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Over the last 30 years derivatives - instruments whose value depends on underlying assets as stocks, interest rates or foreignexchange rates have become increasingly important in finance. The amount of outstanding derivatives positions is close to $700 trillion now. Due to the world financial crisis in 2007, derivatives products for mortgages required more regulation and securization than ever. Financial institutions focus more attention risk measurement, investment portfolio management systems need to be improved to place emphasis on accuracy and performance of possible different scenarios computation. This work presents an approach to strengthen risk management systems by utilizing combination of sophisticated numerical methods and parallel processing on different HPC platforms.
 
Introduction
Option – a contract that allows buying or selling underlying assets at the fixed time in the future (expiration time) for the price negotiatiedat the present time. Traders invest money in options to neutralize (hedge) further commodity price fluctuations on the market (gains/loss on the commodity market are compensated by loss/gains on derivatives market).
There arise several questions...
How to describe dynamics of commodities and price options? Stochastic models?How to solve stochastic models fast and accurately? How to measure the risk of these models --an impact of model parameters on future scenarios? How to fit these models to today's market-data to forecast more accurately?
 
Financial Risk Management
To price options, the future commodity price must be forecast to know how this price differs from the strike price.
Assumptions:
The future commodity price has its own volatility over time and depends on several market factors (model parameters)
Solution: Heston model
How to solve?
Monte-Carlo method as dW1 and dW2 –random variables
The future commodity price –an expected value of all scenarios
 
 
Numerical methods + HPC(FPGA, GPUs, Xeon-Phi)
Monte-Carlo method:
• An embarrasinglyparallel problem, potential to run on HPC
To measure the impact of model parameters on the future
commodity and option price:
• Automatic Differentiation (backward differentiation) on HPC
To fit the model to market-data:
• the Levenberg-Marquardt algorithm on HPC
To reduce the variance of Monte-Carlo method:
• Multilevel Monte Carlo method on HPC
 
Solution
 
 
Features
The software supports:
• different High Performance Computing platforms as MaxelerFPGA, Intel Xeon-Phi, NVIDIA CUDA, OpenCLand OpenMP
• risk calculation (the first-and second-order Greeks are calculated in a single Monte-Carlo simulation) and calibration of financial models on HPC
• a wide range of financial option and interest rates models (Black-Scholes, Heston, LIBOR, Vasicek, etc.)
• Multilevel Monte Carlo method, jump processes and CVA models (in progress)
Speedup achieviedso far (vs. Intel Sandybridge):
• Black-Scholes (1200x -FPGA, 90x -CUDA, 80x -OpenCL)
• Heston (95x -CUDA, 98 -OpenCL)
• LIBOR (49x -CUDA, 48x -OpenCL)
 
 
 
 

HPC Adjoint Risk Senstivity Calculator

HPC Adjoint Risk Senstivity Calculator

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MAN_002-3494548-v2-UMIP Annual Research Licence C2G final 1.00

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