separate derivs, add specific test, update parameters and example (#52)

* separate derivs, add specific test

* fix function name to be in correct order

* Tests Passing

* compat bound

* upate version

* min Julia Version

.github/workflows/CI.yml

@@ -18,7 +18,7 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.9'
+          - '1.10'
           - '1'
         os:
           - ubuntu-latest

Project.toml

@@ -1,10 +1,7 @@
 name = "EconomicScenarioGenerators"
 uuid = "1d18cbdc-9ca7-45fd-a8b2-b9434f9145be"
 authors = ["Alec Loudenback <alecloudenback@gmail.com> and contributors"]
-version = "0.6.1"
-
-[weakdeps]
-FinanceModels = "77f2ae65-bdde-421f-ae9d-22f1af19dd76"
+version = "0.7.0"
 
 [deps]
 Copulas = "ae264745-0b69-425e-9d9d-cf662c5eec93"
@@ -14,17 +11,20 @@ ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Transducers = "28d57a85-8fef-5791-bfe6-a80928e7c999"
 
+[weakdeps]
+FinanceModels = "77f2ae65-bdde-421f-ae9d-22f1af19dd76"
+
 [extensions]
 FinanceModelsExt = "FinanceModels"
 
 [compat]
 Copulas = "0.1"
-FinanceCore = "2"
-FinanceModels = "4 - 4.7"
-Transducers = "0.4"
 Distributions = "0.25"
+FinanceCore = "2"
+FinanceModels = "4.9"
 ForwardDiff = "^0.10"
-julia = "1.9"
+Transducers = "0.4"
+julia = "1.10"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

README.md

@@ -64,7 +64,7 @@ YieldCurve(s)
 
 ```
 
-will produce a yield curve object:
+will produce a yield curve object (if `UnicodePlots.jl` has also been imported):
 
 ```julia-repl
               ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Yield Curve (FinanceModels.Yield.Spline)⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀           
@@ -102,24 +102,22 @@ Construct a yield curve and use that as the arbitrage-free forward curve within
 
 ```julia
 using FinanceModels, EconomicScenarioGenerators
-rates =[0.01, 0.01, 0.03, 0.05, 0.07, 0.16, 0.35, 0.92, 1.40, 1.74, 2.31, 2.41] ./ 100
-mats = [1/12, 2/12, 3/12, 6/12, 1, 2, 3, 5, 7, 10, 20, 30]
-
-
-curve = FinanceModels.fit(
-    Spline.Cubic(),
-    CMTYield.(rates,mats),
-    Fit.Bootstrap()
+rates = [0.01, 0.01, 0.03, 0.05, 0.07, 0.16, 0.35, 0.92, 1.40, 1.74, 2.31, 2.41] ./ 100
+mats = [1 / 12, 2 / 12, 3 / 12, 6 / 12, 1, 2, 3, 5, 7, 10, 20, 30]
+c = FinanceModels.fit(
+    FinanceModels.Spline.Cubic(),
+    FinanceModels.ZCBYield.(rates, mats),
+    FinanceModels.Fit.Bootstrap()
 )
 
+m = HullWhite(2.0, 0.025, c)
 
-m = HullWhite(.1,.002,curve) # a, σ, curve
+s = EconomicScenarioGenerators.ScenarioGenerator(
+    0.01,                              # timestep
+    30.0,                             # projection horizon
+    m
+)
 
-s = ScenarioGenerator(
-        1/12,  # timestep
-        30., # projection horizon
-        m,  # model
-    )
 ```
 
 Create 1000 yield curves from the scenario generator:
@@ -132,22 +130,21 @@ curves = [YieldCurve(s) for i in 1:n]
 Plot the result:
 
 ```julia
-using Plots
+using CairoMakie
 
 times = 1:30
-p=plot(title="EconomicScenarioGenerators.jl Hull White Model")
 
+fig = Figure()
+axis = Axis(fig[1,1],title="EconomicScenarioGenerators.jl Hull White Model",xlabel="time",ylabel="rate")
 # plot the zero rates
 for d in curves
-    plot!(p,times,rate.(zero.(d,times)),alpha=0.2,label="")
+    lines!(axis,times,rate.(zero.(d,times)),alpha=0.1,label="")
 end
-
-plot!(times,rate.(zero.(curve,times)),line=(:black, 5), label="Given Yield Curve")
-p
-
+lines!(axis,times,rate.(zero.(c,times)),color=:black,linewidth=7)
+fig
 ```
 
-![image](https://user-images.githubusercontent.com/711879/182291819-66a0fa9e-7aab-4e52-b434-58494257d005.svg)
+![image](https://github.com/JuliaActuary/EconomicScenarioGenerators.jl/assets/711879/09ef7136-30bf-44cf-865c-987d0df92a4a)
 
 ### Equity Model Examples
 

ext/FinanceModelsExt.jl

@@ -14,9 +14,7 @@ function ESG.θ(M::ESG.HullWhite{T}, time, timestep) where {T<:Union{FinanceMode
     # https://quant.stackexchange.com/questions/8724/how-to-calibrate-hull-white-from-zero-curve
     # https://mdpi-res.com/d_attachment/mathematics/mathematics-08-01719/article_deploy/mathematics-08-01719-v2.pdf?version=1603181408
     a = M.a
-    f(t) = log(FinanceCore.discount(M.curve, t[1]))
-    δf = -only(ForwardDiff.hessian(f, [time]))::Float64
-    f_t = -only(ForwardDiff.gradient(f, [time]))::Float64
+    δf, f_t = ESG.__δf(M, time)
 
     return δf + f_t * a + M.σ^2 / (2 * a) * (1 - exp(-2 * a * time))
 

src/interest.jl

@@ -155,6 +155,7 @@ end
 # See FinanceModels.jl for HullWhite with a YieldCurve defining theta
 
