Calibration of Exotic Pricing Models

MoCaX enables fast, cost-effective, and scalable exotic pricing frameworks by reducing calibration compute effort several orders of magnitude

The Problem

Many advanced pricing models for OTC derivatives offer strong theoretical benefits but are impractical in commercial settings due to high calibration costs.

An example is the Bergomi rough volatility model for equities, which relies on Monte Carlo simulations. While a single optimized C++ simulation takes around 2.6 seconds, calibrating the model requires thousands of runs, making it computationally expensive and slow.

Deep Neural Networks (DNNs) have been proposed as a solution, offering efficient execution post-calibration. However, DNN calibration itself is highly costly, typically requiring:

• 3,500,000 to 7,000,000 sampling points

• Over 5,000 CPU-hours (212 CPU-days) of compute effort

These extreme costs make DNN-based calibration commercially difficult.

The Solution

With MoCaX, we can create a replica of the Bergomi rough volatility model Monte Carlo simulation, without any meaningful loss of accuracy, but so that the MoCaX version takes only 0.00001 seconds to evaluate. When compared to the 2.6 seconds the Monte Carlo simulation takes to be evaluated, we obtain a 260,000x performance gain.

When compared with DNNs, MoCaX’s Smart Sampling Machine Learning techniques offer a superior approach. MoCaX provides accuracy comparable to (or better than) DNNs while requiring dramatically fewer resources for the ML model calibration:

• Only 15,000–20,000 sampling points

• Just ~15 CPU-hours of compute effort

This represents a 100x efficiency gain over traditional DNN-based solutions.

A comparison of MoCaX ML vs. DNNs is summarized in the table below:

Conclusions

MoCaX’s Smart Sampling Machine Learning methods enable the rapid and efficient calibration of exotic pricing models. Additionally, MoCaX outperforms standard DNN-based solutions by orders of magnitude.

This breakthrough makes previously impractical models viable in real-world commercial environments by reducing infrastructure costs and ensuring fast, scalable calibration.

For further details on MoCaX techniques for calibration of exotic models, you can read this paper

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