American implied vol with fractional days

[Chris Pernoud]

Hi,

I've been struggling to recreate an old functionality in the new version
0.9.7.  In an old post from 2002, an American implied volatility could
be solved with the maturity argument in floating-point years.  All
recent examples I've seen use a specific evaluation date and maturity
date with no concept of fractional days.  This functionality is valuable
for near-maturity options when time-of-day matters.

I don't need any dividends, so I'm just using the BlackProcess right now.

Any help would be appreciated, thanks in advance.  Below is a copy of
the old post (See maturity=.25 for 3 months):


At 02:43 PM 2/26/02 -0600, Vadim Ogranovich wrote:
 >Before I go and read the source code I wonder
 >if someone can save me time and tell how easy/difficult it is with
QuantLib
 >to compute implied volatility of an American option on a divident paying
 >stock (either cash or stock).
Below I give you an example with continuous dividends. The class
FdDividendAmericanOption handle discrete dividends

hope this helps

ciao -- Nando

==============================

#include <ql/quantlib.hpp>

using namespace QuantLib;

using QuantLib::Pricers::FdAmericanOption;


int main(int argc, char* argv[])
{
try {
// our option
double underlying = 102;
double strike = 100; // at the money
Spread dividendYield = 0.03; // no dividends
Rate riskFreeRate = 0.05; // 5%
Time maturity = 0.25; // 3 months
double volatility = 0.20; // 20%
std::cout << "Time to maturity = " << maturity
<< std::endl;
std::cout << "Underlying price = " << underlying
<< std::endl;
std::cout << "Strike = " << strike
<< std::endl;
std::cout << "Risk-free interest rate = " << riskFreeRate
<< std::endl;
std::cout << "Volatility = " << volatility
<< std::endl;
std::cout << std::endl;


Size timeSteps=100, assetSteps = 20;
FdAmericanOption myAmericanOption(Option::Call, underlying, strike,
dividendYield, riskFreeRate, maturity, volatility, timeSteps,
assetSteps);
double value = myAmericanOption.value();
std::cout
<< "vol " << DoubleFormatter::toString(volatility, 6)
<< " value " << DoubleFormatter::toString(value, 6)
<< std::endl;

double impliedVol = myAmericanOption.impliedVolatility(value*1.1);
std::cout
<< "a value of " << DoubleFormatter::toString(value*1.1, 6)
<< " implies a vol " << DoubleFormatter::toString(impliedVol, 6)
<< std::endl;


return 0;
} catch (std::exception& e) {
std::cout << e.what() << std::endl;
return 1;
} catch (...) {
std::cout << "unknown error" << std::endl;
return 1;
}
}

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