Signaloid Cloud Compute Engine API

Use Case Family:

Quantitative Finance

### Use Case

# Using the Heath-Jarrow-Morton (HJM) Framework for Pricing a Portfolio of Swaptions

This use case uses the Heath-Jarrow-Morton (HJM) framework to price a basket of swaptions. Traditional implementations use Monte Carlo simulation, typically with thousands to hundreds of thousands of iterations.

When running on the Signaloid Compute Engine, we can replace the use of individual random variates drawn from some distribution with a direct computation on a representation of the probability distribution across paths. This allows the code kernel running on the Signaloid Compute Engine to compute the same kind of distribution, in a single pass over the time steps, as the Monte Carlo simulation across the thousands or hundreds of thousands of paths.

An implementation on the Signaloid C0 processor runs 2.7x faster than an already fast C-language Monte-Carlo-based implementation of the same model running on an AWS r7iz high-performance instance.

Plot (see Note 1 below for details) of output distribution when running on Signaloid C0-Pro-XS+ core that provides the 2.7x speedup.

Plot (see Note 1 below for details) of the output of an 8.9k-iteration Monte Carlo for this use case. This Monte Carlo iteration count provides the same or better Wasserstein distance to ground truth (large, converged) Monte Carlo as execution on a Signaloid C0Pro-XS+ core (which is 2.7x faster).

Plot (see Note 1 below for details) of ground truth (1M-iteration) Monte Carlo.

### Note 1:

The underlying distribution representations are not literal histograms: The distribution plots use an adaptive algorithm to render a mutually-consistent and human-interpretable depiction for both the Signaloid distribution representations and the Monte Carlo samples, to permit qualitative comparison.

### Note 2:

Because Monte Carlo works by statistical sampling, each set of multi-iteration Monte Carlo runs (e.g., each time a 200k-iteration Monte Carlo is run) will result in a slightly different final distribution. By contrast, the results from Signaloid's platform are completely deterministic and yield the same distribution each time, for a given Signaloid C0 core type. The performance improvement over Monte Carlo results above show the performance speedup of running on Signaloid's platform, compared to running a Monte Carlo on an AWS r7iz high-performance AWS instance, for the same quality of distribution while accounting for the variations inherent in Monte Carlo. To compare the quality of distribution, we run a large Monte Carlo until convergence (e.g., 1M iterations) and use this as a baseline or ground truth reference for distribution quality (not for performance). We then compare performance of the Signaloid solution against a Monte Carlo iteration count for which the output distributions of 100 out of 100 repetitions are all at smaller Wasserstein distance (than the Signaloid-core-executed algorithm's output distribution) to the output distribution of the baseline reference. Intuitively, this analysis gives the Monte Carlo iteration count that results in an output distribution that is never worse than the Signaloid-core-executed computation's output distribution. 2.7x speedup achieved with C0Pro-XS+. Performance data based on Spring 2024 release of Signaloid's technology.