Choosing Expiry Interpolation for Caplet and Floorlet Volatility Surfaces

Summary

The document considers how to interpolate implied volatility across expiry when bootstrapping a caplet or floorlet surface from cap and floor quotes on a fixed strike grid. It compares a left-continuous rule with linear interpolation. The author observes that left-continuous interpolation appears to preserve smoother smiles at quoted expiries, while linear interpolation can look spikier. However, the left-continuous choice can create jumps in theta when a portfolio cap’s schedule aligns with one used in the surface bootstrap, leading the author to favor linear interpolation as a simple starting point.

The post also asks whether linear interpolation of variance is preferable to linear interpolation of implied caplet volatility. It notes that different caplets have different underlying rates, so the author sees no direct calendar-arbitrage issue from that feature. No answer, quantitative comparison, or validation is included, and more elaborate approaches such as interpolating SABR parameters are mentioned but set aside. The trade-off is therefore exploratory: the document identifies potential smoothness and theta concerns without establishing which interpolation method performs best in practice.

Key ideas

• Left-continuous expiry interpolation may produce smoother-looking smiles at quoted cap expiries.
• Linear expiry interpolation is considered as a way to avoid theta jumps tied to matching cap schedules.
• The post raises, but does not resolve, whether interpolating variance is preferable to interpolating implied volatility.
• Interpolation choices are presented as a simple starting point rather than a validated method.

Tags

# Which expiry interpolation method for caplet/floorlet surfaces?


# Which expiry interpolation method for caplet/floorlet surfaces?












I want to bootstrap an (implied volatility) caplet/floorlet surface from quoted cap/floor volatilities on a fixed strike grid. I'm thinking about either using a left-continuous or a linear interpolation in expiry dimension. If one just looks at the smiles of each quoted cap expiry left-continuous (1st picture) seems to be preferable as the linear smiles (2nd picture) are more spiky. However, a left-continuous interpolation will produce theta jumps. The jump always happens for a (standard) cap in the portfolio on the day when it's schedule aligns with schedule of the caps used to bootstrap the surface.

Therefore, out of these 2 candidates, I would go for the linear expiry interpolation. Does anybody have an opinion on that?

How about linear interpolation in variance. As each caplet has a different underlying rate, there is no direct problem with calendar arbitrage. Is linear interpolation in variance nevertheless the better choice than linear interpolation in implied caplet volatility?

Thanks, Bernd

p.s.: I know that there are more fancy interpolation methods out there (e.g. using SABR smiles with interpolation on the SABR parameters) but I want to go for a simple interpolation as a starting point

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