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/*
 Copyright (C) 2000-2003 Sadruddin Rejeb
 
 This file is part of QuantLib, a free-software/open-source library
 for financial quantitative analysts and developers - http://quantlib.org/
 
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/*! \defgroup shortrate Short-rate modelling framework
 
    This framework (corresponding to the ql/models/shortrate directory)
    implements some single-factor and two-factor short rate models. The models 
    implemented in this library are widely used by practitioners. For the 
    moment, the ShortRateModel class defines the short-rate dynamics
    with stochastic equations of the type 
    \f[ 
        dx_i = \mu(t,x_i) dt + \sigma(t,x_i) dW_t 
    \f]
    where \f$ r = f(t,x) \f$. If the model is affine (i.e. derived from the
    QuantLib::AffineModel class), analytical formulas 
    for discount bonds and discount bond options are given (useful for 
    calibration). 
 
    \section singlefactormodels Single-factor models
    
    \par The Hull & White model
    \f[
        dr_t = (\theta(t) - \alpha(t) r_t)dt + \sigma(t) dW_t
    \f]
    When \f$ \alpha \f$ and \f$ \sigma \f$ are constants, this model
    has analytical formulas for discount bonds and discount bond options.
 
    \par The Black-Karasinski model
    \f[
        d\ln{r_t} = (\theta(t) - \alpha \ln{r_t})dt + \sigma dW_t
    \f]
    No analytical tractability here.
 
    \par The extended Cox-Ingersoll-Ross model
    \f[
        dr_t = (\theta(t) - k r_t)dt + \sigma \sqrt{r_t} dW_t
    \f]
    There are analytical formulas for discount bonds (and soon for discount 
    bond options).
 
    \section calibration Calibration
 
    The class CalibrationHelper is a base class that facilitates the 
    instantiation of market instruments used for calibration. It has
    a method marketValue() that gives the market price using a Black
    formula, and a modelValue() method that gives the price according to
    a model
 
    Derived classed are
    QuantLib::CapHelper and
    QuantLib::SwaptionHelper. 
 
    For the calibration itself, you must choose an optimization method that
    will find constant parameters such that the value:
    \f[
        V = \sqrt{\sum_{i=1}^{n} \frac{(T_i - M_i)^2}{M_i}},
    \f]
    where \f$ T_i \f$ is the price given by the model and \f$ M_i \f$ is the
    market price, is minimized. A few optimization methods are available in 
    the ql/Optimization directory.
 
    \section twofactormodels Two-factor models
 
    \section pricers Pricers
 
    \par Analytical pricers
 
    If the model is affine, i.e. discount bond options formulas exist, caps are
    easily priced since they are a portfolio of discount bond options. Such a
    pricer is implemented in QuantLib::AnalyticalCapFloor.
    In the case of single-factor affine models, swaptions can be priced using
    the Jamshidian decomposition, implemented in 
    QuantLib::JamshidianSwaption.
 
    \par Using Trees
 
    Each model derived from the single-factor model class has the ability to 
    return a trinomial tree. For yield-curve consistent models, the fitting
    parameter can be determined either analytically (when possible) or 
    numerically. When a tree is built, it is then pretty straightforward to 
    implement a pricer for any path-independent derivative. Just implement
    a class derived from NumericalDerivative (see 
    QuantLib::NumericalSwaption for example) and roll it back until 
    the present time...
    Just look at QuantLib::TreeCapFloor and 
    QuantLib::TreeSwaption for working pricers.
 
*/