 __initial_value(m::HullWhite, timestep) = FinanceCore.forward(m.curve, 0.0, timestep)
+__initial_value(m::HullWhite{T}, timestep) where {T<:Real} = m.curve
 
 # how would HullWhite be constructed if not giving it a curve?
 function nextvalue(M::HullWhite{T}, prior, time, timestep, variate) where {T}
@@ -170,8 +171,16 @@ function θ(M::HullWhite{T}, time, timestep) where {T<:Real}
     # https://quant.stackexchange.com/questions/8724/how-to-calibrate-hull-white-from-zero-curve
     a = M.a
     δf = 0
-    f_t = M.θ
+    f_t = M.curve
 
     return δf + f_t * a + M.σ^2 / (2 * a) * (1 - exp(-2 * a * time))
 
+end
+
+function __δf(model, time)
+    f(t) = log(FinanceCore.discount(model.curve, t[1]))
+    δf = -only(ForwardDiff.hessian(f, [time]))::Float64
+    f_t = -only(ForwardDiff.gradient(f, [time]))::Float64
+    # @show time, f(time) / time, f_t, δf, f(time) / time + f_t
+    return δf, f_t
 end

test/Correlated.jl

@@ -35,7 +35,7 @@
                 Fit.Bootstrap()
             )
 
-            m = HullWhite(0.1, 0.01, c)
+            m = HullWhite(2.0, 0.01, c)
 
             s = ScenarioGenerator(
                 0.1,                              # timestep
@@ -142,7 +142,7 @@
                 CMTYield.(rates, mats),
                 Fit.Bootstrap())
 
-            m = HullWhite(0.1, 0.01, c)
+            m = HullWhite(2.0, 0.01, c)
 
             s = ScenarioGenerator(
                 0.1,                              # timestep

test/Project.toml

@@ -1,7 +1,6 @@
 [deps]
 Copulas = "ae264745-0b69-425e-9d9d-cf662c5eec93"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
-EconomicScenarioGenerators = "1d18cbdc-9ca7-45fd-a8b2-b9434f9145be"
 FinanceCore = "b9b1ffdd-6612-4b69-8227-7663be06e089"
 FinanceModels = "77f2ae65-bdde-421f-ae9d-22f1af19dd76"
 HypothesisTests = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"

test/interest.jl

@@ -77,12 +77,12 @@
             rates = [0.01, 0.01, 0.03, 0.05, 0.07, 0.16, 0.35, 0.92, 1.40, 1.74, 2.31, 2.41] ./ 100
             mats = [1 / 12, 2 / 12, 3 / 12, 6 / 12, 1, 2, 3, 5, 7, 10, 20, 30]
             c = FinanceModels.fit(
-                FinanceModels.Spline.Quadratic(),
-                FinanceModels.CMTYield.(rates, mats),
+                FinanceModels.Spline.Cubic(),
+                FinanceModels.ZCBYield.(rates, mats),
                 FinanceModels.Fit.Bootstrap()
             )
 
-            m = HullWhite(0.1, 0.001, c)
+            m = HullWhite(2.0, 0.01, c)
 
             s = ScenarioGenerator(
                 1.0,                              # timestep
@@ -95,14 +95,14 @@
 
 
             s = EconomicScenarioGenerators.ScenarioGenerator(
-                0.05,                              # timestep
+                0.01,                              # timestep
                 30.0,                             # projection horizon
                 m,
                 StableRNG(1)
             )
 
             v = collect(s)
-            @test length(v) == 601
+            @test length(v) == 3001
 
             @test YieldCurve(s) isa FinanceModels.Yield.AbstractYieldModel
 
@@ -119,7 +119,7 @@
 
         @testset "with Rate" begin
             c = FinanceCore.Continuous(0.03)
-            m = HullWhite(0.1, 0.001, c)
+            m = HullWhite(2.0, 0.001, c)
 
             s = ScenarioGenerator(
                 1.0,                              # timestep
@@ -152,8 +152,52 @@
             end
 
         end
-    end
+        @testset "constant derivative" begin
+
+            import FinanceModels: AbstractYieldModel, discount
+
+            # a yield curve where the rate of change of the instantaneous forward is constant
+            struct ConstDeriv <: FinanceModels.Yield.AbstractYieldModel
+                d::Float64
+                initial::Float64
+            end
+
+            FinanceCore.discount(c::ConstDeriv, time) = exp(-(time^2 * c.d) / 2 - c.initial * time)
+
+
+            m = HullWhite(0.1, 0.001, ConstDeriv(0.01, 0.02))
+            a, b = EconomicScenarioGenerators.__δf(m, 1)
+            @test a ≈ 0.01
+            @test b ≈ 0.02 + 0.01 * 1
+            a, b = EconomicScenarioGenerators.__δf(m, 2)
+            @test a ≈ 0.01
+            @test b ≈ 0.02 + 0.01 * 2
+
+        end
+
+        @testset "other functional forms" begin
 
+            # discount = exp(-time^power/denom)
+            struct Power <: FinanceModels.Yield.AbstractYieldModel
+                p::Float64
+                denom::Float64
+            end
+
+            FinanceCore.discount(c::Power, time) = exp(-(time)^c.p / c.denom)
+
+            m = HullWhite(0.1, 0.001, Power(2, 10))
+            a, b = EconomicScenarioGenerators.__δf(m, 1)
+            @test a ≈ 1 / 5
+            @test b ≈ 1 / 5
+            a, b = EconomicScenarioGenerators.__δf(m, 2)
+            @test a ≈ 1 / 5
+            @test b ≈ 2 / 5
+
+
+
+
+        end
+    end
 
 
 end