public void visit(AssetOrNothingPayoff payoff)
{
black_.beta_ = black_.DbetaDd2_ = 0.0;
switch (payoff.optionType())
{
case Option.Type.Call:
black_.alpha_ = black_.cum_d1_;
black_.DalphaDd1_ = black_.n_d1_;
break;
case Option.Type.Put:
black_.alpha_ = 1.0 - black_.cum_d1_;
black_.DalphaDd1_ = -black_.n_d1_;
break;
default:
Utils.QL_FAIL("invalid option type");
break;
}
}
public AmericanPayoffAtHit(double spot, double discount, double dividendDiscount, double variance, StrikedTypePayoff payoff)
{
spot_ = spot;
discount_ = discount;
dividendDiscount_ = dividendDiscount;
variance_ = variance;
Utils.QL_REQUIRE(spot_ > 0.0, () => "positive spot value required");
Utils.QL_REQUIRE(discount_ > 0.0, () => "positive discount required");
Utils.QL_REQUIRE(dividendDiscount_ > 0.0, () => "positive dividend discount required");
Utils.QL_REQUIRE(variance_ >= 0.0, () => "negative variance not allowed");
stdDev_ = Math.Sqrt(variance_);
Option.Type type = payoff.optionType();
strike_ = payoff.strike();
log_H_S_ = Math.Log(strike_ / spot_);
double n_d1;
double n_d2;
double cum_d1_;
double cum_d2_;
if (variance_ >= Const.QL_EPSILON)
{
if (discount_.IsEqual(0.0) && dividendDiscount_.IsEqual(0.0))
{
mu_ = -0.5;
lambda_ = 0.5;
}
else if (discount_.IsEqual(0.0))
{
Utils.QL_FAIL("null discount not handled yet");
}
else
{
mu_ = Math.Log(dividendDiscount_ / discount_) / variance_ - 0.5;
lambda_ = Math.Sqrt(mu_ * mu_ - 2.0 * Math.Log(discount_) / variance_);
}
D1_ = log_H_S_ / stdDev_ + lambda_ * stdDev_;
D2_ = D1_ - 2.0 * lambda_ * stdDev_;
CumulativeNormalDistribution f = new CumulativeNormalDistribution();
cum_d1_ = f.value(D1_);
cum_d2_ = f.value(D2_);
n_d1 = f.derivative(D1_);
n_d2 = f.derivative(D2_);
}
else
{
// not tested yet
mu_ = Math.Log(dividendDiscount_ / discount_) / variance_ - 0.5;
lambda_ = Math.Sqrt(mu_ * mu_ - 2.0 * Math.Log(discount_) / variance_);
if (log_H_S_ > 0)
{
cum_d1_ = 1.0;
cum_d2_ = 1.0;
}
else
{
cum_d1_ = 0.0;
cum_d2_ = 0.0;
}
n_d1 = 0.0;
n_d2 = 0.0;
}
switch (type)
{
// up-and-in cash-(at-hit)-or-nothing option
// a.k.a. american call with cash-or-nothing payoff
case Option.Type.Call:
if (strike_ > spot_)
{
alpha_ = 1.0 - cum_d1_; // N(-d1)
DalphaDd1_ = -n_d1; // -n( d1)
beta_ = 1.0 - cum_d2_; // N(-d2)
DbetaDd2_ = -n_d2; // -n( d2)
}
else
{
alpha_ = 0.5;
DalphaDd1_ = 0.0;
beta_ = 0.5;
DbetaDd2_ = 0.0;
}
break;
// down-and-in cash-(at-hit)-or-nothing option
// a.k.a. american put with cash-or-nothing payoff
case Option.Type.Put:
if (strike_ < spot_)
{
alpha_ = cum_d1_; // N(d1)
DalphaDd1_ = n_d1; // n(d1)
beta_ = cum_d2_; // N(d2)
DbetaDd2_ = n_d2; // n(d2)
}
else
{
alpha_ = 0.5;
DalphaDd1_ = 0.0;
beta_ = 0.5;
DbetaDd2_ = 0.0;
}
break;
default:
Utils.QL_FAIL("invalid option type");
break;
}
muPlusLambda_ = mu_ + lambda_;
muMinusLambda_ = mu_ - lambda_;
inTheMoney_ = (type == Option.Type.Call && strike_ < spot_) || (type == Option.Type.Put && strike_ > spot_);
if (inTheMoney_)
{
forward_ = 1.0;
X_ = 1.0;
}
else
{
forward_ = Math.Pow(strike_ / spot_, muPlusLambda_);
X_ = Math.Pow(strike_ / spot_, muMinusLambda_);
}
// Binary Cash-Or-Nothing payoff?
