parallel shifts of the rate curve .
T he recent s urge of inflation and subsequent interest rate hikes by central banks resulted in a rare phenomenon known as an inverted yield curve i.e. a situation where short-term rates are higher than long-term rates. Under such market conditions, more and more practitioners are willing to use a 2-factor model to achieve de-correlation between the short- and long-term rates. Murex 's Gaussian Heath-Jarrow-Morton (HJM) 2-factor model is a perfect candidate to address this client requirement!
Under supervision of the Front Office Financial Engineering team, you will conduct the validation of HJM 2F model for Bermuda swaptions under the new market conditions . More precisely, you will elaborate and execute a test strategy to
- Validate theoretical model assumptions and assess perimeter of their validity
- Validate accuracy and robustness of the calibration
- Validate pricing and calculation of model sensitivities
The ultimate deliverable of your mission is a model validation document summarizing the tests results, as well as a list of model gaps and limitations.
Validation activity will be mostly conducted via Murex Pricing API using python for tests execution and visualization of results.
Who you ar e?
- You are in the last year of a master's degree looking for a 6 - months internship
- You are passionate about technology and financial mathematics
- Strong academic background in a quantitative field (Computer Science, E ngineering, Physics, Mathematic s )
- Unders tanding of stochastic processes and f inancial mathematics
- You practice python
- You can efficiently communicate in multicultural environment : English is a must
- You have strong analytical and problem-solving skills
- Duration : 6 months
Location: Paris, FR
Posted Date: 11/5/2024
Contact Information
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