Volatility Surface

Live implied volatility surface from market options data. Crypto assets (BTC, ETH) use the Deribit volatility surface loader; equities (SPY, AAPL, NVDA) use the Yahoo Finance volatility surface loader.

The forwards are calibrated from put call parity and price the options directly. The quote and asset discount curves are then derived from the calibrated forwards: the asset curve is an interpolated curve through the implied discount factors, while the quote curve is kept at no discounting for crypto assets, whose inverse options settle without discounting, and fitted as an interpolated curve for equity assets.

Volatility Smile

The dots are the market implied volatilities of the bid and offer option quotes at each strike.

The solid lines are the fitted eSSVI model: each maturity has its own ATM total variance , curvature and correlation , calibrated slice by slice so the surface is free of static arbitrage by construction.

eSSVI Parameters

The calibrated parameter term structure at each maturity node. The curvature is shown in standard deviation units, , the ATM slope scale of the total standard deviation smile : unlike the raw , which grows mechanically with the total variance, it is comparable across maturities. The correlation tilts the smile (negative values produce the put skew); the ATM slope of the std dev smile is their product.

Volatility Term Structure

The dots are the market implied volatilities of the quotes closest to the money. The line is the fitted eSSVI ATM standard deviation , which should track the market points closely.

Forward Curve

Discount Curves