Posted by
MH_quant on
URL: http://quantlib.414.s1.nabble.com/LocalvolSurface-cpp-tp12806p12818.html
Hallo Nando,
-----Original Message-----
On Mon, Apr 27, 2009 at 11:20 AM, Michael Heckl <
[hidden email]>
wrote:
> I set up a constant extrapolation for both, Strike and
> Maturity in my BlackVarianceSurface.
I don't work on equities but constant variance extrapolation in strike
and maturity seems plain wrong to me. In time it implies zero forward
volatility, in strike it violates concavity smile requirement
ciao -- Nando
--------------------------
What is done with the time extrapolation is the following:
if (t<=times_.back())
return varianceSurface_(t, strike, true);
else // t>times_.back() || extrapolate
return varianceSurface_(times_.back(), strike, true) *
t/times_.back();
I.e. the implied variance surface is not extrapolated constant in time, but
the implied volatility surface.
What exactly do you mean by zero forward volatility. IMHO the forward
volatility would be in that case (between two dates past at extrapolation)
exactly the constant extrapolated volatility (analog as with interest rates
for instance).
And at Strikes past the maximum/minimum Strike the implied variance surface
is indeed extrapolated flat, i.e.
// enforce constant extrapolation when required
if (strike < strikes_.front()
&& lowerExtrapolation_ == ConstantExtrapolation)
strike = strikes_.front();
if (strike > strikes_.back()
&& upperExtrapolation_ == ConstantExtrapolation)
strike = strikes_.back();
Well, I don't know what you mean with your concavity smile requirement. But
I cant see what the problem should be with this extrapolation?
If you look at the No-Arbitrage requirements for the implied volatility
surface they only give limites to the slope.
But constant extrapolation means zero slope. So I cant see any restrictions
to that.
You can find no-arbitrage restrictions for the implied volatility for
instance at Roger W. Lee ("Implied Volatility: Statics, Dynamics, and
Probabalistic Interpretation")
The paper is online here:
http://www.math.uchicago.edu/~rl/Can you send me a paper which works out the arguments you stated?
Greetings,
Michael
------------------------------------------------------------------------------
Register Now & Save for Velocity, the Web Performance & Operations
Conference from O'Reilly Media. Velocity features a full day of
expert-led, hands-on workshops and two days of sessions from industry
leaders in dedicated Performance & Operations tracks. Use code vel09scf
and Save an extra 15% before 5/3.
http://p.sf.net/sfu/velocityconf_______________________________________________
QuantLib-dev mailing list
[hidden email]
https://lists.sourceforge.net/lists/listinfo/quantlib-dev