Skip to content
All library documents

Pricing an Option from a Sticky-Strike Implied Volatility Surface

Article Quant Q&A · Author: Tim
Read the original

Summary

The document asks how to use a fitted two-dimensional implied volatility surface to price an option at a later time. Its answer says that, under a sticky-strike assumption, the volatility associated with a given strike remains tied to that strike as time passes. In that setup, the surface can be queried at the target strike and at the reduced time to expiry to obtain the volatility input for pricing.

The example uses a cubic spline surface and adjusts the maturity to account for one minute passing. The response also corrects the placement of parentheses in the time adjustment. This guidance depends on the sticky-strike model assumption; it does not discuss alternative dynamics such as sticky moneyness, recalibration, changes in market conditions, or the option pricing formula itself. The document therefore explains a modeling choice for updating a surface lookup, rather than establishing that the assumption is appropriate in every market.

Key ideas

  • A two-dimensional volatility surface can provide volatility as a function of maturity and strike.
  • Under sticky strike, the volatility assigned to a strike does not change merely because moneyness changes.
  • As time passes, use the remaining time to expiry when querying the surface.
  • The lookup rule depends on the sticky-strike assumption and may not describe other volatility dynamics.

Tags

OptionsVolatilityDerivatives pricing
Full text
# pricing with implied volatility surface


# pricing with implied volatility surface












I am a newbee in Quantive finance.

supposing I calibrate a smoothing implied volatility surface with cubic spline now.

A minute later I want to price K=100,t=1 option, can I just find the point on the volatility surface which K=100 and t=(1-1/24*60*360)?

Many thanks.

## Answer by onlyvix.blogspot.com (score 0, accepted)

https://quant.stackexchange.com/a/22082

If you have 2-dimensional model (spline or otherwise) of vol surface vol = f(t,K), and assuming that vol is sticky-strike, that is changes in moneyness have no effect on strike vol, then you can use your function with K=100 and t=1-1/(24*60*360) - note the parenthesis.

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.