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# Pricing Namespace Reference

## Detailed Description

Standalone function templates for Monte Carlo and lattice pricing of options.

## Functions

template<typename LatticeType, typename OptionType> Real latticeForwardPrice (LatticeType *theLattice, OptionType *theOption)
template<typename OptionType> Real monteCarloForwardPrice (OptionType *theOption, int N)
template<typename OptionType> Real betaCoefficient (OptionType *theOption, int N)
template<typename OptionType> Real controlledMonteCarloForwardPrice (OptionType *theOption, int nPaths)
template<class OptionType> Real correlationWithControlVariate (OptionType *theOption, int N)

## Function Documentation

 template Real latticeForwardPrice ( LatticeType * theLattice, OptionType * theOption )
 The forward price of theOption when priced in theLattice. Read the source code to see what member functions the types LatticeType and OptionType must implement. The routine is written under the assumption that the transition probabilities are computed by the lattice and are both time and state independent. This is rather restrictive but true for the lattices we consider. The code can easily be rewritten to cover the general case of both time and state dependent transition probabilities. Simply define `LatticeType::transitionProbability` to be a function of the edge i, time t and the node n. For reasons of speed this approach is not taken here. Please read the source code to determine the precise syntactic assumptions which the code makes about the type of lattice `LatticeType`, the type of nodes within the lattice `LatticeType::NodeType` and the type `OptionType` of option to be priced in the lattice. Definition at line 95 of file Pricing.h. References Array1D< S >::getDimension(), and Real.

 template Real monteCarloForwardPrice ( OptionType * theOption, int N )
 The forward price of theOption computed from N sample payoffs compounded forward to the horizon. Definition at line 165 of file Pricing.h. References N(), and Real.

 template Real betaCoefficient ( OptionType * theOption, int N )
 The beta coefficient of option payoff and control variate computed from N forwardPayoff - controlVariate pairs (book, 2.8). See controlledMonteCarloForwardPrice for the assumptions. Definition at line 178 of file Pricing.h. References N(), Real, and LiborFunctional::X(). Referenced by controlledMonteCarloForwardPrice().

 template Real controlledMonteCarloForwardPrice ( OptionType * theOption, int nPaths )
 The forward price of theOption computed from nPaths paths of thePathGenerator supplied by the option and using the control variate implemented for the option. See book, 2.8. Definition at line 208 of file Pricing.h. References betaCoefficient(), and Real.

 template Real correlationWithControlVariate ( OptionType * theOption, int N )
 The correlation of the forward payoff of theOption with its control variate computed from N paths of thePathGenerator supplied by the option. Definition at line 234 of file Pricing.h. References N(), and Real.

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