Average Spot Basket Option Pricing with Analytical Approximation
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Solution Overview
Problem
Current methods for pricing exotic options, such as basket options, are computationally intensive and fail to accurately account for the correlation between spot prices of distinct underlying assets at different instants, leading to restricted accuracy and long computation times, especially in real-time financial analysis.
Innovation Solution
A method and system that use an analytical approximative approach to quickly calculate the net present value (NPV) of exotic options, allowing for arbitrary fixing schedules and weighting factors, and incorporating the correlation between spot prices of distinct underlying assets, providing a 'closed form' solution for evaluating Average Spot Basket Options (ASpBO) on personal computers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo analysis is used to price basket options, then accuracy can be improved, but computation time increases significantly
Solution Approach 1:
The patent segments the complex basket option pricing problem into two separate analytical components: (1) pricing the basket option component and (2) pricing the average spot option component. By sequentially applying analytical approximations to each segment rather than using full Monte Carlo simulation, the method achieves comparable accuracy with dramatically reduced computation time, enabling near-real-time pricing.
Solution Approach 2:
The patent transforms the pricing approach by changing from numerical simulation parameters (Monte Carlo) to analytical approximation parameters (closed-form solutions). This parameter change allows the system to maintain pricing accuracy while reducing computation time from hours to seconds, as analytical solutions directly compute results without requiring numerous random sampling iterations.
2Productivity
If sequential application of analytical approximations is used, then computation time is reduced, but accuracy deteriorates due to neglecting correlation
Solution Approach 1:
The patent introduces correlation matrices as an intermediary element that captures the relationship between spot prices of distinct underlying assets at distinct instants. This intermediary structure allows the sequential analytical approximation method to account for correlations that would otherwise be neglected, thereby maintaining pricing accuracy while benefiting from the computational efficiency of the segmented analytical approach.
3Productivity
If standard analytical methods are used, then computation time is reduced, but they cannot handle arbitrary fixing schedules and weighting factors
Solution Approach 1:
The patent creates a universal analytical framework that can handle multiple types of basket options with different fixing schedules and weighting factors through a single integrated methodology. The system uses general matrix operations and iterative procedures that adapt to various contract specifications, making the analytical approach as versatile as Monte Carlo methods while maintaining computational efficiency.
Solution Approach 2:
The patent implements a dynamic iterative procedure that adjusts the pricing calculation based on the specific fixing schedule and weighting factors of each option contract. Rather than using fixed rigid formulas, the system dynamically modifies its calculation approach to accommodate arbitrary fixing schedules, allowing the analytical method to maintain both speed and adaptability.
Data Source
AI summary
Methods and systems of calculating a net present value (“NPV”) of an average spot basket option are provided. One method includes reading an evaluation date, contract data and market data associated with a basket, and calculating net present value of the average spot basket option by applying Black-Scholes theory to the sum of spot prices of the underlying assets of the basket, wherein the sum of spot prices of the underlying assets of the basket is represented as a single underlying asset. Another method includes calculating first and second moments of a sum of weighted spot price values of underlying assets of a basket and applying Black-Scholes theory using these moments to calculate NPV. Another method includes calculating a NPV according to a set of equations and displaying the calculated NPV. A system includes a memory and a processor that executes code to in accordance with the methods described herein.