int main()
{ // All options are European
// Call option on a stock (b = r by default)
EuropeanOption callOption;
cout << "S: "; double S; cin >> S;
cout << "Option on a stock: " << callOption.Price(S) << endl;
// Option on a stock index
/* EuropeanOption indexOption;
indexOption.optType = "C";
indexOption.K = 50.0;
indexOption.T = 0.41667;
indexOption.r = 0.1;
indexOption.sig = 0.00;
double q = 0.0; // Dividend yield
indexOption.b = indexOption.r - q;
cout << indexOption.optType << " option on an index: " << indexOption.Price(50.0) << endl;
// Options on a future
EuropeanOption futureOption;
futureOption.optType = "P";
futureOption.K = 19.0;
futureOption.T = 0.75;
futureOption.r = 0.10;
futureOption.sig = 0.28;
futureOption.b = 0.0;
cout << "Put option on a future: " << futureOption.Price(20.0) << endl;
// Now change over to a call on the option
futureOption.toggle();
cout << "Call option on a future: " << futureOption.Price(20.0) << endl;
// Call option on currency
EuropeanOption currencyOption;
currencyOption.optType = "C";
currencyOption.K = 1.60;
currencyOption.T = 0.5;
currencyOption.r = 0.06;
currencyOption.sig = 0.12;
double rf = 0.08; // risk-free rate of foreign currency
currencyOption.b = currencyOption.r - rf;
cout << endl << "** Other pricing examples **" << endl << endl;
cout << "Call option on a currency: " << currencyOption.Price(1.56) << endl;
//////// NOW CALCULATIONS OF SENSITIVITIES //////////////////////////////////
// Call and put options on a future: Delta and Elasticity
EuropeanOption futureOption2;
futureOption2.optType = "P";
futureOption2.K = 100.0;
futureOption2.T = 0.5;
futureOption2.r = 0.10;
futureOption2.sig = 0.36;
futureOption2.b = 0.0;
cout << "Delta on a put future: " << futureOption2.Delta(105.0) << endl;
// Now change over to a call on the option
futureOption2.toggle();
cout << "Delta on a call future: " << futureOption2.Delta(105.0) << endl;
// Some more data for testing; Calcuate price and delta a
EuropeanOption stockOption;
stockOption.optType = "C";
stockOption.K = 60.0;
stockOption.T = 0.75;
stockOption.r = 0.10;
stockOption.sig = 0.30;
stockOption.b = stockOption.r;
stockOption.toggle();
// Calculating theta of a European stock index
EuropeanOption indexOption2;
indexOption2.optType = "P";
indexOption2.K = 405.0;
indexOption2.T = 0.0833; // One month expiration
indexOption2.r = 0.07;
indexOption2.sig = 0.20;
double divYield = 0.05; // Dividend yield, 5% per annum
indexOption2.b = indexOption2.r - divYield;
// Stock Option: Rho
EuropeanOption stockOption2;
stockOption2.optType = "C";
stockOption2.K = 75.0;
stockOption2.T = 1.0;
stockOption2.r = 0.09;
stockOption2.sig = 0.19;
stockOption2.b = stockOption2.r;
// Calculating Cost of Carry of a European stock index
EuropeanOption indexOption3;
indexOption3.optType = "P";
indexOption3.K = 490.0;
indexOption3.T = 0.222225;
indexOption3.r = 0.08;
indexOption3.sig = 0.15;
double divYield3 = 0.05; // Dividend yield, 5% per annum
indexOption3.b = indexOption3.r - divYield3 ;
*/
return 0;
}
//pricers
//
double PutOption::Price(const EuropeanOption &Opt) const
{
// black scholes
double tmp = Opt.sig_() * sqrt(Opt.T_());
double d1 = ( log(Opt.U_()/Opt.K_()) + (Opt.b_()+ (Opt.sig_()*Opt.sig_())*0.5 ) * Opt.T_() )/ tmp;
double d2 = d1 - tmp;
return (Opt.K_() * exp((-Opt.r_())*Opt.T_()) * N(-d2)) - (Opt.U_() * exp((Opt.b_()- Opt.r_()) * Opt.T_())* N(-d1));
}
void exercise2(void)
{
std::cout<<"Exercise 2"<<std::endl;
EuropeanOption option;
std::cout<<"Initial values:"<<std::endl;
option.print();
//(a)
std::cout<<"K in range [80,120] step 2:"<<std::endl;
double tempK = 80;
while (tempK<120.01)
{
std::cout<<"K = "<<tempK;
option.K=tempK;
std::cout<<";\tCall Price="<<option.Price();
option.toggle();
std::cout<<";\tPut Price="<<option.Price()<<std::endl;
tempK = tempK + 2;
}
option.K=100;
//(b)
std::cout<<"T in range [0.2,5] step 0.2:"<<std::endl;
double tempT= 0.2;
while (tempT<5.01)
{
std::cout<<"T = "<<tempT;
option.T=tempT;
std::cout<<";\tCall Price="<<option.Price();
option.toggle();
std::cout<<";\tPut Price="<<option.Price()<<std::endl;
tempT = tempT + 0.2;
}
option.T=1;
//(c)
std::cout<<"r in range [0, 0.2] step 0.01:"<<std::endl;
double tempr= 0;
while (tempr<0.2001)
{
std::cout<<"r = "<<tempr;
option.r=tempr;
std::cout<<";\tCall Price="<<option.Price();
option.toggle();
std::cout<<";\tPut Price="<<option.Price()<<std::endl;
tempr = tempr + 0.01;
}
option.r=0.05;
}