Volatility surface interpolation/extrapolation

[Ferghil O'Rourke]

Does anyone know if I can use QuantLib to interpolate or extrapolate

from given volatilities to a target volatility? I want to price a European

Option using a volatility derived from Listed American Options. To do

this I’m using QuantLib to back-out the implied volatilities from the

4 “nearest” listed options to the target Date and Strike of the European

option I want to price (using DividendVanillaOption).

 

Once I have those 4 volatilities I’m manually interpolating from them to

a reasonable volatility to price my target European Option. This seems

to work ok, but now I need to also price European Options that are

way beyond data available on the listed market (36 month “leaps”).

To do this I’ve been told I can straight-line extrapolation from the

latest data available to the target volatility.

 

Anyone know if QuantLib can help me out with this extrapolation?

Or anyone know any easy straight-line extrapolation algorithms?

 

Thanks for any pointers,

Ferghil O’Rourke

[Ferdinando M. Ametrano-3]

> Does anyone know if I can use QuantLib to interpolate or extrapolate
> from given volatilities to a target volatility?
I wouldn't use any QuantLib out-of-the-box class for extrapolating
volatilities. Interpolating it's easier, but still I would recheck
what is available.

Latest time I worked on these issues I wasn't happy about the code I
wrote, and as of today I know I wouldn't use my old QuantLib code.

> I want to price a European
> Option using a volatility derived from Listed American Options. To do
> this I'm using QuantLib to back-out the implied volatilities from the
> 4 "nearest" listed options to the target Date and Strike of the European
> option I want to price (using DividendVanillaOption).
> Once I have those 4 volatilities I'm manually interpolating from them
ok. I would pay attention to interpolate variances instead of
volatility, and you might consider interpolating along the strike
direction using log-moneyness, and along the time direction in a
strictly increasing monotone way (monotone convex spline or at least
linear)

> I need to also price European Options that are
> way beyond data available on the listed market (36 month "leaps").
you mean that you would extrapolate in time, not in strike?
Extrapolation in time its relatively easier, extrapolation in strike
is quite problematic.

> Anyone know if QuantLib can help me out with this extrapolation?
> Or anyone know any easy straight-line extrapolation algorithms?
QuantLib has many interpolation/extrapolation algorithms, but it won't
help you if you to use them without being fully aware of the financial
meaning of your extrapolation procedure, especially if you have strike
dependence (i.e. smile)

sorry for being more on the warning side than the help side

ciao -- Nando