/*! \warning currently, this method returns the Black-Scholes
implied volatility using analytic formulas for
European options and a finite-difference method
for American and Bermudan options. It will give
unconsistent results if the pricing was performed
with any other methods (such as jump-diffusion
models.)
\warning options with a gamma that changes sign (e.g.,
binary options) have values that are <b>not</b>
monotonic in the volatility. In these cases, the
calculation can fail and the result (if any) is
almost meaningless. Another possible source of
failure is to have a target value that is not
attainable with any volatility, e.g., a target
value lower than the intrinsic value in the case
of American options.
*/
//public double impliedVolatility(double price, GeneralizedBlackScholesProcess process,
// double accuracy = 1.0e-4, int maxEvaluations = 100, double minVol = 1.0e-7, double maxVol = 4.0) {
public double impliedVolatility(double targetValue, GeneralizedBlackScholesProcess process,
double accuracy, int maxEvaluations, double minVol, double maxVol) {
if(isExpired()) throw new ApplicationException("option expired");
SimpleQuote volQuote = new SimpleQuote();
GeneralizedBlackScholesProcess newProcess = ImpliedVolatilityHelper.clone(process, volQuote);
// engines are built-in for the time being
IPricingEngine engine;
switch (exercise_.type()) {
case Exercise.Type.European:
engine = new AnalyticEuropeanEngine(newProcess);
break;
case Exercise.Type.American:
engine = new FDAmericanEngine(newProcess);
break;
case Exercise.Type.Bermudan:
engine = new FDBermudanEngine(newProcess);
break;
default:
throw new ArgumentException("unknown exercise type");
}
return ImpliedVolatilityHelper.calculate(this, engine, volQuote, targetValue, accuracy,
maxEvaluations, minVol, maxVol);
}
public override void calculate()
{
Utils.QL_REQUIRE(process_.x0() > 0.0, () => "negative or null underlying given");
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
Exercise exercise = arguments_.exercise;
double t = process_.riskFreeRate().link.dayCounter().yearFraction(process_.riskFreeRate().link.referenceDate(),
exercise.lastDate());
double a = model_.link.parameters()[0];
double sigma = model_.link.parameters()[1];
double eta = process_.blackVolatility().link.blackVol(exercise.lastDate(), payoff.strike());
double varianceOffset;
if (a * t > Math.Pow(Const.QL_EPSILON, 0.25))
{
double v = sigma * sigma / (a * a) * (t + 2 / a * Math.Exp(-a * t) - 1 / (2 * a) * Math.Exp(-2 * a * t) - 3 / (2 * a));
double mu = 2 * rho_ * sigma * eta / a * (t - 1 / a * (1 - Math.Exp(-a * t)));
varianceOffset = v + mu;
}
else
{
// low-a algebraic limit
double v = sigma * sigma * t * t * t * (1 / 3.0 - 0.25 * a * t + 7 / 60.0 * a * a * t * t);
double mu = rho_ * sigma * eta * t * t * (1 - a * t / 3.0 + a * a * t * t / 12.0);
varianceOffset = v + mu;
}
Handle <BlackVolTermStructure> volTS = new Handle <BlackVolTermStructure>(
new ShiftedBlackVolTermStructure(varianceOffset, process_.blackVolatility()));
GeneralizedBlackScholesProcess adjProcess =
new GeneralizedBlackScholesProcess(process_.stateVariable(),
process_.dividendYield(),
process_.riskFreeRate(),
volTS);
AnalyticEuropeanEngine bsmEngine = new AnalyticEuropeanEngine(adjProcess);
VanillaOption option = new VanillaOption(payoff, exercise);
option.setupArguments(bsmEngine.getArguments());
bsmEngine.calculate();
results_ = bsmEngine.getResults() as OneAssetOption.Results;
}
/*! \warning currently, this method returns the Black-Scholes
* implied volatility using analytic formulas for
* European options and a finite-difference method
* for American and Bermudan options. It will give
* unconsistent results if the pricing was performed
* with any other methods (such as jump-diffusion
* models.)
