Add Monte-Carlo Path and methods

src/DiffFusion.jl

@@ -9,6 +9,7 @@ using QuadGK
 using Sobol
 using SparseArrays
 
+import Base.length
 
 """
 A type alias for variables representing time.
@@ -35,11 +36,14 @@ include("models/rates/SeparableHjmModel.jl")
 include("models/rates/GaussianHjmModel.jl")
 include("models/futures/MarkovFutureModels.jl")
 
-include("paths/Context.jl")
-
 include("simulations/RandomNumbers.jl")
 include("simulations/Simulation.jl")
 
+include("paths/AbstractPath.jl")
+include("paths/Context.jl")
+include("paths/Path.jl")
+include("paths/PathMethods.jl")
+
 include("utils/Integrations.jl")
 include("utils/InterpolationMethods.jl")
 

src/paths/AbstractPath.jl

@@ -0,0 +1,240 @@
+
+"""
+    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.
+"""
+abstract type AbstractPath end
+
+"""
+    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.
+"""
+function length(p::AbstractPath)
+    error("AbstractPath needs to implement length method.")
+end
+
+"""
+    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.
+"""
+function numeraire(p::AbstractPath, t::ModelTime, curve_key::String)
+    error("AbstractPath needs to implement numeraire method.")
+end
+
+
+"""
+    bank_account(p::AbstractPath, t::ModelTime, key::String)
+
+Calculate a continuous compounded bank account value.
+"""
+function bank_account(p::AbstractPath, t::ModelTime, key::String)
+    error("AbstractPath needs to implement bank_account method.")
+end
+
+
+"""
+    zero_bond(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+
+Calculate a zero coupon bond price.
+"""
+function zero_bond(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+    error("AbstractPath needs to implement zero_bond method.")
+end
+
+
+"""
+    asset(p::AbstractPath, t::ModelTime, key::String)
+
+Calculate asset price.
+"""
+function asset(p::AbstractPath, t::ModelTime, key::String)
+    error("AbstractPath needs to implement asset method.")
+end
+
+
+"""
+    forward_asset(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+
+Calculate forward asset price as expectation in T-forward measure.
+"""
+function forward_asset(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+    error("AbstractPath needs to implement forward_asset method.")
+end
+
+
+"""
+    fixing(p::AbstractPath, t::ModelTime, key::String)
+
+Return a fixing from a term structure.
+
+This is used to handle fixings for indices etc.
+"""
+function fixing(p::AbstractPath, t::ModelTime, key::String)
+    error("AbstractPath needs to implement fixing method.")
+end
+
+"""
+    asset_convexity_adjustment(
+        p::AbstractPath,
+        t::ModelTime,
+        T0::ModelTime,
+        T1::ModelTime,
+        T2::ModelTime,
+        key::String
+        )
+
+Return the convexity adjustment for a YoY asset payoff.
+"""
+function asset_convexity_adjustment(
+    p::AbstractPath,
+    t::ModelTime,
+    T0::ModelTime,
+    T1::ModelTime,
+    T2::ModelTime,
+    key::String
+    )
+    error("AbstractPath needs to implement asset_convexity_adjustment method.")
+end
+
+"""
+    forward_index(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+
+Expectation E_t^T[S_T] of a tradeable asset.
+"""
+function forward_index(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+    error("AbstractPath needs to implement forward_index method.")
+end
+
+"""
+    index_convexity_adjustment(
+        p::AbstractPath,
+        t::ModelTime,
+        T0::ModelTime,
+        T1::ModelTime,
+        T2::ModelTime,
+        key::String
+        )
+
+Return the convexity adjustment for a YoY index payoff.
+"""
+function index_convexity_adjustment(
+    p::AbstractPath,
+    t::ModelTime,
+    T0::ModelTime,
+    T1::ModelTime,
+    T2::ModelTime,
+    key::String
+    )
+    error("AbstractPath needs to implement index_convexity_adjustment method.")
+end
+
+
+"""
+    future_index(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+
+Expectation E_t^Q[F(T,T)] of a Future index/price.
+"""
+function future_index(p::AbstractPath, t::ModelTime, T::ModelTime, key::String)
+    error("AbstractPath needs to implement future_index method.")
+end
+
+
+"""
+    swap_rate_variance(
+        p::AbstractPath,
+        t::ModelTime,
+        T::ModelTime,
+        swap_times::AbstractVector,
+        yf_weights::AbstractVector,
+        key::String,
+        )
+
+Calculate the normal model variance of a swap rate via Gaussian
+swap rate approximation.
+"""
+function swap_rate_variance(
+    p::AbstractPath,
+    t::ModelTime,
+    T::ModelTime,
+    swap_times::AbstractVector,
+    yf_weights::AbstractVector,
+    key::String,
+    )
+    error("AbstractPath needs to implement swap_rate_variance method.")
+end
+
+
+"""
+    forward_rate_variance(
+    p::AbstractPath,
+    t::ModelTime,
+    T::ModelTime,
+    T0::ModelTime,
+    T1::ModelTime,
+    key::String,
+    )
+
+Calculate the lognormal model variance of a forward looking or
+backward looking forward rate.
+"""
+function forward_rate_variance(
+    p::AbstractPath,
+    t::ModelTime,
+    T::ModelTime,
+    T0::ModelTime,
+    T1::ModelTime,
+    key::String,
+    )
+    error("AbstractPath needs to implement forward_rate_variance method.")
+end
+
+
+"""
+    asset_variance(
+        p::AbstractPath,
+        t::ModelTime,
+        T::ModelTime,
+        key::String,
+        )
+
+Calculate the lognormal model variance of an asset spot price
+over the time period [t,T].
+"""
+function asset_variance(
+    p::AbstractPath,
+    t::ModelTime,
+    T::ModelTime,
+    key::String,
+    )
+    error("AbstractPath needs to implement asset_variance method.")
+end
+
+
+"""
+    @enum(
+        PathInterpolation,
+        NoPathInterpolation,
+        LinearPathInterpolation,
+    )
+
+PathInterpolation encodes how simulated states can be interpolates.
+"""
+@enum(
+    PathInterpolation,
+    NoPathInterpolation,
+    LinearPathInterpolation,
+)
+