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net.finmath.montecarlo.interestrate.products

## Class SwaptionGeneralizedAnalyticApproximation

• All Implemented Interfaces:
Product, Swaption, TermStructureMonteCarloProduct, MonteCarloProduct

public class SwaptionGeneralizedAnalyticApproximation
extends AbstractLIBORMonteCarloProduct
implements Swaption
This class implements an analytic swaption valuation formula under a LIBOR market model. The algorithm implemented here is the OIS discounting version of the algorithm described in ISBN 0470047224 (see SwaptionSingleCurveAnalyticApproximation). The approximation assumes that the forward rates (LIBOR) follow a normal model or log-normal model and that the model provides the integrated instantaneous covariance of the forward rates or the integrated instantaneous covariance of the log-forward rates The getValue method calculates the approximated integrated instantaneous variance of the swap rate, using the approximation $\frac{d log(S(t))}{d log(L(t))} \approx \frac{d log(S(0))}{d log(L(0))} = : w.$ Since $$L$$ is a vector, $$w$$ is a gradient (vector). The class then approximates the Black volatility of a swaption via $\sigma_S^{2} T := \sum_{i,j} w_{i} \gamma_{i,j} w_{j}$ where $$(\gamma_{i,j})_{i,j = 1,...,m}$$ is the covariance matrix of the forward rates. The valuation can be performed in terms of value or implied Black volatility.
Version:
1.0
Author:
Christian Fries, Lorenzo Torricelli
Date:
17.05.2007.
• ### Nested Class Summary

Nested Classes
Modifier and Type Class and Description
static class  SwaptionGeneralizedAnalyticApproximation.StateSpace
static class  SwaptionGeneralizedAnalyticApproximation.ValueUnit
• ### Constructor Summary

Constructors
Constructor and Description
SwaptionGeneralizedAnalyticApproximation(double swaprate, double[] swapTenor, SwaptionGeneralizedAnalyticApproximation.ValueUnit valueUnit, SwaptionGeneralizedAnalyticApproximation.StateSpace stateSpace)
Create an analytic swaption approximation product for log normal forward rate model.
SwaptionGeneralizedAnalyticApproximation(double swaprate, TimeDiscretization swapTenor, SwaptionGeneralizedAnalyticApproximation.StateSpace stateSpace)
Create an analytic swaption approximation product for log normal forward rate model.
• ### Method Summary

All Methods
Modifier and Type Method and Description
static double[][][] getIntegratedLIBORCovariance(LIBORMarketModelFromCovarianceModel model)
Map<String,double[]> getLogSwapRateDerivative(TimeDiscretization liborPeriodDiscretization, DiscountCurve discountCurve, ForwardCurve forwardCurve)
This function calculate the partial derivative d log(S) / d log(Lk) for a given swap rate with respect to a vector of forward rates (on a given forward rate tenor).
Map<String,double[]> getSwapRateDerivative(TimeDiscretization liborPeriodDiscretization, AnalyticModel model, DiscountCurve discountCurve, ForwardCurve forwardCurve)
Returns the derivative of the swap rate (associated with this swap) with respect to the forward rates dS/dL_{i}.
RandomVariable getValue(double evaluationTime, LIBORModelMonteCarloSimulationModel model)
This method returns the value random variable of the product within the specified model, evaluated at a given evalutationTime.
RandomVariable getValues(double evaluationTime, LIBORMarketModel model)
Calculates the approximated integrated instantaneous variance of the swap rate, using the approximation d S/d L (t) = d S/d L (0).
• ### Methods inherited from class net.finmath.montecarlo.interestrate.products.AbstractLIBORMonteCarloProduct

getFactorDrift, getValue, getValueForModifiedData, getValues
• ### Methods inherited from class net.finmath.montecarlo.AbstractMonteCarloProduct

getCurrency, getValue, getValue, getValues, getValues, getValues, getValuesForModifiedData, getValuesForModifiedData, getValuesForModifiedData, getValuesForModifiedData, toString
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
• ### Methods inherited from interface net.finmath.montecarlo.MonteCarloProduct

getCurrency, getValue, getValue, getValues, getValues, getValues, getValuesForModifiedData, getValuesForModifiedData, getValuesForModifiedData, getValuesForModifiedData
• ### Constructor Detail

