analysis of the relationships between vix options and underlying index options

This paper studies the relationship between vix options and their corresponding underlying index options to determine the necessary conditions for eliminating arbitrage opportunities within the framework of financial mathematics. employing the heston model and taylor series analysis, uncovered analytical relationships among various parameters governing market instruments. one key finding is that, by assuming a specific model for the density function, the price of the underlying asset can be predicted based on the available vix option strike prices in the market. this research contributes to the theoretical foundations of option pricing models and provides practical insights for risk management and derivative pricing strategies in financial markets.