Term Structures Functions

abstract type Termstructure end

An abstract term structure that provides an alias for identification.

alias(ts::Termstructure)

Return the term structure's alias.

@enum(
    TermstructureResultSize,
    TermstructureVector,
    TermstructureScalar
)

Specify the dimensions/shape of the values modelled by a term structure.

For some term structures (e.g. ParameterTermstructure and VolatilityTermstructure) the result may be either a vector or a scalar.

abstract type CorrelationTermstructure <: Termstructure end

An abstract correlation term structure that provides methods to calculate instantaneous correlations.

correlation(ts::CorrelationTermstructure, alias1::String, alias2::String)

Return a scalar instantaneous correlation.

correlation(ts::CorrelationTermstructure, aliases::AbstractVector{String})

Return a symmetric matrix of instantaneous correlations.

correlation(ts::CorrelationTermstructure, aliases1::AbstractVector{String}, aliases2::AbstractVector{String})

Return a matrix of instantaneous correlations, each element of aliases1 versus each element of aliases2. The size of the resulting matrix is (length(aliases1), length(aliases2)).

correlation(ts::CorrelationTermstructure, alias1::String, aliases2::AbstractVector{String})

Return an (1,N) matrix of instantaneous correlations.

correlation(ts::CorrelationTermstructure, aliases1::AbstractVector{String}, alias2::String)

Return an (N, 1) matrix of instantaneous correlations.

abstract type CreditDefaultTermstructure <: Termstructure end

An abstract credit default term structure that provides methods to calculate survival probabilities.

survival(ts::CreditDefaultTermstructure, t::ModelTime)

Return the survival probability with observation time t.

abstract type FuturesTermstructure <: Termstructure end

An abstract futures term structure that provides methods to calculate prices of futures. Such prices represent risk-neutral expectations of spot prices.

future_price(ts::FuturesTermstructure, t::ModelTime)

Return the price of a future with settlement time t.

abstract type InflationTermstructure <: Termstructure end

An abstract inflation term structure that provides methods to calculate forward inflation index. Forward inflation index is a T-forward measure expectation of (spot) inflation index values.

inflation_index(ts::InflationTermstructure, t::ModelTime)

Return the forward inflation index with observation time t.

abstract type ParameterTermstructure <: Termstructure end

An abstract generic parameter term structure that provides methods to retrieve parameter values for various incarnations of signatures.

value(ts::ParameterTermstructure, result_size::TermstructureResultSize = TermstructureVector)

Return a value for constant/time-homogeneous parameters.

value(ts::ParameterTermstructure, t::ModelTime, result_size::TermstructureResultSize = TermstructureVector)

Return a value for a given observation time t.

abstract type YieldTermstructure <: Termstructure end

An abstract yield term structure that provides methods to calculate discount factors zero rates and forward rates.

discount(ts::YieldTermstructure, t::ModelTime)

Return the discount factor with observation time t.

zero_rate(ts::YieldTermstructure, t0::ModelTime, t1::ModelTime)

Return the continuous compounded zero rate over a period t0 to t1.

zero_rate(ts::YieldTermstructure, t::ModelTime)

Return the continuous compounded zero rate as of today with observation time t.

forward_rate(ts::YieldTermstructure, t::ModelTime, dt=1.0e-6)

Return the instantaneous forward rate with observation time t.

abstract type VolatilityTermstructure <: Termstructure end

An abstract volatility term structure that provides methods to calculate volatility values for various incarnations of signatures.

volatility(ts::VolatilityTermstructure, t::ModelTime, result_size::TermstructureResultSize = TermstructureVector)

Return a volatility for a given observation time t.

volatility(ts::VolatilityTermstructure, t::ModelTime, x::ModelValue)

Return a scalar volatility for a given observation time t and underlying or strike value x.

struct CorrelationHolder <: CorrelationTermstructure
    alias::String
    correlations::Dict{String, ModelValue}
    sep::String
    value_type::DataType
end

A container holding correlation values.

A CorrelationHolder allows to calculate correlation matrices based on String alias keys (identifiers).

value_type specifies the type of correlation entries. This ensures that all values are of consistent type. This feature is required for correlation sensitivity calculation.

correlation_holder(
    alias::String,
    correlations::Dict,
    sep::String = "<>",
    value_type::DataType = ModelValue,
    )

Create a CorrelationHolder object from dictionary.

correlation_holder(
    alias::String,
    sep::String = "<>",
    value_type::DataType = ModelValue,
    )

Create an empty CorrelationHolder object.

correlation_holder(m::AssetModel)

Return the correlation holder term structure.