*
* \warning options with a gamma that changes sign (e.g.,
* binary options) have values that are <b>not</b>
* monotonic in the volatility. In these cases, the
* calculation can fail and the result (if any) is
* almost meaningless. Another possible source of
* failure is to have a target value that is not
* attainable with any volatility, e.g., a target
* value lower than the intrinsic value in the case
* of American options.
*/
//public double impliedVolatility(double price, GeneralizedBlackScholesProcess process,
// double accuracy = 1.0e-4, int maxEvaluations = 100, double minVol = 1.0e-7, double maxVol = 4.0) {
public double impliedVolatility(double targetValue, GeneralizedBlackScholesProcess process,
double accuracy, int maxEvaluations, double minVol, double maxVol)
{
if (isExpired())
{
throw new ApplicationException("option expired");
}
SimpleQuote volQuote = new SimpleQuote();
GeneralizedBlackScholesProcess newProcess = ImpliedVolatilityHelper.clone(process, volQuote);
// engines are built-in for the time being
IPricingEngine engine;
switch (exercise_.type())
{
case Exercise.Type.European:
engine = new AnalyticEuropeanEngine(newProcess);
break;
case Exercise.Type.American:
throw new NotImplementedException();
// engine = new FDAmericanEngine(newProcess);
break;
case Exercise.Type.Bermudan:
throw new NotImplementedException();
// engine = new FDBermudanEngine(newProcess);
break;
default:
throw new ArgumentException("unknown exercise type");
}
return(ImpliedVolatilityHelper.calculate(this, engine, volQuote, targetValue, accuracy,
maxEvaluations, minVol, maxVol));
}
public override void calculate()
{
AmericanExercise ex = arguments_.exercise as AmericanExercise;
Utils.QL_REQUIRE(ex != null, () => "non-American exercise given");
Utils.QL_REQUIRE(ex.payoffAtExpiry(), () => "payoff must be at expiry");
Utils.QL_REQUIRE(ex.dates()[0] <= process_.blackVolatility().link.referenceDate(), () =>
"American option with window exercise not handled yet");
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
double spot = process_.stateVariable().link.value();
Utils.QL_REQUIRE(spot > 0.0, () => "negative or null underlying given");
double variance = process_.blackVolatility().link.blackVariance(ex.lastDate(), payoff.strike());
double?barrier = arguments_.barrier;
Utils.QL_REQUIRE(barrier > 0.0, () => "positive barrier value required");
Barrier.Type barrierType = arguments_.barrierType;
// KO degenerate cases
if ((barrierType == Barrier.Type.DownOut && spot <= barrier) ||
(barrierType == Barrier.Type.UpOut && spot >= barrier))
{
// knocked out, no value
results_.value = 0;
results_.delta = 0;
results_.gamma = 0;
results_.vega = 0;
results_.theta = 0;
results_.rho = 0;
results_.dividendRho = 0;
return;
}
// KI degenerate cases
if ((barrierType == Barrier.Type.DownIn && spot <= barrier) ||
(barrierType == Barrier.Type.UpIn && spot >= barrier))
{
// knocked in - is a digital european
Exercise exercise = new EuropeanExercise(arguments_.exercise.lastDate());
IPricingEngine engine = new AnalyticEuropeanEngine(process_);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
results_.value = opt.NPV();
results_.delta = opt.delta();
results_.gamma = opt.gamma();
results_.vega = opt.vega();
results_.theta = opt.theta();
results_.rho = opt.rho();
results_.dividendRho = opt.dividendRho();
return;
}
double riskFreeDiscount = process_.riskFreeRate().link.discount(ex.lastDate());
AnalyticBinaryBarrierEngine_helper helper = new AnalyticBinaryBarrierEngine_helper(
process_, payoff, ex, arguments_);
results_.value = helper.payoffAtExpiry(spot, variance, riskFreeDiscount);
}
VanillaOption makeOption(StrikedTypePayoff payoff, Exercise exercise, Quote u, YieldTermStructure q,