CashOrNothingPayoff coo = payoff as CashOrNothingPayoff;
if (coo != null)
{
K_ = coo.cashPayoff();
}
// Binary Asset-Or-Nothing payoff?
AssetOrNothingPayoff aoo = payoff as AssetOrNothingPayoff;
if (aoo != null)
{
if (inTheMoney_)
{
K_ = spot_;
}
else
{
K_ = aoo.strike();
}
}
}
public double payoffAtExpiry(double spot, double variance, double discount)
{
double dividendDiscount = process_.dividendYield().link.discount(exercise_.lastDate());
Utils.QL_REQUIRE(spot > 0.0, () => "positive spot value required");
Utils.QL_REQUIRE(discount > 0.0, () => "positive discount required");
Utils.QL_REQUIRE(dividendDiscount > 0.0, () => "positive dividend discount required");
Utils.QL_REQUIRE(variance >= 0.0, () => "negative variance not allowed");
Option.Type type = payoff_.optionType();
double strike = payoff_.strike();
double? barrier = arguments_.barrier;
Utils.QL_REQUIRE(barrier > 0.0, () => "positive barrier value required");
Barrier.Type barrierType = arguments_.barrierType;
double stdDev = Math.Sqrt(variance);
double mu = Math.Log(dividendDiscount / discount) / variance - 0.5;
double K = 0;
// binary cash-or-nothing payoff?
CashOrNothingPayoff coo = payoff_ as CashOrNothingPayoff;
if (coo != null)
{
K = coo.cashPayoff();
}
// binary asset-or-nothing payoff?
AssetOrNothingPayoff aoo = payoff_ as AssetOrNothingPayoff;
if (aoo != null)
{
mu += 1.0;
K = spot * dividendDiscount / discount; // forward
}
double log_S_X = Math.Log(spot / strike);
double log_S_H = Math.Log(spot / barrier.GetValueOrDefault());
double log_H_S = Math.Log(barrier.GetValueOrDefault() / spot);
double log_H2_SX = Math.Log(barrier.GetValueOrDefault() * barrier.GetValueOrDefault() / (spot * strike));
double H_S_2mu = Math.Pow(barrier.GetValueOrDefault() / spot, 2 * mu);
double eta = (barrierType == Barrier.Type.DownIn ||
barrierType == Barrier.Type.DownOut ? 1.0 : -1.0);
double phi = (type == Option.Type.Call ? 1.0 : -1.0);
double x1, x2, y1, y2;
double cum_x1, cum_x2, cum_y1, cum_y2;
if (variance >= Const.QL_EPSILON)
{
// we calculate using mu*stddev instead of (mu+1)*stddev
// because cash-or-nothing don't need it. asset-or-nothing
// mu is really mu+1
x1 = phi * (log_S_X / stdDev + mu * stdDev);
x2 = phi * (log_S_H / stdDev + mu * stdDev);
y1 = eta * (log_H2_SX / stdDev + mu * stdDev);
y2 = eta * (log_H_S / stdDev + mu * stdDev);
CumulativeNormalDistribution f = new CumulativeNormalDistribution();
cum_x1 = f.value(x1);
cum_x2 = f.value(x2);
cum_y1 = f.value(y1);
cum_y2 = f.value(y2);
}
else
{
if (log_S_X > 0)
{
cum_x1 = 1.0;
}
else
{
cum_x1 = 0.0;
}
if (log_S_H > 0)
{
cum_x2 = 1.0;
}
else
{
cum_x2 = 0.0;
}
if (log_H2_SX > 0)
{
cum_y1 = 1.0;
}
else
{
cum_y1 = 0.0;
}