• #### SwaptionGeneralizedAnalyticApproximation

public SwaptionGeneralizedAnalyticApproximation(double swaprate,
double[] swapTenor,
SwaptionGeneralizedAnalyticApproximation.ValueUnit valueUnit,
SwaptionGeneralizedAnalyticApproximation.StateSpace stateSpace)
Create an analytic swaption approximation product for log normal forward rate model. Note: It is implicitly assumed that swapTenor is the exercise date (no forward starting).
Parameters:
swaprate - The strike swap rate of the swaption.
swapTenor - The swap tenor in doubles.
valueUnit - The unit of the quantity returned by the getValues method.
stateSpace - The state space of the LMM (lognormal or normal)
• #### SwaptionGeneralizedAnalyticApproximation

public SwaptionGeneralizedAnalyticApproximation(double swaprate,
TimeDiscretization swapTenor,
SwaptionGeneralizedAnalyticApproximation.StateSpace stateSpace)
Create an analytic swaption approximation product for log normal forward rate model. Note: It is implicitly assumed that swapTenor.getTime(0) is the exercise date (no forward starting).
Parameters:
swaprate - The strike swap rate of the swaption.
swapTenor - The swap tenor in doubles.
stateSpace - The state space of the LMM (lognormal or normal)
• ### Method Detail

• #### getValue

public RandomVariable getValue(double evaluationTime,
LIBORModelMonteCarloSimulationModel model)
Description copied from interface: TermStructureMonteCarloProduct
This method returns the value random variable of the product within the specified model, evaluated at a given evalutationTime. Note: For a lattice this is often the value conditional to evalutationTime, for a Monte-Carlo simulation this is the (sum of) value discounted to evaluation time. Cashflows prior evaluationTime are not considered.
Specified by:
getValue in interface TermStructureMonteCarloProduct
Specified by:
getValue in class AbstractLIBORMonteCarloProduct
Parameters:
evaluationTime - The time on which this products value should be observed.
model - The model used to price the product.
Returns:
The random variable representing the value of the product discounted to evaluation time
• #### getValues

public RandomVariable getValues(double evaluationTime,
LIBORMarketModel model)
Calculates the approximated integrated instantaneous variance of the swap rate, using the approximation d S/d L (t) = d S/d L (0).
Parameters:
evaluationTime - Time at which the product is evaluated.
model - A model implementing the LIBORModelMonteCarloSimulationModel
Returns:
Depending on the value of value unit, the method returns either the approximated integrated instantaneous variance of the swap rate (ValueUnit.INTEGRATEDVARIANCE) or the value using the Black formula (ValueUnit.VALUE).
To dos:
make initial values an arg and use evaluation time.
• #### getLogSwapRateDerivative

public Map<String,double[]> getLogSwapRateDerivative(TimeDiscretization liborPeriodDiscretization,
DiscountCurve discountCurve,
ForwardCurve forwardCurve)
This function calculate the partial derivative d log(S) / d log(Lk) for a given swap rate with respect to a vector of forward rates (on a given forward rate tenor). It also returns some useful other quantities like the corresponding discount factors and swap annuities.
Parameters:
liborPeriodDiscretization - The libor period discretization.
discountCurve - The discount curve. If this parameter is null, the discount curve will be calculated from the forward curve.
forwardCurve - The forward curve.
Returns:
A map containing the partial derivatives (key "value"), the discount factors (key "discountFactors") and the annuities (key "annuities") as vectors of double[] (indexed by forward rate tenor index starting at swap start)
• #### getSwapRateDerivative

public Map<String,double[]> getSwapRateDerivative(TimeDiscretization liborPeriodDiscretization,
AnalyticModel model,
DiscountCurve discountCurve,
ForwardCurve forwardCurve)
Returns the derivative of the swap rate (associated with this swap) with respect to the forward rates dS/dL_{i}.
Parameters:
liborPeriodDiscretization - Forward rate discretization.
model - The analytic model providing the context for discountCurve and forwardCurve.
discountCurve - The discount curve.
forwardCurve - The forward curve.
Returns:
A map containing the derivative of the swap rate with respect to the forward rates dS/dL_{i} under the key "values".
• #### getIntegratedLIBORCovariance

public static double[][][] getIntegratedLIBORCovariance(LIBORMarketModelFromCovarianceModel model)
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Copyright © 2018 Christian P. Fries.

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