[Quantlib-dev] Analytic Discrete Geometric Average Strike Asian Engine

[Kakhkhor A. <kab...@gm...>]

My average-price formula agrees with QuanLib, but my average-strike
formula doesn't.
When the dividend yield is zero, the QuanLib results agree with my own
implementation perfectly. When the dividend yield isn't zero, they
differ in 3rd digit.

Could it be that average-strike engine doesn't handle non-zero
dividend yield properly?

I coded up a special case.

(*) No past fixings.
(*) Two remaining fixings at dt and 2*dt (midpoint and maturity).
(*) Time step dt = 45/365 (i.e. 45 days).
(*) Set yield = rate - 0.5*volatility*volatility (for easy derivation).
(*) Use NullCalendar and ActualActual (calendar and day counter for
theoretical calculations).
(*) Set Settings::instance().evaluationDate() to the settlement date.

A simple code which implements the above special case is below. QL
example and the derivation of formula are in the attachments.

The spacial case code agrees with my general implementation. Could
someone compare it to QuantLib implementation.

Regards,
Kakhkhor Abdijalilov.

//-----------------------------------------------------------------------------------
// Special Case
// Analytic Discrete Geometric Average Strike Asian Option
//-----------------------------------------------------------------------------------
#include <iostream>
#include <boost/math/distributions/normal.hpp>

int main() {

    double spot = 22.0;
    double r = 0.1; // risk free rate
    double dt = 45.0/365.0; // time between fixings
    double v = 0.2; // volatility
    double yield = r - 0.5*v*v; // set dividend yeild

    std::cout << "Average-strike Call and Put prices:\n";
    double a = v*std::sqrt(dt);
    double s = spot*std::exp(a*a/2 - 2*r*dt);
    double x = std::exp(a*a/2);
    double y = std::exp(a*a/8);
    boost::math::normal_distribution<double> nd;
    double n1 = boost::math::cdf(nd,a);
    double n2 = boost::math::cdf(nd,a/2);
    double c = s*(x*n1 - y*n2); // call
    double p = s*(x*(n1-1) - y*(n2-1)); // put
    std::cout << c << '\t' << p << '\n';

}