Question about Black Formula results

[Benjamin Janson]

Hi,

just to get a feel for the QuandLib I tried to implement a simple call
option with the Black formula. But the results won't make sense to me.

underlying         = 42.5;
vola               = 0.2390;
discount_factor    = 0.99;
strike_price       = 42.5;
settlementDate(8, December, 2005);

Results are:
Black Value: 8.12504
Black Delta: 0.590589
Black Gamma: 0.0184494
Black Vega: 10.1256
Black Rho: 6.55746


First, the option value seems to be too high. I excepted it to be somewhere
aroung 4.70 - 4.90. Second the delta should be pretty exactly 0.5?? Third
isn't it necessary to pass the maturity as an argument to calculate the
black value??

I guess I am using it wrong or something. Any help is appreciated.

Thanks a lot in advance for your help.

Cheers,

Benjamin
------------------------
Here is the code I used:
#include <cstdlib>
#include <string>
#include <stdexcept>
#include <iostream>
#include <ql/quantlib.hpp>

using namespace QuantLib;

int main(int argc, char *argv[])
{
    try
    {
       QL_IO_INIT
             
        Real underlying         = 42.5;
        Real vola               = 0.2390;
        Real discount_factor    = 0.99;
        Real strike_price       = 42.5;
        Date todaysDate(20, July, 2005);
        Settings::instance().evaluationDate() = todaysDate;

        Date settlementDate(8, December, 2005);
        DayCounter dayCounter = Actual365Fixed();
        Time maturity = dayCounter.yearFraction(todaysDate, settlementDate);

   
        Option::Type option_type(Option::Call);
        boost::shared_ptr<StrikedTypePayoff> payoff(
                                             new
PlainVanillaPayoff(option_type,
                                             strike_price));
                                             
        BlackFormula Black(underlying, discount_factor, vola, payoff);
       
        std::cout << "Black Value: " << Black.value() << std::endl;
        std::cout << "Black Delta: " << Black.delta(underlying) <<
std::endl;
        std::cout << "Black Gamma: " << Black.gamma(underlying) <<
std::endl;
        std::cout << "Black Vega: " << Black.vega(maturity) << std::endl;
        std::cout << "Black Rho: " << Black.rho(maturity) << std::endl;
                 
        std::cout <<  std::endl;
        std::cout <<  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;
     }
}
-------------------------

[David Palmer-2]

Discount factor seems high. If it is, then the drift of the asset price
due to an increased rate will imply a higher delta.

-----Original Message-----
From: [hidden email]
[mailto:[hidden email]] On Behalf Of
Benjamin Janson
Sent: Tuesday, July 26, 2005 2:21 AM
To: [hidden email]
Subject: [Quantlib-users] Question about Black Formula results

Hi,

just to get a feel for the QuandLib I tried to implement a simple call
option with the Black formula. But the results won't make sense to me.

underlying         = 42.5;
vola               = 0.2390;
discount_factor    = 0.99;
strike_price       = 42.5;
settlementDate(8, December, 2005);

Results are:
Black Value: 8.12504
Black Delta: 0.590589
Black Gamma: 0.0184494
Black Vega: 10.1256
Black Rho: 6.55746


First, the option value seems to be too high. I excepted it to be
somewhere aroung 4.70 - 4.90. Second the delta should be pretty exactly
0.5?? Third isn't it necessary to pass the maturity as an argument to
calculate the black value??

I guess I am using it wrong or something. Any help is appreciated.

Thanks a lot in advance for your help.

Cheers,

Benjamin
------------------------
Here is the code I used:
#include <cstdlib>
#include <string>
#include <stdexcept>
#include <iostream>
#include <ql/quantlib.hpp>

using namespace QuantLib;

int main(int argc, char *argv[])
{
    try
    {
       QL_IO_INIT
             
        Real underlying         = 42.5;
        Real vola               = 0.2390;
        Real discount_factor    = 0.99;
        Real strike_price       = 42.5;
        Date todaysDate(20, July, 2005);
        Settings::instance().evaluationDate() = todaysDate;

        Date settlementDate(8, December, 2005);
        DayCounter dayCounter = Actual365Fixed();
        Time maturity = dayCounter.yearFraction(todaysDate,
settlementDate);

   
        Option::Type option_type(Option::Call);
        boost::shared_ptr<StrikedTypePayoff> payoff(
                                             new
PlainVanillaPayoff(option_type,
                                             strike_price));
                                             
        BlackFormula Black(underlying, discount_factor, vola, payoff);
       
        std::cout << "Black Value: " << Black.value() << std::endl;
        std::cout << "Black Delta: " << Black.delta(underlying) <<
std::endl;
        std::cout << "Black Gamma: " << Black.gamma(underlying) <<
std::endl;
        std::cout << "Black Vega: " << Black.vega(maturity) <<
std::endl;
        std::cout << "Black Rho: " << Black.rho(maturity) << std::endl;
                 
        std::cout <<  std::endl;
        std::cout <<  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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[Luigi Ballabio]

Benjamin Janson wrote:
>
> just to get a feel for the QuandLib I tried to implement a simple  
> call option with the Black formula. But the results won't make sense  
> to me.

Benjamin,
        the signature of the BlackFormula constructor is:

BlackFormula(Real forward,
              DiscountFactor discount,
              Real variance,
              const boost::shared_ptr<StrikedTypePayoff>& payoff);

You should pass as the first argument the forward price, and as the  
third argument its variance (that's where the maturity comes in.)

In your code, you should replace:

BlackFormula Black(underlying, discount_factor, vola, payoff);

with:

Real forward = underlying/discount_factor;
Real variance = vola*vola*maturity;

BlackFormula Black(forward, discount_factor, variance, payoff);

to use the class as intended.

This said, the results are still now what you expect---namely, I get:

Black Value: 2.72193
Black Delta: 0.556433
Black Gamma: 0.0625584
Black Vega: 10.4325
Black Rho: 8.08392

but the above are consistent with the results on a few other  
calculators I checked them against. Maybe there's something else  
missing? For instance, did your estimate include any cost of carry?

Later,
        Luigi


----------------------------------------

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         than done.