Backward DNN Solver for Callable Instrument Pricing

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Solution Overview

Problem

Traditional methods for determining the value of callable instruments, such as numerical methods and Monte Carlo methods, are inefficient and computationally expensive, making it difficult to obtain real-time or near real-time pricing, especially for instruments with multiple exercise dates.

Innovation Solution

The use of a backward deep neural network (DNN) solver that poses the problem as a partial differential equation or backward stochastic differential equation, trained to determine the value of callable instruments by projecting the final value backward through intermediate values to an initial value, reducing computational complexity and providing real-time pricing.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If Monte Carlo methods are used to determine callable instrument values, then accuracy is improved, but computation time increases significantly

Engineering Contradiction:

Improvecallable instrument value accuracyVSAvoidcomputation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The system pre-computes and stores callable instrument values using Monte Carlo methods during offline training phases. These pre-computed values are stored in data structures that can be quickly queried during real-time operations, eliminating the need for expensive on-demand Monte Carlo simulations.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The system creates simplified representations or proxies of the complex callable instrument valuation problem. By training machine learning models on historical Monte Carlo simulation data, the system creates a lightweight copy that can predict values instantly without re-running the full Monte Carlo simulation.

Inventive Principle:

Principle #26Copying

2Productivity

If traditional numerical methods are used, then computation speed is improved, but the ability to handle high-dimensional problems deteriorates

Engineering Contradiction:

Improvecomputation speedVSAvoidhandling high-dimensional problems

Core Design Contradiction:

ProductivityVSAdaptability or versatility

Solution Approach 1:

The system transforms the valuation problem from a high-dimensional partial differential equation into a lower-dimensional regression problem by using machine learning models. This parameter transformation allows the system to maintain computational speed while handling complex, high-dimensional callable instruments with multiple exercise dates and underlying assets.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The system replaces traditional numerical methods (finite difference methods, Monte Carlo simulations) with machine learning-based approaches. This substitution enables the system to solve high-dimensional valuation problems efficiently by leveraging the pattern recognition capabilities of neural networks rather than relying on computationally intensive numerical algorithms.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Speed

If real-time pricing is implemented, then decision-making speed is improved, but computational resource requirements increase

Engineering Contradiction:

Improvepricing speedVSAvoidcomputational resource consumption

Core Design Contradiction:

SpeedVSUse of energy by moving object

Solution Approach 1:

The system performs computationally intensive training operations in advance, storing the results in optimized data structures. During real-time pricing operations, the system only needs to perform simple lookups or lightweight predictions, dramatically reducing computational resource consumption while maintaining real-time pricing capability.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The system uses lightweight, approximate models for real-time pricing that consume minimal computational resources. These simplified models provide sufficiently accurate pricing for decision-making purposes without requiring the full computational power of traditional methods, effectively using cheaper computational alternatives for time-critical operations.

Inventive Principle:

Principle #27Cheap short-living objects (Disposable)

Data Source

PatentUS11569278B1Systems and methods for callable options values determination using deep machine learning

Publication Date: 2023.01.31 WELLS FARGO BANK NA

AI summary

Systems, apparatuses, methods, and computer program products are disclosed for pricing a callable instrument. A plurality of corresponding pairs of Brownian motion paths and index value paths are determined corresponding to a set of dates. A deep neural network (DNN) of a backward DNN solver is trained until a convergence requirement is satisfied by for each pair of corresponding Brownian motion path and index value path, using the backward DNN solver to determine by iterating in reverse time order from a final discounted option payoff to an initial value. A statistical measure of spread of a set of initial values is determined and parameters of the DNN are modified based on the statistical measures of spread. Pricing information is determined by the backward DNN solver and provided such that a representation thereof is provided via an interactive user interface of a user computing device.