Return the model's CorrelationHolder.

correlation_key(ch::CorrelationHolder, alias1::String, alias2::String)

Derive the key for correlation dictionary from two aliases.

set_correlation!(
    ch::CorrelationHolder,
    alias1::String,
    alias2::String,
    value::ModelValue
    )

Insert a new correlation value into CorrelationHolder. If a correlation already exists it is overwritten.

get(ch::CorrelationHolder, alias1::String, alias2::String)

Implement methodology to obtain a scalar correlation from a CorrelationHolder.

struct FlatSpreadCurve <: CreditDefaultTermstructure
    alias::String
    spread::ModelValue
end

A flat credit spread curve.

flat_spread_curve(alias::String, spread::ModelValue)

Create a FlatSpreadCurve.

flat_spread_curve(spread::ModelValue)

Create a FlatSpreadCurve without alias.

struct LogSurvivalCurve <: CreditDefaultTermstructure
    alias::String
    times::AbstractVector
    values::AbstractVector
end

Log-interpolated survival probabilities.

survival_curve(
    alias::String,
    times::AbstractVector,
    survival_probs::AbstractVector,
    interp_method = (x,y) -> linear_interpolation(x, y, extrapolation_bc = Line()),
    )

Create a LogSurvivalCurve.

survival_curve(
    alias::String,
    times::AbstractVector,
    survival_probs::AbstractVector,
    method_alias::String,
    )

Create a LogSurvivalCurve for pre-defined interpolation methods.

abstract type PiecewiseFlatParameter <: ParameterTermstructure end

A generic vector-valued model parameter term structure with piece-wise constant interpolation and constant extrapolation.

struct BackwardFlatParameter <: PiecewiseFlatParameter
    alias::String
    times::AbstractVector
    values::AbstractMatrix
end

A generic vector-valued model parameter term structure with piece-wise constant backward-flat interpolation and constant extrapolation.

backward_flat_parameter(
     alias::String,
     times::AbstractVector,
     values::AbstractMatrix,
     )

Create a BackwardFlatParameter object for vector-valued parameters.

backward_flat_parameter(
    alias::String,
    times::AbstractVector,
    values::AbstractVector,
    )

Create a BackwardFlatParameter object for scalar parameters.

flat_parameter(value::ModelValue)

Create a constant BackwardFlatParameter object.

flat_parameter(alias::String, value::ModelValue)

Create a constant BackwardFlatParameter object.

flat_parameter(value::AbstractVector)

Create a constant BackwardFlatParameter object.

flat_parameter(alias::String, value::AbstractVector)

Create a constant BackwardFlatParameter object.

struct ForwardFlatParameter <: PiecewiseFlatParameter
    alias::String
    times::AbstractVector
    values::AbstractMatrix
end

A generic vector-valued model parameter term structure with piece-wise constant forward-flat interpolation and constant extrapolation.

forward_flat_parameter(
    alias::String,
    times::AbstractVector,
    values::AbstractMatrix,
    )

Create a ForwardFlatParameter object for vector-valued parameters.

forward_flat_parameter(
    alias::String,
    times::AbstractVector,
    values::AbstractVector,
    )

Create a ForwardFlatParameter object for scalar parameters.

time_idx(ts::BackwardFlatParameter, t)

Find the index such that T[idx-1] < t <= T[idx]. If t is larger than the last (or all) times T then return length(T)+1.

time_idx(ts::ForwardFlatParameter, t)

Find the index such that T[idx] >= t > T[idx+1]. If t is smaller than the first (or all) times T then return 0.

struct FlatForward <: YieldTermstructure
    alias::String
    rate
end

A constant yield term structure.

flat_forward(alias::String, rate)

Create a FlatForward yield curve.

flat_forward(rate)

Create a FlatForward yield curve without alias.

struct ZeroCurve <: YieldTermstructure
    alias::String
    times::AbstractVector
    values::AbstractVector
    interpolation
end

A yield term structure based on interpolated continuous compounded zero rates.

zero_curve(
    alias::String,
    times::AbstractVector,
    values::AbstractVector,
    interp_method = (x,y) -> linear_interpolation(x, y, extrapolation_bc = Line()),
    )

Create a ZeroCurve object.

zero_curve(
    times::AbstractVector,
    values::AbstractVector,
    interp_method = (x,y) -> linear_interpolation(x, y, extrapolation_bc = Line()),
    )

Create a ZeroCurve object without alias.

zero_curve(
    alias::String,
    times::AbstractVector,
    values::AbstractVector,
    method_alias::String,
    )

Create a ZeroCurve object using interpolation string.

zero_curve(
    times::AbstractVector,
    values::AbstractVector,
    method_alias::String,
    )

Create a ZeroCurve object using interpolation string.

struct LinearZeroCurve <: YieldTermstructure
    alias::String
    times::AbstractVector
    values::AbstractVector
end

A yield term structure based on continuous compounded zero rates with linear interpolation and flat extrapolation.

