Add functions for Vanilla asset option simulation

src/DiffFusion.jl

@@ -70,8 +70,10 @@ include("payoffs/BinaryNodes.jl")
 include("payoffs/RatesPayoffs.jl")
 include("payoffs/RatesOptions.jl")
 include("payoffs/AmcPayoffs.jl")
+include("payoffs/AssetOptions.jl")
 
 include("products/Cashflows.jl")
+include("products/AssetOptionFlows.jl")
 include("products/RatesCoupons.jl")
 include("products/CashFlowLeg.jl")
 include("products/SwaptionLeg.jl")

src/models/hybrid/CompositeModel.jl

@@ -187,6 +187,75 @@ function forward_rate_variance(
     )
 end
 
+"""
+    asset_variance(
+        m::CompositeModel,
+        ast_alias::Union{String, Nothing},
+        dom_alias::Union{String, Nothing},
+        for_alias::Union{String, Nothing},
+        t::ModelTime,
+        T::ModelTime,
+        X::ModelState,
+        )
+
+Calculate the lognormal model variance of an asset spot price
+over the time period [t,T].
+"""
+function asset_variance(
+    m::CompositeModel,
+    ast_alias::Union{String, Nothing},
+    dom_alias::Union{String, Nothing},
+    for_alias::Union{String, Nothing},
+    t::ModelTime,
+    T::ModelTime,
+    X::ModelState,
+    )
+    # we implement a staged approach to determine the correlation holder
+    ch = nothing
+    ast_model = nothing
+    dom_model = nothing
+    for_model = nothing
+    if !isnothing(for_alias)
+        for_model = m.models[m.model_dict[for_alias]]
+        ch = correlation_holder(for_model)
+    end
+    if !isnothing(dom_alias)
+        dom_model = m.models[m.model_dict[dom_alias]]
+        if !isnothing(ch)
+            # this is only a plausibility check
+            alias(ch) == alias(correlation_holder(dom_model))
+        end
+        ch = correlation_holder(dom_model)
+    end
+    if !isnothing(ast_alias)
+        ast_model = m.models[m.model_dict[ast_alias]]
+        if !isnothing(ch)
+            # this is only a plausibility check
+            alias(ch) == alias(correlation_holder(ast_model))
+        end
+        ch = correlation_holder(ast_model)
+    end
+    if isnothing(ch)
+        # in this case all models are deterministic
+        return 0.0
+    end
+    if !state_dependent_Sigma(m)
+        # We need to make sure that the Sigma_T(...) call in covaiance(...)
+        # method can be executed.
+        X = nothing
+    end
+    return asset_variance(
+        ast_model,
+        dom_model,
+        for_model,
+        ch,
+        t,
+        T,
+        X,
+    )
+end
+
+
 """
     state_dependent_Theta(m::CompositeModel)
 

src/paths/PathMethods.jl

@@ -503,7 +503,7 @@ function forward_rate_variance(
         return zeros(length(p))  # deterministic model
     end
     #
-    return ones(length(p)) * forward_rate_variance(
+    return ones(length(p)) .* forward_rate_variance(
         p.sim.model,
         entry.model_alias,
         t,
@@ -512,3 +512,45 @@ function forward_rate_variance(
         T1,
     )
 end
+
+
+"""
+    asset_variance(
+        p::Path,
+        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::Path,
+    t::ModelTime,
+    T::ModelTime,
+    key::String,
+    )
+    (context_key, ts_key_1, ts_key_2, op) = context_keys(key)
+    @assert op in (_empty_context_key, "-")
+    entry = p.context.assets[context_key]
+    #
+    if isnothing(entry.asset_model_alias) &&
+        isnothing(entry.domestic_model_alias) &&
+        isnothing(entry.foreign_model_alias)
+        return zeros(length(p))  # deterministic model
+    end
+    #
+    X = state_variable(p.sim, t, p.interpolation)
+    SX = model_state(X, p.state_alias_dict)
+    #
+    return ones(length(p)) .* asset_variance(
+        p.sim.model,
+        entry.asset_model_alias,
+        entry.domestic_model_alias,
+        entry.foreign_model_alias,
+        t,
+        T,
+        SX,
+    )
+end

