monte carlo: valuation of barrier options

This adds support for the valuation of simple barrier options via monte
carlo.

Project.toml

@@ -7,6 +7,7 @@ version = "1.2.1"
 BusinessDays = "4f18b42c-503e-5345-9536-bb0f25fc7038"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+LanguageServer = "2b0e0bc5-e4fd-59b4-8912-456d1b03d8d7"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

src/contracts.jl

@@ -184,6 +184,9 @@ The maturity date of a contract `c` is the date at which contract is completed o
 """
 maturitydate(c::WhenAt{C}) where {C} = c.p.a[2].val
 maturitydate(c::AnytimeBefore{C}) where {C} = c.p.a[2].val
+maturitydate(c::Anytime{LiftObs{F,Tuple{ValueObs{S, A},ConstObs{A}},Bool},C}) where {S,F,A,C} = maturitydate(c.c)
+maturitydate(c::Anytime{LiftObs{F,Tuple{ConstObs{A}, ValueObs{S, A}},Bool},C}) where {S,F,A,C} = maturitydate(c.c)
+maturitydate(c::Give{C}) where {C} = maturitydate(c.c) 
 
 """
     strikeprice(c::Contract)

src/models/lsmc.jl

@@ -6,8 +6,6 @@ end
 
 function value(m::LeastSquaresMonteCarlo, c::AnytimeBefore{C}) where C
     uc = c.c # underlying contract
-    uc1 = uc.c1
-    uc2 = uc.c2
     N = date2index(m.m, maturitydate(c))
     R = discount(m.m.core.yieldcurve, m.m.dates[2]) # TODO: could be better...
 

src/models/montecarlo.jl

@@ -67,8 +67,20 @@ function value(m::MonteCarloModel, c::WhenAt{SingleStock})
 end
 value(m::MonteCarloModel, c::SingleStock) = value(m.core, c)
 
+# value of a barrier option
+function value(m::MonteCarloModel, c::Anytime{LiftObs{F,Tuple{ValueObs{SingleStock, A},ConstObs{A}},Bool},C}) where {F,A,C} 
+    N = date2index(m, maturitydate(c))
+    discount(m.core.yieldcurve, maturitydate(c)) * mean(valueat(ms, c.c, N) for ms in scenarios(m) if observe(ms, c.p, any))
+end
+
+function value(m::MonteCarloModel, c::Anytime{LiftObs{F,Tuple{ConstObs{A},ValueObs{SingleStock,A}},Bool},C}) where {F,A,C} 
+    N = date2index(m, maturitydate(c))
+    discount(m.core.yieldcurve, maturitydate(c)) * mean(valueat(ms, c.c, N) for ms in scenarios(m) if observe(ms, c.p, any))
+end
+
 function value(m::MonteCarloModel, c::Cond{O, C1, C2}) where {O<:Observable{Bool}, C1<:Contract, C2<:Contract}
-    mean([observeat(ms, c.p, 1) ? valueat(ms, c.c1, 1) : valueat(ms, c.c2, 1) for ms in scenarios(m)])
+    N = date2index(m, maturitydate(c))
+    discount(m.core.yieldcurve, maturitydate(c)) * mean(valueat(ms, c, N) for ms in scenarios(m))
 end
 
 
@@ -149,6 +161,13 @@ function valueat(m::MonteCarloScenario, c::WhenAt{Either{C1,C2}}, i::Int) where
     forward_rate(m.core.yieldcurve, t, T) * maximum
 end
 
+function observe(ms::MonteCarloScenario, o::LiftObs{F,Tuple{ValueObs{SingleStock,A},ConstObs{A}},Bool}, predicateFold::Function)::Bool where {F,A}
+    predicateFold(p -> o.f(p, o.a[2].val), ms.path)    
+end
+function observe(ms::MonteCarloScenario, o::LiftObs{F,Tuple{ConstObs{A}, ValueObs{SingleStock,A}},Bool}, predicateFold::Function)::Bool where {F,A}
+    predicateFold(p -> o.f(o.a[1].val, p), ms.path)    
+end
+
 observeat(_::MonteCarloScenario, o::ConstObs{T}, _::Int) where T = o.val 
 function observeat(m::MonteCarloScenario, o::LiftObs{F, Tuple{DateObs, ConstObs{Date}}, Bool}, i::Int) where F
     (_, t2) = o.a

test/montecarlo.jl

@@ -1,7 +1,9 @@
 using Miletus, Dates
 using Test
 
-import Miletus: WhenAt
+import Miletus: WhenAt, ConstObs, ValueObs, LiftObs
+using Miletus.Currency
+using Miletus.Currency: @defcurrency
 
 d1 = today()
 d2 = d1 + Day(120)
@@ -32,3 +34,20 @@ c = WhenAt(d2, SingleStock())
 
 o = EuropeanCall(d2, SingleStock(), 100.00USD) # std(y)/mean(y) = 0.013
 @test isapprox(value(m, o), value(mcm, o), rtol=0.013*4)
+
+# barrier options
+@defcurrency CHF
+
+initialFixing = Date("2020-12-15")
+maturity = Date("2023-12-15")
+faceValue = 1000CHF
+
+smi = SingleStock()
+
+euput = EuropeanPut(maturity, smi, 100.00CHF)
+bond = ZCB(maturity, faceValue)
+knockedIn = LiftObs(<, ConstObs(1.0CHF), ValueObs{SingleStock, CurrencyQuantity{CurrencyUnit{:CHF}, Float64}}(smi))
+brc = Both(bond, Anytime(knockedIn, Give(euput)))
+m = GeomBMModel(initialFixing, faceValue, 0.05, 0.0, 0.3)
+mcm = montecarlo(m, initialFixing:Day(1):maturity, 10_000)
+@test isapprox(value(mcm, brc), 860.70CHF, rtol=1e-2)