Implied Volatility Surface

Implied volatility represents the market's forecast of a likely movement in underlying assets price and is derived from the market price of an option. However, the Black-Scholes Model (BSM), which assumes constant volatility, often diverges from reality, leading to the phenomenon known as "volatility smile."

This occurs because various assumptions of the model, such as constant volatility and log-normal distribution of stock prices, do not perfectly align with real market behaviour, causing implied volatility to vary for options with different strike prices.

While the volatility smile highlights the imperfections of the BSM, its evaluation still provides useful insights. There is empirical evidence suggesting that the volatility surface, while varying across strike prices, remains relatively consistent over time. This consistency is indicative of the intrinsic characteristics specific to the underlying asset. It suggests that while the model may not perfectly capture market realities, the derived volatility surface can be a valuable tool for understanding and predicting market behaviour related to that particular asset.

CVEX Protocol's Volatility Surface

The CVEX Protocol assesses the volatility surface for each call and put option using an interpolation method. This method is based on predefined ratios of strike prices $C_j$ to futures prices $F$. This technique aligns with the Sticky Moneyness Hypothesis, which posits that the implied volatility of an option is more closely linked to its moneyness (the relationship futures and the strike prices) rather than its absolute price level. In essence, the hypothesis suggests that as the market moves, the implied volatility for options at a certain moneyness level tends to remain constant.

The CVEX Protocol updates its volatility surface in sync with the frequency of Futures Mark Price updates. During each update, the calculated implied volatility for each strike price contributes to the two closest predefined moneyness control points $(\frac {C_j} {F}, \sigma_j)$, weighted by their proximity.

Implied Volatility Calculation

Subsequently, these weighted sums of implied volatilities are averaged over a specified time window for each control point on the volatility surface, ensuring a dynamic and responsive adaptation to market changes. This process maintains the accuracy and relevance of the volatility surface, crucial for effective options pricing and risk management on the platform.

$$\sigma_j = \frac {\sum \sigma_i |ln(K_i) - ln(C_j)|} {\sum |ln(K_i) - ln(C_j)|}$$

Solving the Black-Scholes equation for volatility isn't feasible with algebraic methods alone. The CVEX Protocol employs the Newton-Raphson method, a numerical approach, to determine current implied volatility based on the option's premium price, strike price, and other relevant parameters.