if (log_H_S > 0)
{
cum_y2 = 1.0;
}
else
{
cum_y2 = 0.0;
}
}
double alpha = 0;
switch (barrierType)
{
case Barrier.Type.DownIn:
if (type == Option.Type.Call)
{
// down-in and call
if (strike >= barrier)
{
// B3 (eta=1, phi=1)
alpha = H_S_2mu * cum_y1;
}
else
{
// B1-B2+B4 (eta=1, phi=1)
alpha = cum_x1 - cum_x2 + H_S_2mu * cum_y2;
}
}
else
{
// down-in and put
if (strike >= barrier)
{
// B2-B3+B4 (eta=1, phi=-1)
alpha = cum_x2 + H_S_2mu * (-cum_y1 + cum_y2);
}
else
{
// B1 (eta=1, phi=-1)
alpha = cum_x1;
}
}
break;
case Barrier.Type.UpIn:
if (type == Option.Type.Call)
{
// up-in and call
if (strike >= barrier)
{
// B1 (eta=-1, phi=1)
alpha = cum_x1;
}
else
{
// B2-B3+B4 (eta=-1, phi=1)
alpha = cum_x2 + H_S_2mu * (-cum_y1 + cum_y2);
}
}
else
{
// up-in and put
if (strike >= barrier)
{
// B1-B2+B4 (eta=-1, phi=-1)
alpha = cum_x1 - cum_x2 + H_S_2mu * cum_y2;
}
else
{
// B3 (eta=-1, phi=-1)
alpha = H_S_2mu * cum_y1;
}
}
break;
case Barrier.Type.DownOut:
if (type == Option.Type.Call)
{
// down-out and call
if (strike >= barrier)
{
// B1-B3 (eta=1, phi=1)
alpha = cum_x1 - H_S_2mu * cum_y1;
}
else
{
// B2-B4 (eta=1, phi=1)
alpha = cum_x2 - H_S_2mu * cum_y2;
}
}
else
{
// down-out and put
if (strike >= barrier)
{
// B1-B2+B3-B4 (eta=1, phi=-1)
alpha = cum_x1 - cum_x2 + H_S_2mu * (cum_y1 - cum_y2);
}
else
{
// always 0
alpha = 0;
}
}
break;
case Barrier.Type.UpOut:
if (type == Option.Type.Call)
{
// up-out and call
if (strike >= barrier)
{
// always 0
alpha = 0;
}
else
{
// B1-B2+B3-B4 (eta=-1, phi=1)
alpha = cum_x1 - cum_x2 + H_S_2mu * (cum_y1 - cum_y2);
}
}
else
{
// up-out and put
if (strike >= barrier)
{
// B2-B4 (eta=-1, phi=-1)
alpha = cum_x2 - H_S_2mu * cum_y2;
}
else
{
// B1-B3 (eta=-1, phi=-1)
alpha = cum_x1 - H_S_2mu * cum_y1;
}
}
break;
default:
Utils.QL_FAIL("invalid barrier type");
break;
}
return(discount * K * alpha);
}
public AmericanPayoffAtExpiry(double spot, double discount, double dividendDiscount, double variance,
StrikedTypePayoff payoff, bool knock_in = true)
{
spot_ = spot;
discount_ = discount;
dividendDiscount_ = dividendDiscount;
variance_ = variance;
knock_in_ = knock_in;
Utils.QL_REQUIRE(spot_ > 0.0, () => "positive spot value required");
Utils.QL_REQUIRE(discount_ > 0.0, () => "positive discount required");
Utils.QL_REQUIRE(dividendDiscount_ > 0.0, () => "positive dividend discount required");
Utils.QL_REQUIRE(variance_ >= 0.0, () => "negative variance not allowed");
stdDev_ = Math.Sqrt(variance_);
Option.Type type = payoff.optionType();
strike_ = payoff.strike();
forward_ = spot_ * dividendDiscount_ / discount_;
mu_ = Math.Log(dividendDiscount_ / discount_) / variance_ - 0.5;
// binary cash-or-nothing payoff?
