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Screenshot of the Esther Cloud IDE, showing the Compiler and Esther code
Esther Compiler

Esther Compiler

Esther empowers clients across the full spectrum of Financial Services to develop and maintain proprietary risk and pricing analytics with unparalleled simplicity and numerical efficiency.


Esther's modelling language is a superset of a general-purpose programming language. It is based on language extensions that can be nested on top of the user's favourite language specification. We currently support C# as the base language and are planning to release support for TypeScript and Python, but other languages such as Java or Scala are also supportable in priciple. The addition of new languages does not impact the Esther Solver.


The Esther language extensions enable the user to formulate all problems in the Pricing and Risk domain in full generality. Modelers using Esther focus on the business logic (e.g. pay-offs, model parameters, aggregations, etc.) and delegate the complexities of model solution and orchestration to the Esther Solver platform.


The Esther Compiler is accessible through a web browser interface and supports debugging of all user codes, including the automatically generated GPU server logic. It also provides an integrated development environment for building bespoke models for applications such as derivatives, structured products, and counterparty credit risk. Esther Compiler is designed to make it easy for financial services professionals to quickly develop, debug and deploy models.

Esther Solver

Esther Solver

Mathematics and the low-level model execution are abstracted away from the model developer.  Esther takes care of the entire execution process using its universal Solver for all risk and pricing models emitted as intermediate language by the Esther Compiler. This means that quants do not have to spend time on performance optimisation.

The Esther Solver is entirely generic and does not rely on any model specific mathematical short-cuts such as solutions expressed as special functions or PDE solvers using sparse or banded matrix algebra. Esther Solver instead calculates all model scenarios for all time steps in full and accurately, without approximations. Furthermore, with its highly efficient memory architecture, scenarios can be retained for further analysis, such as reverse stress testing.

Both Esther Compiler and Esther Server are available in a Docker container and can be accessed via either a SaaS service from a public cloud providers or as a local installation with direct licensing. Hardware requirements for Esther solver range from Enterprise AI servers to professional laptops with high-end GPUs. This makes it easy to embed the Esther solver in the model development workflow.

Demos & Videos

Demonstrations and Videos

Performance Metrics on Apple M2

Perf Metrics on Apple M2

XVA Model Run Metrics

We test for performance two multi-asset counterparty credit risk portfolios with about 720,000 trades in 6 currencies, interest rate, equity and FX derivatives. The two portfolios differ in that one has 500 counterparties and the other 3000.  This approximates a medium-sized and large-sized  "core" XVA portfolio by banks, where core implies that counterparty credit factors are best modeled dynamically.

We simulate over 90 monthly time intervals for a total of 60,000 (resp. 10,800) scenarios. Interest rate derivatives are modeled by two factor interest rate models with local volatility, stochastic drift and jumps. Equity and FX derivatives are modeled by stochastic local vol models with jumps (SLVJ). Counterparty credit is modeled with a credit-equity model of the SLVJ type. We calculate counterparty specific and legal-entity-level XVA metrics including CVA, FVA, KVA, PFE and carry out a reverse stress analysis.

We run on a single Apple M2 Max processor with 96 GB of unified memory for its 12 CPU and 38 GPU cores.  The first model runs in under 9 minutes and consumes 3 WHr. The second runs in 16'20'' and consumes 4.26 WHr.  These numbers are fractions of traditional models' timings and energy consumptions.

Here are the recorded performance demos:

and here is a sample model run report for this sort of analysis with results and additional details.

Wrong-way Risk Model Run Metrics

We consider a portfolio of single stock and index equity options, including forwards, futures, European and American put and call options. The portfolio is automatically generated and includes about 500k trades and we assume the Clearing House has 60 members.


Members are divided by trading strategy: random, only-long, only-short, insurance portfolios (with only short puts) and portfolios with a random allocation. We run a total of 10,000,000 correlated scenarios assuming that both the underlying equity risk factors and the counterparty credit risk factors are modeled by defaultable stochastic-local volatility models with jumps. We postulate two kinds of jumps, small and frequent ones and large and rare ones. Both kinds of jumps are correlated with the stochastic driver for volatility which jumps up whenever the underlying jumps.


We define the WWR add-on as the collateral amount such that the counterparty CVA calculated assuming correlation and including the WWR add-on equals the CVA calculating neglecting correlations. We also carry out a Reverse Stress Testing analysis identifying the riskiest scenarios. All metrics are calculated at the legal entity level. The calculation completes in 10':16" and consumes 2.88 WHr of energy on the same Apple M2 Max processor as above.

Here is the recorded porformance demo:

For here is the model run report with the results and additional details.

Risk Analytics and AI

Risk Analytics in the Age of AI

The video introduces Esther in the context of Artificial Intelligence and Wrong-way Risk. It covers the technological and mathematical break-through developments that made Esther possible in the past 20 years. 

The video also includes a brief demonstration of the Esther modelling language and Cloud IDE.

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