Using SVI Volatility Surfaces to Estimate Option Greeks

Summary

The document explains how an empirically calibrated SVI volatility surface can support option pricing and Greek estimates. SVI maps maturity and strike to an implied volatility; that volatility can then be supplied to a Black–Scholes routine to obtain a price and its Greeks. The surface is useful for estimating values at strikes or maturities without a traded option, or for smoothing prices considered noisy by fitting across multiple options.

For a listed option with an observable market price, the response notes that implied volatility and Greeks can instead be derived from that price. It does not claim SVI Greeks are inherently more realistic than Black–Scholes Greeks: the result depends on the fitted surface and the option data, and the answer cautions that market prices are generally accurate. No calibration procedure, error comparison, or validation results are provided.

Key ideas

• An SVI surface maps strike and maturity to a fitted Black–Scholes implied volatility.
• That implied volatility can be used with Black–Scholes calculations to estimate option prices and Greeks.
• The surface can fill in estimates for strikes or maturities with no directly traded option.
• Fitting across several options may smooth a price believed to be noisy or distorted.
• The document gives no evidence that SVI-based estimates are generally more accurate than estimates from observed market prices.

Tags

# SVI model and Greeks calculation


# SVI model and Greeks calculation












The option pricing model I am referring to is this one:

- Arbitrage-free SVI volatility surfaces

I calibrated that model by using a set of European options, now I have a set of 5 parameters per maturity that allow to draw volatility skews.

As these curves can be used to price options, I am looking for the best way to get Greeks from that: is it possible to use SVI's output to have Greeks that are more accurate and "realistic" than Black & Scholes' ones?

## Answer by Alex C (score 5, accepted)

https://quant.stackexchange.com/a/29616

The SVI is simply a function (empirically fit to the data) which given a maturity and a strike price K, computes a BS implied volatility $\sigma$. Once you have that implied volatility you can plug it into a Black Scholes routine which can compute the BS price and the Black Scholes greeks.

Note that if an option is actually traded with that strike and maturity you could have directly observed the price, and computed the volatility and greeks directly from that.

So the SVI technique helps compute Greeks in 2 circumstances: (1) if there is no option traded for the strike and maturity you have in mind (you could call this a "what if" calculation of the greeks), (2) if you think the price of the option is somehow noisy or distorted, in which case the SVI based calculation might be more accurate because it is fit to multiple options, not just the one you are interested in. However IMHO the market prices of options are pretty accurate.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.