![]() QuantLib 0.3.7Getting startedReference manual |
Lattice methodsDetailed DescriptionThe framework (corresponding to the ql/Lattices directory) contains basic building blocks for pricing instruments using lattice methods (trees). A lattice, i.e. an instance of the abstract class QuantLib::Lattice, relies on one or several trees (each one approximating a diffusion process) to price an instance of the DiscretizedAsset class. Trees are instances of classes derived from QuantLib::Tree, classes which define the branching between nodes and transition probabilities.Binomial treesThe binomial method is the simplest numerical method that can be used to price path-independent derivatives. It is usually the preferred lattice method under the Black-Scholes-Merton model. As an example, let's see the framework implemented in the bsmlattice.hpp file. It is a method based on a binomial tree, with constant short-rate (discounting). There are several approaches to build the underlying binomial tree, like Jarrow-Rudd or Cox-Ross-Rubinstein.Trinomial treesWhen the underlying stochastic process has a mean-reverting pattern, it is usually better to use a trinomial tree instead of a binomial tree. An example is implemented in the QuantLib::TrinomialTree class, which is constructed using a diffusion process and a time-grid. The goal is to build a recombining trinomial tree that will discretize, at a finite set of times, the possible evolutions of a random variable![]()
At each node, there is a probability
and
where k (the index of the node at the end of the middle branch) is the index of the node which is the nearest to the expected future value,
Bidimensional latticesTo come...The QuantLib::DiscretizedAsset classThis class is a representation of the price of a derivative at a specific time. It is roughly an array of values, each value being associated to a state of the underlying stochastic variables. For the moment, it is only used when working with trees, but it should be quite easy to make a use of it in finite-differences methods. The two main points, when deriving classes from QuantLib::DiscretizedAsset, are:
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