The Solvency II EU Directive came into effect at the beginning of the year. It harmonizes insurance regulation in the European Union with an economic and risk based approach, which considers the full balance sheet of insurers and re-insurers. In the case of life insurers and pension funds, this requires the calculation of the economic value of the liabilities—the contractual commitments the company has to meet—for long term contracts.
Calculating the economic value of the liabilities and capturing the dependence of the liabilities to different scenarios such as movements of the interest rate or changes of mortality cannot be achieved without detailed models of the underlying contracts and requires a significant computational effort.
A Perfect GPU Use Case
The calculations have to be executed for millions of pension and life insurance contracts and have to be performed for thousands of interest rate and mortality scenarios. Because of the level of parallelism, this is an excellent case for the application of GPUs and GPU clusters. In addition, variations in the products have to be captured. While implementing a separate code for many products is possible, a lot can be gained from abstractions at a higher level.
To solve these problem, we use the following technologies.
- The Actulus Modeling Language (AML), a domain specific language for actuarial modeling;
- Alea GPU, QuantAlea’s high performance GPU compiler for .NET C# and F#. See this previous post on Alea GPU;
- The modern functional-first programming language F#.
Armed with these technologies, we can significantly improve the level of abstraction and increase generality. Our system will allow actuaries to be more productive and to harness the power of GPUs without any GPU coding. The performance gain of GPU computing makes it much more practical and attractive to use proper stochastic models and to experiment with a large and diverse set of risk scenarios.
The Actulus Modeling Language
The Actulus Modeling Language (AML) is a domain-specific language for rapid prototyping in which actuaries can describe life-based pension and life insurance products, and computations on them. The idea is to write declarative AML product descriptions and from these automatically generate high-performance calculation kernels to compute reserves and cash flows under given interest rate curves and mortality curves and shocks to these. Continue reading
STAC Research develops financial benchmarks in partnership with leading banks and software or hardware vendors. The STAC-A2 suite of benchmarks aims to represent the standard risk analysis workload that banks and insurance companies use to measure exposure on the financial markets. Earlier this year we published a Parallel Forall post on Monte Carlo simulation for the pricing of American options in STAC-A2.
Record Performance with Tesla K80
Recently, STAC Research published astonishing performance results for the STAC-A2 benchmarks on an NVIDIA Tesla K80. In short, a single Tesla K80 driven by two CPU cores outperforms all previously audited systems in terms of pure performance and power efficiency.
For more on these results, read “Bank on It: Tesla Platform Shatters Record on Risk-Management Benchmark” on the NVIDIA Blog.
We obtained these new results after several optimizations of our previously audited code. First of all, a large fraction of the computations are now avoided due to a better factorization of the underlying mathematical process. Secondly, we tuned some of the kernel parameters to take advantage of the larger register file of the Tesla K80. Finally, we were able to significantly reduce the latency in one of the main loops of the benchmark. Let’s take a look at these optimizations. Continue reading
In finance, an option (or derivative) is the common name for a contract that, under certain conditions, gives a firm the right or obligation to receive or supply certain assets or cash flows. A financial firm uses options to hedge risks when it operates in the markets. It is critical for a firm to be able to accurately price those instruments and understand their dynamics to evaluate its positions, balance its portfolio and limit exposure to potential threats. The calculation of risk and prices for options is a computationally intensive task for which GPUs have a lot to offer. This post describes an efficient implementation of American Option Pricing using Monte Carlo Simulation with a GPU-optimized implementation of the Longstaff Schwarz algorithm.
NVIDIA recently partnered with IBM and STAC to implement the STAC-A2™ benchmark on two NVIDIA Tesla K20X GPUs. It is the first system that was able to calculate the risk and pricing of this particular complex option in less than a second. A system with two Tesla K20X GPUs is up to 6 times faster than a state-of-the-art configuration using only CPUs. Even more interestingly, adding one or two Tesla K20X GPUs to a system offers speedups of slightly more than 5x and 9x, respectively, compared to the same system without GPUs. Continue reading