YieldTermStructure r, BlackVolTermStructure vol, EngineType engineType, int binomialSteps, int samples)
{
GeneralizedBlackScholesProcess stochProcess = makeProcess(u, q, r, vol);
IPricingEngine engine;
switch (engineType)
{
case EngineType.Analytic:
engine = new AnalyticEuropeanEngine(stochProcess);
break;
case EngineType.JR:
engine = new BinomialVanillaEngine<JarrowRudd>(stochProcess, binomialSteps);
break;
case EngineType.CRR:
engine = new BinomialVanillaEngine<CoxRossRubinstein>(stochProcess, binomialSteps);
break;
case EngineType.EQP:
engine = new BinomialVanillaEngine<AdditiveEQPBinomialTree>(stochProcess, binomialSteps);
break;
case EngineType.TGEO:
engine = new BinomialVanillaEngine<Trigeorgis>(stochProcess, binomialSteps);
break;
case EngineType.TIAN:
engine = new BinomialVanillaEngine<Tian>(stochProcess, binomialSteps);
break;
case EngineType.LR:
engine = new BinomialVanillaEngine<LeisenReimer>(stochProcess, binomialSteps);
break;
case EngineType.JOSHI:
engine = new BinomialVanillaEngine<Joshi4>(stochProcess, binomialSteps);
break;
case EngineType.FiniteDifferences:
engine = new FDEuropeanEngine(stochProcess, binomialSteps, samples);
break;
case EngineType.Integral:
engine = new IntegralEngine(stochProcess);
break;
//case EngineType.PseudoMonteCarlo:
// engine = MakeMCEuropeanEngine<PseudoRandom>(stochProcess)
// .withSteps(1)
// .withSamples(samples)
// .withSeed(42);
// break;
//case EngineType.QuasiMonteCarlo:
// engine = MakeMCEuropeanEngine<LowDiscrepancy>(stochProcess)
// .withSteps(1)
// .withSamples(samples);
// break;
default:
throw new ArgumentException("unknown engine type");
}
VanillaOption option = new EuropeanOption(payoff, exercise);
option.setPricingEngine(engine);
return option;
}
public override void calculate()
{
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-plain payoff given");
Utils.QL_REQUIRE(payoff.strike() > 0.0, () => "strike must be positive");
double K = payoff.strike();
double S = process_.x0();
Utils.QL_REQUIRE(S >= 0.0, () => "negative or null underlying given");
Utils.QL_REQUIRE(!triggered(S), () => "barrier touched");
DoubleBarrier.Type barrierType = arguments_.barrierType;
Utils.QL_REQUIRE(barrierType == DoubleBarrier.Type.KnockOut ||
barrierType == DoubleBarrier.Type.KnockIn, () =>
"only KnockIn and KnockOut options supported");
double L = arguments_.barrier_lo.GetValueOrDefault();
double H = arguments_.barrier_hi.GetValueOrDefault();
double K_up = Math.Min(H, K);
double K_down = Math.Max(L, K);
double T = residualTime();
double rd = riskFreeRate();
double dd = riskFreeDiscount();
double rf = dividendYield();
double df = dividendDiscount();
double vol = volatility();
double mu = rd - rf - vol * vol / 2.0;
double sgn = mu > 0 ? 1.0 :(mu < 0 ? -1.0: 0.0);
//rebate
double R_L = arguments_.rebate.GetValueOrDefault();
double R_H = arguments_.rebate.GetValueOrDefault();
//european option
EuropeanOption europeanOption = new EuropeanOption(payoff, arguments_.exercise);
IPricingEngine analyticEuropeanEngine = new AnalyticEuropeanEngine(process_);
europeanOption.setPricingEngine(analyticEuropeanEngine);
double european = europeanOption.NPV();
double barrierOut = 0;
double rebateIn = 0;
for (int n = -series_; n < series_; n++)
{
double d1 = D(S / H * Math.Pow(L / H, 2.0 * n), vol * vol + mu, vol, T);
double d2 = d1 - vol * Math.Sqrt(T);
double g1 = D(H / S * Math.Pow(L / H, 2.0 * n - 1.0), vol * vol + mu, vol, T);
double g2 = g1 - vol * Math.Sqrt(T);
double h1 = D(S / H * Math.Pow(L / H, 2.0 * n - 1.0), vol * vol + mu, vol, T);
double h2 = h1 - vol * Math.Sqrt(T);
double k1 = D(L / S * Math.Pow(L / H, 2.0 * n - 1.0), vol * vol + mu, vol, T);
