new faster method to price American option with discrete dividends

[Xavier.Abulker]

Hello Quantlib,

I've added the Roll, Geske, Whaley method to price American Call with
discrete dividends like it is discribed in Hull 4th P271.
I've added new things:

RGWAmericanOption is the new class
cumulativebinormaldistribution(x,y,rho) is the cumulative binormal
distribution.
impliedCriticalStock is used to find the critical stock value S : c(S) = S
+ D1 - X.

In term of performance it looks like it really improves the Binonial
method.
It took me 195 seconds to price 2 000 American Options with discrete
dividends with the fddividend class,
now it takes  20 seconds to price the same 100 000 American Options with
discrete dividends.

this is how I use it:

double underlyingPrice =4000;
double strike =4000;
vector<Time> divdate;
vector<double> divamount;
divdate.push_back(0.16);
divdate.push_back(0.41);
divamount.push_back(50);
divamount.push_back(50);
Time maturity =0.5;

RGWAmericanOption
Europeanoptioniv2(Option::Call,underlyingPrice,strike,dividend,zero_rate,maturity,implvol,divamount,divdate,4331);
// the 4331 has no effect here
double criticalstrike=Europeanoptioniv2.impliedCriticalStock(4000); //
retreive the critical stock value the  4000 is the strike value
RGWAmericanOption
Europeanoptioniv3(Option::Call,underlyingPrice,strike,dividend,zero_rate,maturity,implvol,divamount,divdate,criticalstrike);
std::cout<<"American option value "<<Europeanoptioniv3.value()<<std::endl;
std::cout<<"Implied Vol value "
<<Europeanoptioniv3.impliedVolatility(327.68)<<std::endl;


Is there a good soul who would like to help me to debug it and check the
way I developped that?

Also, I have a problem with American Put options. I don' know how to apply
the Roll Geske Whaley formula.
It looks like with a critical stock price very small (e.g 1), the pricing
is not too bad but I don't know if there's something better to do.
Here, I'm just using a standard European option Pricer if I understand
correclty.

Quantlib Admin: is it something you could add in a next release please?
Thanks

Xavier

(See attached file: quantlib.hpp)(See attached file: singleassetoption.hpp)
(See attached file: rgwamericanoption.hpp)(See attached file:
singleassetoption.cpp)(See attached file: rgwamericanoption.cpp)



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[Luigi Ballabio-2]

At 2:17 PM +0100 10/31/02, [hidden email] wrote:
>I've added the Roll, Geske, Whaley method to price American Call with
>discrete dividends like it is discribed in Hull 4th P271.

Hi Xavier,
        great. I'll have a look at it.

>Quantlib Admin: is it something you could add in a next release please?

Sure.


Xavier: I had to tame QuantLib in order to deploy it to a customer of
ours which uses Solaris. After applying a few patches, it seems like
it works with gcc now. Can you check it? If you get the current CVS
version and run:

./solaris.setup
./bootstrap
./configure
make
make check

it should compile and pass the tests.

Thanks,
        Luigi