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pcaspers
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time interpolation in variance vs volatility

April 3rd, 2021, 6:12 pm

For equity and fx vol surfaces you'd generally prefer to interpolate linearly in [$]\sigma^2t[$] over [$]\sigma[$] (keeping the forward moneyness constant) to avoid calendar arbitrage. For swaption or caplet vol interpolation it's not so clear why [$]\sigma^2t[$] is the better choice, since the underlying changes with [$]t[$] and hence there is no arbitrage argument supporting the decision.

Are there other reasons why you'd still interpolate IR Vols in [$]\sigma^2t[$] rather than [$]\sigma[$]. And what do people / systems actually do? Always assuming you do not something completely different like interpolating SABR parameters. 
 
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Alan
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Re: time interpolation in variance vs volatility

April 9th, 2021, 2:02 pm

Not my area, but since no one has answered, one suggestion. Take some market data, holding out some observations. Interpolate with both methods to estimate the hold-outs and compare. If both results are within bid-ask spreads, there's an answer: it doesn't matter. 
 
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pcaspers
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Re: time interpolation in variance vs volatility

April 15th, 2021, 2:39 pm

Good idea, thanks Alan. I'll try that.
 
Mercadian
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Re: time interpolation in variance vs volatility

Yesterday, 5:51 pm

My 2 cents here... for Pricing I see mostly SABR parameters being interpolated rather than actual Vols, for Risk Management I see V2T or V in Moneyness as Nb Scenarios and Performance are a constraint.

This will all probably change once RFRs indices become more prevalent in Swaptions and Cap/Floors.

Bang's paper on SABR is a good read btw.

M