CashOrNothingPayoff coo = payoff as CashOrNothingPayoff;
if (coo != null)
{
K_ = coo.cashPayoff();
}
// binary asset-or-nothing payoff?
AssetOrNothingPayoff aoo = payoff as AssetOrNothingPayoff;
if (aoo != null)
{
K_ = forward_;
mu_ += 1.0;
}
log_H_S_ = Math.Log(strike_ / spot_);
double log_S_H_ = Math.Log(spot_ / strike_);
double eta = 0.0;
double phi = 0.0;
switch (type)
{
case Option.Type.Call:
if (knock_in_)
{
// up-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american call with cash-or-nothing payoff
eta = -1.0;
phi = 1.0;
}
else
{
// up-and-out cash-(at-expiry)-or-nothing option
eta = -1.0;
phi = -1.0;
}
break;
case Option.Type.Put:
if (knock_in_)
{
// down-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american put with cash-or-nothing payoff
eta = 1.0;
phi = -1.0;
}
else
{
// down-and-out cash-(at-expiry)-or-nothing option
eta = 1.0;
phi = 1.0;
}
break;
default:
Utils.QL_FAIL("invalid option type");
break;
}
if (variance_ >= Const.QL_EPSILON)
{
D1_ = phi * (log_S_H_ / stdDev_ + mu_ * stdDev_);
D2_ = eta * (log_H_S_ / stdDev_ + mu_ * stdDev_);
CumulativeNormalDistribution f = new CumulativeNormalDistribution();
cum_d1_ = f.value(D1_);
cum_d2_ = f.value(D2_);
n_d1_ = f.derivative(D1_);
n_d2_ = f.derivative(D2_);
}
else
{
if (log_S_H_ * phi > 0)
{
cum_d1_ = 1.0;
}
else
{
cum_d1_ = 0.0;
}
if (log_H_S_ * eta > 0)
{
cum_d2_ = 1.0;
}
else
{
cum_d2_ = 0.0;
}
n_d1_ = 0.0;
n_d2_ = 0.0;
}
switch (type)
{
case Option.Type.Call:
if (strike_ <= spot_)
{
if (knock_in_)
{
// up-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american call with cash-or-nothing payoff
cum_d1_ = 0.5;
cum_d2_ = 0.5;
}
else
{
// up-and-out cash-(at-expiry)-or-nothing option
// already knocked out
cum_d1_ = 0.0;
cum_d2_ = 0.0;
}
n_d1_ = 0.0;
n_d2_ = 0.0;
}
break;
case Option.Type.Put:
if (strike_ >= spot_)
{
if (knock_in_)
{
// down-and-in cash-(at-expiry)-or-nothing option
// a.k.a. american put with cash-or-nothing payoff
cum_d1_ = 0.5;
cum_d2_ = 0.5;
}
else
{
// down-and-out cash-(at-expiry)-or-nothing option
// already knocked out
cum_d1_ = 0.0;
cum_d2_ = 0.0;
}
n_d1_ = 0.0;
n_d2_ = 0.0;
}
break;
default:
Utils.QL_FAIL("invalid option type");
break;
}
inTheMoney_ = (type == Option.Type.Call && strike_ < spot_) ||
(type == Option.Type.Put && strike_ > spot_);
if (inTheMoney_)
{
X_ = 1.0;
Y_ = 1.0;
}
else
{
X_ = 1.0;
if (cum_d2_.IsEqual(0.0))
{
Y_ = 0.0; // check needed on some extreme cases
}
else
{
Y_ = Math.Pow((strike_ / spot_), (2.0 * mu_));
}
}
if (!knock_in_)
{
Y_ *= -1.0;
}
}