src/payoffs/AssetOptions.jl

@@ -0,0 +1,106 @@
+
+"""
+    struct VanillaAssetOption <: Payoff
+        obs_time::ModelTime
+        expiry_time::ModelTime
+        forward_price::ForwardAsset
+        strike_price::Payoff
+        call_put::ModelValue
+    end
+
+The time-t forward price of an option paying [ϕ(F-K)]^+. Forward asset price *F* is determined
+at `expiry_time`.
+
+Option forward price is calculated as expectation in T-forward measure where T corresponds
+to the expiry time. Conditioning (for time-t price) is on information at `obs_time`.
+"""
+struct VanillaAssetOption <: Payoff
+    obs_time::ModelTime
+    expiry_time::ModelTime
+    forward_price::ForwardAsset
+    strike_price::Payoff
+    call_put::ModelValue
+end
+
+"""
+    VanillaAssetOption(
+        forward_price::ForwardAsset,
+        strike_price::Payoff,
+        call_put::ModelValue,
+        )
+
+Create a `VanillaAssetOption` payoff.
+"""
+function VanillaAssetOption(
+    forward_price::ForwardAsset,
+    strike_price::Payoff,
+    call_put::ModelValue,
+    )
+    #
+    @assert obs_time(strike_price) ≤ forward_price.obs_time  # payoff must be time-t measurable
+    @assert call_put in (+1.0, -1.0)
+    return VanillaAssetOption(
+        forward_price.obs_time,
+        forward_price.maturity_time,
+        forward_price,
+        strike_price,
+        call_put,
+    )
+end
+
+
+"""
+    obs_time(p::VanillaAssetOption)
+
+Return VanillaAssetOption observation time.
+"""
+function obs_time(p::VanillaAssetOption)
+    return p.obs_time
+end
+
+
+"""
+    obs_times(p::VanillaAssetOption)
+
+Return all VanillaAssetOption observation times. 
+"""
+function obs_times(p::VanillaAssetOption)
+    times = Set(obs_time(p))
+    times = union(times, obs_times(p.strike_price))
+    return times
+end
+
+
+"""
+    at(p::VanillaAssetOption, path::AbstractPath)
+
+Evaluate a `VanillaAssetOption` at a given `path`, *X(omega)*.
+"""
+function at(p::VanillaAssetOption, path::AbstractPath)
+    F = at(p.forward_price, path)
+    K = at(p.strike_price, path)
+    ν² = asset_variance(path, p.obs_time, p.expiry_time, p.forward_price.key)
+    if all(ν² .≤ 0.0)
+        # calculate intrinsic value
+        return max.(p.call_put*(F - K), 0.0)
+    end
+    V = black_price(K, F, sqrt.(ν²), p.call_put)
+    return V
+end
+
+
+"""
+    string(p::VanillaAssetOption)
+
+Formatted (and shortened) output for VanillaAssetOption payoff.
+"""
+string(p::VanillaAssetOption) = begin
+    type = ""
+    if p.call_put == 1.0
+        type = "Call"
+    end
+    if p.call_put == -1.0
+        type = "Put"
+    end
+    @sprintf("%s(%s, %s)", type, string(p.forward_price), string(p.strike_price))
+end

src/products/AssetOptionFlows.jl

@@ -0,0 +1,48 @@
+
+"""
+    struct VanillaAssetOptionFlow <: CashFlow
+        expiry_time::ModelTime
+        pay_time::ModelTime
+        strike_price::ModelValue
+        call_put::ModelValue
+        asset_key::String
+    end
+
+A `CashFlow` representing a Call or Put option on an `Asset`.
+"""
+struct VanillaAssetOptionFlow <: CashFlow
+    expiry_time::ModelTime
+    pay_time::ModelTime
+    strike_price::ModelValue
+    call_put::ModelValue
+    asset_key::String
+end
+
+
+"""
+    amount(cf::VanillaAssetOptionFlow)
+
+Return the payoff of the `VanillaAssetOptionFlow`.
+"""
+function amount(cf::VanillaAssetOptionFlow)
+    S = Asset(cf.expiry_time, cf.asset_key)
+    return Max(cf.call_put*(S - cf.strike_price), 0.0)
+end
+
+
+"""
+    expected_amount(cf::VanillaAssetOptionFlow, obs_time::ModelTime)
+
+Return the payoff representing the simulated expected amount of the `VanillaAssetOptionFlow`.
+
+This implementation is an approximation and does not capture convexity adjustments.
+"""
+function expected_amount(cf::VanillaAssetOptionFlow, obs_time::ModelTime)
+    if obs_time ≥ cf.expiry_time
+        return amount(cf)
+    end
+    F = ForwardAsset(obs_time, cf.expiry_time, cf.asset_key)
+    K = Fixed(cf.strike_price)
+    return VanillaAssetOption(F, K, cf.call_put)
+end
+

test/componenttests/componenttests.jl

@@ -7,9 +7,10 @@ using Test
 
     include("calibration/swap_rate_calibration.jl")
 
