Volatility Surface Explorer

Understanding the Volatility Surface

The volatility surface represents how implied volatility varies with both strike price and time to expiration. It's a crucial concept in options pricing and risk management.

Key Components:

• Volatility Smile/Skew: The pattern where implied volatility changes with strike price
• Term Structure: How implied volatility changes with time to expiration
• Volatility Surface: The 3D combination of smile/skew and term structure

Common Patterns:

• Smile: Higher volatility for both low and high strikes
• Skew: Higher volatility for low strikes (common in equity markets)
• Smirk: Combination of skew and smile

The volatility surface is typically modeled using stochastic volatility models like SABR or local volatility models like Dupire's equation.

SABR Model Formula (simplified):

σ(K,F) ≈ α / (F^(1-β)) * [1 + (1-β)^2/24 * ln^2(F/K) + (1-β)^4/1920 * ln^4(F/K)] * (z / x(z))

Where:

• σ = implied volatility
• K = strike price
• F = forward price
• α = initial volatility level
• β = skew parameter