Interpolating Implied Volatility for Constant Maturity Analysis
Summary
The document discusses constructing a constant-maturity implied volatility measure, such as a 60-day curve, to compare volatility skew across market conditions. A simple starting method is to interpolate between the implied volatility curves for expirations that bracket the target maturity. The example approach assigns weights according to how close each expiration is to the target, with equal weighting when the target lies midway between two maturities.
The answers suggest viewing the task as fitting a volatility surface, which can then provide implied volatility for arbitrary strikes and expirations. Linear interpolation is presented as a basic option, with cautions around curved forward curves, out-of-the-money options, short-dated or seasonal contracts, and implausible implied forward volatility. The excerpt gives no empirical comparison of interpolation methods or detailed implementation recipe. Results may be unreliable when the surface is complex, so a constant-maturity series depends on the quality of the surface model and its inputs.
Key ideas
- Interpolate between expirations that bracket the target maturity to estimate constant-maturity implied volatility.
- Linear interpolation is a basic approach, with weights that depend on distance to the target maturity.
- A fitted volatility surface can provide estimates for arbitrary strikes and expirations.
- Curved forward curves and out-of-the-money options can make simple interpolation less reliable.
- Check that implied forward volatility remains positive and reasonable.
Tags
Full text
# Constant Maturity IV # Constant Maturity IV I want to analyze IV skew under various market conditions but its hard given various expirations. Would it make sense to create a constant maturity IV that say is 60 DTE? Has anyone done this and what are the limitations and things I should look out for? Additionally how do others calculate and compute it? the way I am doing it is really to takes the left and right most closest to expiration. So if I want 60 DTE and the market has only 30DTE and 90 DTE traded options I compute those two IV curves and average them giving them 0.5 weight each. The weight changes as I progress closer. Thanks, ## Answer by pyCthon (score 1) https://quant.stackexchange.com/a/25220 You use a form of interpolation(start with linear) between the 30 day to maturity IV and the 90 to get the 60, ## Answer by weismat (score 1) https://quant.stackexchange.com/a/25226 You could check at the methodology for VIX. The VIX itself yields one number - but you might instead return a set of numbers for your skew analysis. ## Answer by closedloop (score 1) https://quant.stackexchange.com/a/25236 What you are trying to do is fit a volatility surface for a given underlying. Once you have a volatility surface you can price an option for an arbitrary expiration and strike. There are numerous approaches to do this and the linear interpolation methods mentioned in the other examples are okay but be careful in the following situations where there is: - a steep or curved forward curve - you are pricing out of money options - interpolating short term options or highly seasonal options since the surface can be complicated. - finally watch that the implied forward Vols make sense (above 0 & have reasonable values). This is not guaranteed to be true with simple interpolation methods. As an aside: Please do not trade options if you don't understand forward volatility
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.