Volatility Estimation Using High-Low Price Data
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Solution Overview
Problem
Traditional volatility-based futures products are susceptible to bias and inefficiency due to drift, stochastic volatility, and pricing gaps, particularly in standard deviation calculations that rely on closing prices, which fail to accurately reflect market volatility.
Innovation Solution
Implementing a system that uses various volatility estimation techniques, such as the Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang estimators, which incorporate high, low, and open prices to calculate market volatility, thereby compensating for pricing gaps and drift, and determining a cash settlement price for futures contracts based on these calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard deviation calculations relying on closing prices are used to determine volatility, then the calculation method is simple, but the measurement accuracy is poor due to drift, stochastic volatility, and pricing gaps
Solution Approach 1:
The patent changes the parameters used for volatility calculation from only closing prices to multiple price points including high, low, open, and closing prices. This parameter expansion allows the use of advanced estimators (Parkinson, Garman-Klass, Rogers-Satchell, Yang-Zhang) that incorporate additional price dimensions to capture drift, stochastic volatility, and pricing gaps, thereby improving measurement accuracy while accepting increased computational complexity
Solution Approach 2:
The patent transitions from one-dimensional closing price data to multi-dimensional price data by incorporating high, low, open, and close prices. This dimensional expansion enables the application of sophisticated volatility estimators that utilize the additional price dimensions to correct for market inefficiencies and provide more accurate volatility measurements
2Reliability
If closing prices only are used for volatility calculation, then the data requirement is minimal, but the reflection of true market conditions is insufficient
Solution Approach 1:
The patent makes the pricing data multi-functional by using high, low, open, and close prices for multiple purposes: capturing intraday volatility, accounting for drift through open-close comparisons, identifying pricing gaps, and providing comprehensive market condition reflection. Each price point serves multiple analytical functions that collectively improve reliability
3Measurement precision
If traditional volatility estimators are used, then the computational simplicity is maintained, but the bias and inefficiency increase
Solution Approach 1:
The patent applies preliminary corrections to the volatility estimation process by using advanced estimators that pre-adjust for known biases such as drift and pricing gaps. The Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang estimators incorporate preliminary correction factors based on multiple price points, reducing systematic errors before final volatility calculation
Data Source
AI summary
A method of providing a financial product may include obtaining, by a computer device, pricing information about a financial market over a specified duration, the pricing information including at least a high price and a low price occurring within the duration. The computer device may be configured for determining a volatility associated with the market, the volatility based, at least in part, on the pricing information and determining a settlement price for a cash settled futures product using the volatility of the market over the specified duration.