This curve aims at mitigating limitations of Zygote and ZeroCurve.

linear_zero_curve(
    alias::String,
    times::AbstractVector,
    values::AbstractVector,
    )

Create a LinearZeroCurve.

linear_zero_curve(
    times::AbstractVector,
    values::AbstractVector,
    )

Create a LinearZeroCurve with empty alias.

struct BackwardFlatVolatility <: VolatilityTermstructure
    alias::String
    times::AbstractVector
    values::AbstractMatrix
end

A vector-valued volatility term structure with piece-wise constant (backward-flat) interpolation and constant extrapolation.

backward_flat_volatility(
    alias::String,
    times::AbstractVector,
    values::AbstractMatrix,
    )

Create a BackwardFlatVolatility object for vector-valued volatility.

Volatility values are of size (nvols, ntimes).

backward_flat_volatility(
    alias::String,
    times::AbstractVector,
    values::AbstractVector,
    )

Create a BackwardFlatVolatility object for scalar volatility.

flat_volatility(alias::String, value)

Create a BackwardFlatVolatility object for a flat volatility.

flat_volatility(alias::String, value)

Create a BackwardFlatVolatility object for a flat volatility.

time_idx(ts::BackwardFlatVolatility, t)

Find the index such that T[idx-1] < t <= T[idx]. If t is larger than the last (or all) times T then return length(T)+1.

correlation(ts::CorrelationTermstructure, alias1::String, alias2::String)

Return a scalar instantaneous correlation.

correlation(ts::CorrelationTermstructure, aliases::AbstractVector{String})

Return a symmetric matrix of instantaneous correlations.

correlation(ts::CorrelationTermstructure, aliases1::AbstractVector{String}, aliases2::AbstractVector{String})

Return a matrix of instantaneous correlations, each element of aliases1 versus each element of aliases2. The size of the resulting matrix is (length(aliases1), length(aliases2)).

correlation(ts::CorrelationTermstructure, alias1::String, aliases2::AbstractVector{String})

Return an (1,N) matrix of instantaneous correlations.

correlation(ts::CorrelationTermstructure, aliases1::AbstractVector{String}, alias2::String)

Return an (N, 1) matrix of instantaneous correlations.

correlation(ch::CorrelationHolder, alias1::String, alias2::String)

Return a scalar instantaneous correlation.

correlation(ch::CorrelationHolder, aliases1::AbstractVector{String}, aliases2::AbstractVector{String})

Return a matrix of instantaneous correlations, each element of aliases1 versus each element of aliases2. The size of the resulting matrix is (length(aliases1), length(aliases2)).

correlation(ch::CorrelationHolder, aliases::AbstractVector{String})

Return a symmetric matrix of instantaneous correlations.

discount(ts::YieldTermstructure, t::ModelTime)

Return the discount factor with observation time t.

discount(ts::FlatForward, t::ModelTime)

Calculate discount factor.

discount(ts::ZeroCurve, t::ModelTime)

Calculate discount factor.

discount(ts::LinearZeroCurve, t::ModelTime)

Calculate discount factor.

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.

value(ts::ParameterTermstructure, result_size::TermstructureResultSize = TermstructureVector)

Return a value for constant/time-homogeneous parameters.

value(ts::ParameterTermstructure, t::ModelTime, result_size::TermstructureResultSize = TermstructureVector)

Return a value for a given observation time t.

value(ts::PiecewiseFlatParameter, result_size::TermstructureResultSize = TermstructureVector)

Return a value for constant/time-homogeneous parameters.

value(ts::PiecewiseFlatParameter, t::ModelTime, result_size::TermstructureResultSize = TermstructureVector)

Return a value for a given observation time t.

volatility(ts::VolatilityTermstructure, t::ModelTime, result_size::TermstructureResultSize = TermstructureVector)

Return a volatility for a given observation time t.

volatility(ts::VolatilityTermstructure, t::ModelTime, x::ModelValue)

Return a scalar volatility for a given observation time t and underlying or strike value x.

volatility(ts::BackwardFlatVolatility, t::ModelTime, result_size::TermstructureResultSize = TermstructureVector)

Return a vector of volatilities for a given observation time t.

survival(ts::CreditDefaultTermstructure, t::ModelTime)

Return the survival probability with observation time t.

survival(ts::FlatSpreadCurve, t::ModelTime)

Calculate survival probability.

survival(ts::LogSurvivalCurve, t::ModelTime)

Calculate survival probability.