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Scenarios

Scenario Cube

DiffFusion.ScenarioCube — Type
struct ScenarioCube
    X::AbstractArray
    times::AbstractVector
    leg_aliases::AbstractVector
    numeraire_context_key::String
    discount_curve_key::Union{String,Nothing}
end

A ScenarioCube represents the result of MC pricing results of a list of product legs and is calculated for a list of observation times.

Elements are

  • X - tensor of size (N_1, N_2, N_3) and type ModelValue where
    • N_1 is number of Monte Carlo paths,
    • N_2 is number of time steps,
    • N_3 is number of legs.
  • times - a vector representing observation times.
  • leg_aliases - a list of aliases (identifiers) corresponding to each leg
  • numeraire_context_key - the context_key of the NumeraireEntry; this label should indicate the cash flow currency.
  • discount_curve_key - a flag specifying whether prices in X are discounted prices (for XVA) or undiscounted prices (for CCR).
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Pricing Scenarios

DiffFusion.scenarios — Function
scenarios(
    legs::AbstractVector,
    times::AbstractVector,
    path::Path,
    discount_curve_key::Union{String,Nothing};
    with_progress_bar::Bool = true,
    )

Calculate ScenarioCube for a vector of CashFlowLeg objects and a vector of scenario observation times.

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Scenario Cube Operations

DiffFusion.join_scenarios — Function
join_scenarios(cube1::ScenarioCube, cube2::ScenarioCube)

Join two scenario cubes along leg-axis.

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join_scenarios(cubes::AbstractVector{ScenarioCube})

Join a list of scenario cubes along leg-axis.

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DiffFusion.interpolate_scenarios — Function
interpolate_scenarios(
    t::ModelTime,
    cube::ScenarioCube,
    )

Interpolation scenarios along time axis.

We implement linear interpolation with flat extrapolation.

Other interpolations, e.g., piece-wise flat or Brownian Bridge should be incorporated here.

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DiffFusion.aggregate — Function
aggregate(
    scens::ScenarioCube,
    average_paths::Bool=true,
    aggregate_legs::Bool=true,
    )

Average paths and aggregate legs in ScenarioCube.

scens is the input ScenarioCube.

If average_paths is true then reduce scenario cube along path axis. Otherwise, keep individual paths.

If aggregate_legs is true then reduce scenario cube along the axis of legs. Otherwise, keep individual legs.

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Scenario Generation Using Parallel Computations

We implement various strategies for parallelisation of scenario generation: multi-threading multi-processing and a mixed approach.

It turns out that Julia's garbage collection impedes scaling properties of multi-threaded scenario generation. Parallel garbage collection introduced with Julia 1.10 does not seem to help.

Fortunately, multi-processing can be used efficiently for scenario generation. This circumvents the garbage collection limitation.

We also find that a combination of multi-processing and multi-threading can be most efficient. With such a mixed approach we can leverage the lower overhead from multi-threading and mitigate the impact of single-threaded garbage collection.

DiffFusion.scenarios_parallel — Function
scenarios_parallel(
    legs::AbstractVector,
    times::AbstractVector,
    path::DiffFusion.Path,
    discount_curve_key::Union{String,Nothing},
    )

Combined multi-processing (distributed) and multi-threaded calculation of ScenarioCube for a vector of CashFlowLeg objects and a vector of scenario observation times.

Multi-processing is implemented via Distributed module. The number of processes can be controlled via -p argument when calling julia.

For each distributed process, multi-threading is implemented via Threads.@threads.

Number of threads used for parallel calculation is specified by the environment variable JULIA_NUM_THREADS or the -t argument when calling julia.

It is recommended to use this method in conjunction with thread pinning via ThreadPinning.jl and pinthreads(:cores).

Moreover, to avoid over-subscription in conjunction with BLAS it is recommended to set LinearAlgebra.BLAS.set_num_threads(1).

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DiffFusion.scenarios_multi_threaded — Function
scenarios_multi_threaded(
    legs::AbstractVector,
    times::AbstractVector,
    path::Path,
    discount_curve_key::Union{String,Nothing};
    with_progress_bar::Bool = true,
    )

Multi-threaded calculation of ScenarioCube for a vector of CashFlowLeg objects and a vector of scenario observation times.

Multi-threading is implemented via Base.Threads and the Threads.@threads macro.

Number of threads used for parallel calculation is specified by the environment variable JULIA_NUM_THREADS or the -t argument when calling julia.

It is recommended to use this method in conjunction with thread pinning via ThreadPinning.jl and pinthreads(:cores).

Moreover, to avoid over-subscription in conjunction with BLAS it is recommended to set LinearAlgebra.BLAS.set_num_threads(1).

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DiffFusion.scenarios_distributed — Function
scenarios_distributed(
    legs::AbstractVector,
    times::AbstractVector,
    path::DiffFusion.Path,
    discount_curve_key::Union{String,Nothing},
    )

Multi-processing (distributed) calculation of ScenarioCube for a vector of CashFlowLeg objects and a vector of scenario observation times.

Multi-processing is implemented via Distributed module. The number of processes can be controlled via -p argument when calling julia.

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