double k2 = k1 - vol * Math.Sqrt(T);
double d1_down = D(S / K_down * Math.Pow(L / H, 2.0 * n), vol * vol + mu, vol, T);
double d2_down = d1_down - vol * Math.Sqrt(T);
double d1_up = D(S / K_up * Math.Pow(L / H, 2.0 * n), vol * vol + mu, vol, T);
double d2_up = d1_up - vol * Math.Sqrt(T);
double k1_down = D((H * H) / (K_down * S) * Math.Pow(L / H, 2.0 * n), vol * vol + mu, vol, T);
double k2_down = k1_down - vol * Math.Sqrt(T);
double k1_up = D((H * H) / (K_up * S) * Math.Pow(L / H, 2.0 * n), vol * vol + mu, vol, T);
double k2_up = k1_up - vol * Math.Sqrt(T);
if (payoff.optionType() == Option.Type.Call)
{
barrierOut += Math.Pow(L / H, 2.0 * n * mu / (vol * vol)) *
(df * S * Math.Pow(L / H, 2.0 * n) * (f_.value(d1_down) - f_.value(d1))
- dd * K * (f_.value(d2_down) - f_.value(d2))
- df * Math.Pow(L / H, 2.0 * n) * H * H / S * Math.Pow(H / S, 2.0 * mu / (vol * vol)) * (f_.value(k1_down) - f_.value(k1))
+ dd * K * Math.Pow(H / S, 2.0 * mu / (vol * vol)) * (f_.value(k2_down) - f_.value(k2)));
}
else if (payoff.optionType() == Option.Type.Put)
{
barrierOut += Math.Pow(L / H, 2.0 * n * mu / (vol * vol)) *
(dd * K * (f_.value(h2) - f_.value(d2_up))
- df * S * Math.Pow(L / H, 2.0 * n) * (f_.value(h1) - f_.value(d1_up))
- dd * K * Math.Pow(H / S, 2.0 * mu / (vol * vol)) * (f_.value(g2) - f_.value(k2_up))
+ df * Math.Pow(L / H, 2.0 * n) * H * H / S * Math.Pow(H / S, 2.0 * mu / (vol * vol)) * (f_.value(g1) - f_.value(k1_up)));
}
else
{
Utils.QL_FAIL("option type not recognized");
}
double v1 = D(H / S * Math.Pow(H / L, 2.0 * n), -mu, vol, T);
double v2 = D(H / S * Math.Pow(H / L, 2.0 * n), mu, vol, T);
double v3 = D(S / L * Math.Pow(H / L, 2.0 * n), -mu, vol, T);
double v4 = D(S / L * Math.Pow(H / L, 2.0 * n), mu, vol, T);
rebateIn += dd * R_H * sgn * (Math.Pow(L / H, 2.0 * n * mu / (vol * vol)) * f_.value(sgn * v1) - Math.Pow(H / S, 2.0 * mu / (vol * vol)) * f_.value(-sgn * v2))
+ dd * R_L * sgn * (Math.Pow(L / S, 2.0 * mu / (vol * vol)) * f_.value(-sgn * v3) - Math.Pow(H / L, 2.0 * n * mu / (vol * vol)) * f_.value(sgn * v4));
}
//rebate paid at maturity
if (barrierType == DoubleBarrier.Type.KnockOut)
{
results_.value = barrierOut;
}
else
{
results_.value = european - barrierOut;
}
results_.additionalResults["vanilla"] = european;
results_.additionalResults["barrierOut"] = barrierOut;
results_.additionalResults["barrierIn"] = european - barrierOut;
}
public override void calculate(DateTime calcDate, FP_Parameter fp_parameter)
{
// master data load
this.indexOptionDAO_.SelectOwn();
// market data load
// index data
clsHDAT_MARKETDATA_TB clstb = new clsHDAT_MARKETDATA_TB();
string calcDateStr = calcDate.ToString("yyyyMMdd");
QLNet.Settings.setEvaluationDate(calcDate);
clstb.REF_DT = calcDateStr;
clstb.INDEX_CD = this.indexOptionDAO_.UNDERLYING_INDEX_CD;
int checkNum = clstb.SelectOwn();
if (checkNum == 0) { throw new Exception("market data does not exist : " + calcDateStr + " " + clstb.INDEX_CD); }
double indexData = clstb.LAST;
// curveData --------------------------------------------------
string curve_cd = "IRSKRW";
YieldCurve curveManager = new YieldCurve();
curveManager.loadCurveData(calcDate,curve_cd,clsHDAT_CURVEDATA_TB.RATE_TYP_Type.YTM);
QLNet.YieldTermStructure yield_ts = curveManager.yieldCurve();
// calculate
string maturityDateStr = this.indexOptionDAO_.MATURITY_DT;
System.Globalization.CultureInfo us
= new System.Globalization.CultureInfo("en-US");
DateTime maturityDate = DateTime.ParseExact(maturityDateStr, "yyyyMMdd", us);
DayCounter dc = new Actual365Fixed();
Calendar cal = new NullCalendar();
double vol = 0.3;
double strike = this.indexOptionDAO_.STRIKE;
PlainVanillaPayoff strikePayoff = new PlainVanillaPayoff(Option.Type.
