Stock Option Pricing Using Conditional Probability Volatility
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional stock option pricing models, such as the Black-Scholes model, tend to overstate option values due to inaccuracies in volatility estimation and the use of historical investment return data as independent events, failing to account for the dynamic interaction of risk-free and long-term equity-based rates of return.
Innovation Solution
A new theoretical framework that views historical market performance as a single long-term event with periodic observations, employing conditional probability methods and additional parameters like expected long-term rates of return and volatility, to provide a more accurate forecast of stock option prices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Black-Scholes model is used for stock option pricing, then the model is simple and widely accepted, but the model overstates option values due to inaccurate volatility estimation and treating historical returns as independent events
Solution Approach 1:
The patent changes the volatility parameter from a constant to a time-dependent parameter that evolves according to a mean-reverting process. This allows the model to capture the dynamic nature of volatility while maintaining analytical tractability through the use of closed-form solutions that incorporate the time-varying volatility structure.
Solution Approach 2:
The patent introduces dynamics into the volatility parameter by modeling it as a stochastic process that reverts to a long-term mean. This dynamic approach allows volatility to adapt to current market conditions while being anchored to historical averages, resolving the contradiction between model simplicity and valuation accuracy.
2Ease of operation
If historical investment return data is treated as independent events in the Black-Scholes model, then the model is mathematically tractable, but it fails to account for the dynamic interaction of risk-free and long-term equity-based rates of return
Solution Approach 1:
The patent introduces dynamics into the volatility parameter by modeling it as a stochastic process that reverts to a long-term mean. This dynamic approach allows volatility to adapt to current market conditions while being anchored to historical averages, resolving the contradiction between model simplicity and valuation accuracy.
Solution Approach 2:
The patent incorporates feedback mechanisms through the mean-reverting volatility process, where current volatility levels influence future volatility through a systematic feedback loop. This allows the model to account for the interdependence of returns while maintaining mathematical tractability through closed-form solutions.
3Ease of manufacture
If the Black-Scholes model uses constant volatility, then the model is simple to implement, but it does not capture the time-varying nature of market volatility
Solution Approach 1:
The patent changes the volatility parameter from a constant to a time-dependent parameter that evolves according to a mean-reverting process. This allows the model to capture the dynamic nature of volatility while maintaining analytical tractability through the use of closed-form solutions that incorporate the time-varying volatility structure.
Data Source
AI summary
A method, system, and computer program product for determining stock option pricing in which the interplay of short-term interest rates and expected long-term rates of return on the underlying security results are factored to yield a more accurate forecast of options prices as compared to conventional models. The method of the present invention employs an expected long-term rate of return parameter and a conditional probability volatility parameter and an adjustment factor to address the put-call parity theorem which addresses the accuracy problems of the Black-Scholes model. The method can also be applied using a known current option prices to determine an assumed long-term rate of return.