BSM tests (#12)

src/equity.jl

@@ -13,7 +13,12 @@ struct BlackScholesMerton{T,U,V} <:EquityModel
 end
 function nextrate(M::BlackScholesMerton,prior,time,timestep)
     r, q, σ = M.r, M.q, M.σ
-    prior + (r-q)*prior * timestep + prior * M.σ * sqrt(timestep) * randn()
+    # Hull Options, Futures, & Other Derivatives, 10th ed., pg 470
+    return (
+        prior *
+        exp((r- q - σ^2 / 2) *  timestep + 
+         σ * sqrt(timestep) * randn())
+    )
 end
 
 """

test/Project.toml

@@ -1,3 +1,7 @@
 [deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+EconomicScenarioGenerators = "1d18cbdc-9ca7-45fd-a8b2-b9434f9145be"
+HypothesisTests = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
+StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Yields = "d7e99b2f-e7f3-4d9e-9f01-2338fc023ad3"

test/equity.jl

@@ -1,6 +1,6 @@
 @testset "EquityModel" begin
 
-    @testset "Vasicek" begin
+    @testset "BlackScholesMerton" begin
         m = BlackScholesMerton(0.01,0.02,.15,100.)
 
         s = ScenarioGenerator(
@@ -19,6 +19,18 @@
 
         @test length(s) == 61
 
+        prices = [last(collect(s)) for _ in 1:10_000]
+
+        dist = price_distribution(s)
+
+        # we expect that the prices are lognormally distributed
+        # and reject the null hypothesis that they are not if p less than some threshold
+        # therefore, for test to pass we should fail to reject the null hypothesis and p
+        # should be large
+        t = HypothesisTests.ExactOneSampleKSTest(prices,dist)
+        @test HypothesisTests.pvalue(t) > 0.05
+
+
         @testset "#14 - odd time steps" begin
             m = BlackScholesMerton(0.01,0.02,.15,100.)
 

test/interest.jl

@@ -2,7 +2,7 @@
 @testset "InterestRateModel" begin
 
     @testset "Vasicek" begin
-        m = Vasicek(0.136,0.0168,0.0119,Continuous(0.01))
+        m = Vasicek(0.136,0.0168,0.0119,Yields.Continuous(0.01))
         s = ScenarioGenerator(
                 1.,                              # timestep
                 30.,                             # projection horizon
@@ -23,7 +23,7 @@
     end
 
     @testset "CoxIngersollRoss" begin
-        m = CoxIngersollRoss(0.136,0.0168,0.0119,Continuous(0.01))
+        m = CoxIngersollRoss(0.136,0.0168,0.0119,Yields.Continuous(0.01))
         s = ScenarioGenerator(
                 1.,                              # timestep
                 30.,                             # projection horizon
@@ -72,7 +72,7 @@
         end
 
         @testset "with Rate" begin
-            m = HullWhite(.1,.005,Continuous(0.05))
+            m = HullWhite(.1,.005,Yields.Continuous(0.05))
 
             s = ScenarioGenerator(
                 1.,                              # timestep

test/runtests.jl

@@ -1,6 +1,9 @@
 using EconomicScenarioGenerators
 using Test
 using Yields
+using Distributions
+using HypothesisTests
 
+include("utils.jl")
 include("interest.jl")
 include("equity.jl")

test/utils.jl

@@ -0,0 +1,15 @@
+# http://www.timworrall.com/fin-40008/bscholes.pdf
+
+function price_distribution(m::BlackScholesMerton,T)
+    r, q, σ = m.r, m.q, m.σ
+    return LogNormal(
+        log(m.initial) + (r-q-σ^2/2) * T,
+        sqrt(T) * σ
+        )
+end
+
+function price_distribution(s::ScenarioGenerator{N,T}) where {N,T<:BlackScholesMerton}
+    m = s.model
+    t = s.endtime
+    price_distribution(m,t)
+end