Event Driven Option Valuation Using Jump Diffusion Model
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Solution Overview
Problem
Existing methods for valuing event-driven option contracts are inefficient, particularly when the contracts are complex or the underlying financial instruments' values change frequently, as they require excessive processing and degrade in performance.
Innovation Solution
Implementing a jump diffusion model based on the Merton jump diffusion model with arithmetic movement assumptions, using a Bachelier-based arithmetic model to calculate event-driven option contract values, which can be partially or wholly implemented on a computer-readable medium for efficient valuation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If simulation models are used to value event driven option contracts, then valuation accuracy is improved, but processing time and computational requirements increase excessively
Solution Approach 1:
The patent segments the valuation process by separating the event-driven component from the underlying asset pricing. It uses a closed-form solution for the event-driven payoff (binary or linear) combined with a separate model for the underlying asset (Heston, SABR, etc.), allowing each component to be valued independently and efficiently without requiring full simulation of complex interactions.
Solution Approach 2:
The patent replaces the mechanical simulation-based valuation system with an analytical/closed-form mathematical system. Instead of using Monte Carlo simulations or finite difference methods that require extensive computation, it derives closed-form solutions that provide accurate valuations through direct mathematical calculations, dramatically reducing processing time while maintaining precision.
2Productivity
If analytical models are used to value complex event driven option contracts, then processing speed is improved, but valuation accuracy deteriorates
Solution Approach 1:
The patent changes the parameterization approach by allowing flexible specification of underlying asset dynamics (Heston stochastic volatility, SABR interest rate models, etc.) and event specifications (binary events, continuous ranges, multiple events). This parameter flexibility enables the closed-form solution to adapt to complex contract structures while maintaining computational efficiency through the analytical framework.
3Measurement precision
If simulation models are used when underlying financial instrument values change frequently, then valuation accuracy is improved, but practicality and processing efficiency deteriorate
Solution Approach 1:
The patent enables continuous valuation by providing a closed-form solution that can be rapidly recalculated as underlying asset prices and volatility parameters change. The analytical framework allows real-time or near-real-time valuation updates without the computational burden of re-running simulations, making it practical for frequent price changes and dynamic trading environments.
Data Source
AI summary
Systems and methods are provided for valuing event driven option contracts. A jump diffusion based model, such as a Merton jump diffusion based model, is modified to assume arithmetic movement of an underlying price and a single jump. The arithmetic movement of the underlying price may be modeled with a Bachelier based arithmetic model. Calculated values may be used to determine margin account requirements.