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Interpolation of a Implied Volatility Surface

May 19th, 2020, 4:18 am

Hi,

I have an Implied volatility surface. I was using cubic spline interpolation to estimate the volatility at the in between points. However, the volatility data I have is a bit extreme because of rare events like Brexit. This is why the cubic spline isn't working everytime as there are arbitrage opportunities created.

Can you suggest better interpolation techniques such as those probably used by banks to combat such real cases?
 
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Alan
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Re: Interpolation of a Implied Volatility Surface

May 19th, 2020, 4:06 pm

There is a nice method by Fengler 
Note the distinction between interpolating splines and smoothing splines.
 
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Cuchulainn
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Re: Interpolation of a Implied Volatility Surface

May 21st, 2020, 2:47 pm

Cubic splines overshoot for sparse data. This is well known.

http://finmod.co.za/Interpolation%20Summary.pdf

I reckon you need a monotonicity-preserving method.
 
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Cuchulainn
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Re: Interpolation of a Implied Volatility Surface

May 21st, 2020, 2:51 pm

There is a nice method by Fengler 
Note the distinction between interpolating splines and smoothing splines.
Is that link broke?
 
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Alan
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Re: Interpolation of a Implied Volatility Surface

May 21st, 2020, 7:37 pm

There is a nice method by Fengler 
Note the distinction between interpolating splines and smoothing splines.
Is that link broke?
Just tried it in Chrome -- loaded fine.
If not working for you, the title is "Arbitrage-Free Smoothing of the Implied Volatility Surface"
 
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Cuchulainn
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Re: Interpolation of a Implied Volatility Surface

May 24th, 2020, 1:49 pm

Seems to be working now.Thanks.
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