Call, strike);
Exercise exercise = new EuropeanExercise(maturityDate);
VanillaOption q_option = new VanillaOption(strikePayoff,exercise);
Handle<Quote> x0 = new Handle<Quote>(new SimpleQuote(indexData));
FlatForward flatForward = new FlatForward(calcDate,0.01,dc);
Handle<YieldTermStructure> dividendTS = new Handle<YieldTermStructure>(flatForward);
Handle<YieldTermStructure> riskFreeTS = new Handle<YieldTermStructure>(yield_ts);
BlackConstantVol blackConstVol = new BlackConstantVol(calcDate,cal,vol,dc);
Handle<BlackVolTermStructure> blackVolTS = new Handle<BlackVolTermStructure>(blackConstVol);
GeneralizedBlackScholesProcess process =new GeneralizedBlackScholesProcess(x0 ,dividendTS,riskFreeTS,blackVolTS);
AnalyticEuropeanEngine europeanEngine = new AnalyticEuropeanEngine(process);
q_option.setPricingEngine(europeanEngine);
double value = q_option.NPV();
double indexMultiplier = this.indexOptionDAO_.INDEX_MULTIPLIER;
int quantity = this.indexOptionDAO_.QUANTITY;
clsHITM_FP_GREEKRESULT_TB result_tb = new clsHITM_FP_GREEKRESULT_TB();
result_tb.FP_GREEKRESULT_ID = IDGenerator.getNewGreekResultID(this.indexOptionDAO_.INSTRUMENT_ID,calcDateStr);
result_tb.CALC_DT = calcDateStr;
result_tb.INSTRUMENT_ID = this.indexOptionDAO_.INSTRUMENT_ID;
result_tb.INSTRUMENT_TYP = this.indexOptionDAO_.INSTRUMENT_TYP;
result_tb.UNDERLYING_ID = "KOSPI200";
result_tb.UNDERLYING_VALUE = indexData;
//result_tb.SEQ = 1;
result_tb.DELTA = (q_option.delta() * indexData / 100) * indexMultiplier * quantity; // 1% Delta
result_tb.GAMMA = 0.5 * (q_option.gamma() * indexData / 100) * indexMultiplier * quantity; // 1% Gamma
result_tb.VEGA = q_option.vega() / 100 * indexMultiplier * quantity; // 1% point Vega
result_tb.CALC_PRICE = value * indexMultiplier * quantity;
result_tb.CALCULATED_FLAG = (int)clsHITM_FP_GREEKRESULT_TB.CALCULATED_FLAG_Type.CALCULATED;
result_tb.CALCULATED_TIME = DateTime.Now.ToString("HHmmss"); ;
result_tb.CALCULATE_TYP = (int)clsHITM_FP_GREEKRESULT_TB.CALCULATE_TYP_Type.ANALYTICS;
// price
if (result_tb.UpdateDateResult() == 0)
{ throw new Exception("update result fail. no exist , calcDate : " + calcDate.ToString("yyyyMMdd") + " , inst_id : " + result_tb.INSTRUMENT_ID); }
// delta
// gamma and others : no exist ?
}
