GPU Deep Learning Monte Carlo Option Pricing
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Solution Overview
Problem
Monte Carlo option pricing and derivative pricing methods are computationally expensive and slow, especially when the parameter space is large and precision requirements are high, making them cost-ineffective in financial applications.
Innovation Solution
The use of deep learning and graphics processing units (GPUs) to accelerate Monte Carlo simulations through variance reduction techniques, such as the Schoenmakers-Heemink algorithm, and machine learning-based importance sampling, which reduces the number of simulations needed and computational costs by employing an end-to-end machine learning platform on GPUs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Monte Carlo simulations are used for option pricing, then versatility in pricing different derivatives is improved, but computational speed deteriorates
Solution Approach 1:
The system pre-computes and stores pricing results for a comprehensive set of parameter combinations in lookup tables before actual pricing requests. When a pricing query is received, the system performs preliminary checks to determine if the result exists in the lookup table, avoiding the need for full Monte Carlo simulation. This preliminary action significantly reduces computational speed requirements while maintaining pricing versatility across different derivative types.
2Measurement precision
If high precision is required for derivative pricing, then pricing accuracy is improved, but computational cost deteriorates
Solution Approach 1:
The system performs preliminary analysis of the pricing query to determine the required precision level and selects appropriate computational methods accordingly. For queries requiring high precision, the system uses refined Monte Carlo methods with fewer iterations by leveraging pre-computed data. For lower precision requirements, approximate methods or lookup table values are used, significantly reducing computational cost while maintaining adequate accuracy.
Solution Approach 2:
The system applies partial Monte Carlo simulations by pre-computing and storing results for a subset of critical parameter combinations. For new pricing queries, the system retrieves pre-computed results where available and performs partial simulations only for the remaining cases, rather than performing complete simulations for all queries. This partial action reduces computational cost while maintaining pricing accuracy through the use of pre-validated results.
3Adaptability or versatility
If large parameter space is used for comprehensive pricing, then pricing coverage is improved, but computational time deteriorates
Solution Approach 1:
The system segments the large parameter space into multiple discrete dimensions (e.g., volatility, interest rate, time to maturity, strike price) and creates separate lookup tables for each dimension or combination of dimensions. This segmentation allows the system to handle comprehensive parameter coverage by storing results in an organized manner and retrieving only the specific segments needed for each pricing query, significantly reducing computational time compared to treating the entire parameter space as a single unit.
Solution Approach 2:
The system performs preliminary organization of the parameter space by identifying and pre-computing results for boundary conditions and critical parameter combinations. These pre-computed results are stored in lookup tables that cover the full parameter range. When processing pricing queries, the system leverages these preliminary computations to quickly determine results without performing complete simulations across the entire parameter space, thus maintaining comprehensive coverage while reducing computational time.
Data Source
AI summary
A method may include: generating, by a computer program, random values for a plurality of pricing model parameters for a pricing model; receiving, by the computer program, a selection of a plurality of anchors; calculating, by the computer program, simulated prices for the plurality of anchors using the pricing model; training, by the computer program, encoder parameters for an encoder with the simulated prices to predict updated values for the pricing model parameters; predicting, by the pricing model using the updated values for the pricing model parameters, predicted prices for the anchors; computing, by the computer program using an error module, a loss between the simulated prices and the predicted prices; updating, by the computer program, the encoder parameters based on the loss; and deploying, by the computer program, the pricing model to a production environment in response to the loss being within a threshold range.