Improving Binomial Tree Option Pricing: Estimating Volatility via Linear Regression

Abstract

The binomial tree option pricing model, proposed by Cox, Ross and Rubinstein, is widely used due to its intuitive discrete-time structure and flexibility in handling various option types. However, the traditional model often assumes constant volatility, which deviates from actual market conditions. This paper proposes an improvement to relax the constant volatility assumption. Specifically, the study first reviews the basic knowledge of the binomial tree model and transforms it into a semi-parametric model. Unlike traditional methods that assume constant volatility, the author employs linear regression to estimate volatility from real option market data. Under the risk-neutral pricing principle, the fitted volatility is embedded into each node of the binomial tree, allowing the model to reflect marketimplied volatility characteristics. Using SSE 50 ETF call option data as the sample, empirical analysis shows that the proposed semi-parametric model significantly reduces pricing errors compared to the traditional binomial tree model. These results indicate that incorporating market implied volatility through information regression enhances the practicality of the binomial tree model. Future research could extend this approach to more complex volatility structures or other types of options and underlying assets.