Simulated Paths

abstract type AbstractPath end

An AbstractPath specifies the interface for path implementations.

This aims at providing the flexibility to add other types of paths in the future.

struct Path <: AbstractPath
    sim::Simulation
    ts_dict::Dict{String,<:Termstructure}
    state_alias_dict::Dict{String,Int}
    context::Context
    interpolation::PathInterpolation
end

A Path combines a model, simulated model states and term structures. The interface to market references is established by a valuation context.

Paths are used by payoffs to calculate simulated zero bonds, asset prices and further building blocks of financial instrument payoffs.

path(
    sim::Simulation,
    ts_dict::Dict{String,<:Termstructure},
    cxt::Context,
    ip::PathInterpolation = NoPathInterpolation
    )

Create a Path object.

path(
    sim::Simulation,
    ts::Vector{Termstructure},
    cxt::Context,
    ip::PathInterpolation = NoPathInterpolation
    )

Create a Path object from a list of term structures.

@enum(
    PathInterpolation,
    NoPathInterpolation,
    LinearPathInterpolation,
)

PathInterpolation encodes how simulated states can be interpolates.

numeraire(p::AbstractPath, t::ModelTime, curve_key::String)

Calculate the numeraire in the domestic currency.

We allow for curve-specific numeraire calculation e.g. to allow for trade-specific discounting in AMC valuation.

numeraire(p::Path, t::ModelTime, curve_key::String)

Calculate the numeraire in the domestic currency.

We allow for curve-specific numeraire calculation e.g. to allow for trade-specific discounting in AMC valuation.

bank_account(p::AbstractPath, t::ModelTime, key::String)

Calculate a continuous compounded bank account value.

bank_account(p::Path, t::ModelTime, key::String)

Calculate a continuous compounded bank account value.

zero_bond(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)

Calculate a zero coupon bond price.

zero_bond(p::Path, t::ModelTime, T::ModelTime, key::String)

Calculate a zero coupon bond price.

zero_bonds(
    yts::YieldTermstructure,
    m::GaussianHjmModel,
    t::ModelTime,
    T::AbstractVector,
    SX::ModelState,
    )

Zero bond price reconstruction.

Returns a vector of length p where p is the number of paths in SX.

zero_bond(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)

Calculate a zero coupon bond prices.

zero_bonds(p::Path, t::ModelTime, T::AbstractVector, key::String)

Calculate zero coupon bond prices.

compounding_factor(p::AbstractPath, t::ModelTime, T1::ModelTime, T2::ModelTime, key::String)

Calculate a compounding factor P(t,T1) / P(t,T2).

compounding_factor(p::Path, t::ModelTime, T1::ModelTime, T2::ModelTime, key::String)

Calculate a compounding factor P(t,T1) / P(t,T2).

asset(p::AbstractPath, t::ModelTime, key::String)

Calculate asset price.

asset(p::Path, t::ModelTime, key::String)

Calculate asset price.

forward_asset(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)

Calculate forward asset price as expectation in T-forward measure.

forward_asset(p::Path, t::ModelTime, T::ModelTime, key::String)

Calculate forward asset price as expectation in T-forward measure, conditional on time-t.

forward_asset_and_zero_bonds(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)

Calculate asset and zero bond components for forward asset price calculation.

forward_asset_zero_bonds(p::Path, t::ModelTime, T::ModelTime, key::String)

Calculate asset (plus deterministic jumps) as well as domestic and foreign zero bond price associated with an Asset key.

This function implements methodology redundant to forward_asset(...). But it returns asset and zero bonds separately.

This function is used for barrier option pricing.

fixing(p::AbstractPath, t::ModelTime, key::String)

Return a fixing from a term structure.

This is used to handle fixings for indices etc.

fixing(p::Path, t::ModelTime, key::String)

Return a fixing from a term structure.

asset_convexity_adjustment(
    p::AbstractPath,
    t::ModelTime,
    T0::ModelTime,
    T1::ModelTime,
    T2::ModelTime,
    key::String
    )

Return the convexity adjustment for a YoY asset payoff.

asset_convexity_adjustment(
    p::Path,
    t::ModelTime,
    T0::ModelTime,
    T1::ModelTime,
    T2::ModelTime,
    key::String
    )

Return the convexity adjustment for a YoY asset payoff.

forward_index(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)

Expectation Et^T[ST] of a tradeable asset.

forward_index(p::Path, t::ModelTime, T::ModelTime, key::String)

Expectation Et^T[ST] of a tradeable asset.

index_convexity_adjustment(
    p::AbstractPath,
    t::ModelTime,
    T0::ModelTime,
    T1::ModelTime,
    T2::ModelTime,
    key::String
    )

Return the convexity adjustment for a YoY index payoff.

index_convexity_adjustment(
    p::Path,
    t::ModelTime,
    T0::ModelTime,
    T1::ModelTime,
    T2::ModelTime,
    key::String
    )

Return the convexity adjustment for a YoY index payoff.

future_index(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)

Expectation E_t^Q[F(T,T)] of a Future index/price.

future_index(p::Path, t::ModelTime, T::ModelTime, key::String)

Expectation E_t^Q[F(T,T)] of a Future index/price.

length(p::AbstractPath)

Return the number of realisations represented by the AbstractPath object.

We assume that model functions applied to an AbstractPath return a vector of length(p) where p is the number realisations.

length(p::Path)

Derive the number of realisations from the linked simulation.

state_variable(sim::Simulation, t::ModelTime, ip::PathInterpolation)

Derive a state variable for a given observation time.

discount(
    t::ModelTime,
    ts_dict::Dict{String,Termstructure},
    first_alias::String,
    second_alias::Union{String,Nothing} = nothing,
    operation::Union{String,Nothing} = nothing,
    )

Derive the discount factor for one or two of curve alias and a curve operation.