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yondaime
Topic Author
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Joined: May 18th, 2020, 8:46 pm

### Interpolation of a Implied Volatility Surface

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?

Alan
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Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: Interpolation of a Implied Volatility Surface

There is a nice method by
Note the distinction between interpolating splines and smoothing splines.

Cuchulainn
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Joined: July 16th, 2004, 7:38 am
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### Re: Interpolation of a Implied Volatility Surface

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.

Cuchulainn
Posts: 62122
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Interpolation of a Implied Volatility Surface

There is a nice method by
Note the distinction between interpolating splines and smoothing splines.
Is that link broke?

Alan
Posts: 10167
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Interpolation of a Implied Volatility Surface

There is a nice method by
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"

Cuchulainn
Posts: 62122
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Interpolation of a Implied Volatility Surface

Seems to be working now.Thanks.