-    include("scenarios/scenarios.jl")
-    include("scenarios/rates_option.jl")
+    include("scenarios/asset_options.jl")
     include("scenarios/bermudan_swaption.jl")
+    include("scenarios/rates_option.jl")
+    include("scenarios/scenarios.jl")
     include("scenarios/swaptions_expected_exposure.jl")
 
     include("sensitivities/forwards_deltas.jl")

test/componenttests/scenarios/asset_options.jl

@@ -0,0 +1,53 @@
+
+using DiffFusion
+using Test
+using UnicodePlots
+
+@testset "Test asset option simulation" begin
+
+    if !@isdefined(TestModels)
+        include("../../test_models.jl")
+    end
+
+    function plot_scens(scens, title)
+        plt = lineplot(scens.times, scens.X[1,:,:],
+            title = title,
+            name = scens.leg_aliases,
+            xlabel = "obs_time",
+            ylabel = "price (EUR)",
+            width = 80,
+            height = 30,
+        )
+        println()
+        display(plt)
+        println()
+    end
+
+
+    @testset "Test VanillaAssetOption simulation" begin
+        model = TestModels.hybrid_model_full
+        ch = TestModels.ch_full
+        times = 0.0:1.0:6.0
+        n_paths = 2^13
+        sim = DiffFusion.simple_simulation(model, ch, times, n_paths, with_progress_bar = false)
+        path = DiffFusion.path(sim, TestModels.ts_list, TestModels.context, DiffFusion.LinearPathInterpolation)
+        #
+        call_leg = DiffFusion.cashflow_leg(
+            "leg/C/EUR-USD/5y/1.25",
+            [ DiffFusion.VanillaAssetOptionFlow(5.0, 5.0, 1.25, +1.0, "EUR-USD"), ],
+            [ 1.0, ],
+            "USD"
+        )
+        put_leg = DiffFusion.cashflow_leg(
+            "leg/P/EUR-USD/5y/1.25",
+            [ DiffFusion.VanillaAssetOptionFlow(5.0, 5.0, 1.25, -1.0, "EUR-USD"), ],
+            [ 1.0, ],
+            "USD"
+        )
+        scens = DiffFusion.scenarios([call_leg, put_leg], times, path, "")
+        mv = DiffFusion.aggregate(scens, true, false)
+        #
+        plot_scens(mv, "EUR-USD option mv")
+    end
+
+end

test/unittests/models/hybrid/simple_model.jl

@@ -135,6 +135,14 @@ using Test
         @test DiffFusion.swap_rate_variance(m, "EUR", yts, 1.0, 8.0, [8.0, 9.0, 10.0], [1.0, 1.0], SX) == DiffFusion.swap_rate_variance(hjm_model_for, "EUR", yts, 1.0, 8.0, [8.0, 9.0, 10.0], [1.0, 1.0], SX)
         @test DiffFusion.forward_rate_variance(m, "USD", 1.0, 8.0, 8.0, 9.0) == DiffFusion.forward_rate_variance(hjm_model_dom, "USD", 1.0, 8.0, 8.0, 9.0)
         #
+        @test DiffFusion.asset_variance(m, "EUR-USD", "USD", "EUR", 1.0, 8.0, SX) == DiffFusion.asset_variance(asset_model, hjm_model_dom, hjm_model_for, ch, 1.0, 8.0)
+        @test DiffFusion.asset_variance(m, "EUR-USD", "USD", "EUR", 1.0, 8.0, SX) == DiffFusion.asset_variance(asset_model, hjm_model_dom, hjm_model_for, ch, 1.0, 8.0)
+        @test DiffFusion.asset_variance(m, "EUR-USD", nothing, "EUR", 1.0, 8.0, SX) == DiffFusion.asset_variance(asset_model, nothing, hjm_model_for, ch, 1.0, 8.0)
+        @test DiffFusion.asset_variance(m, "EUR-USD", "USD", nothing, 1.0, 8.0, SX) == DiffFusion.asset_variance(asset_model, hjm_model_dom, nothing, ch, 1.0, 8.0)
+        @test DiffFusion.asset_variance(m, "EUR-USD", nothing, nothing, 1.0, 8.0, SX) == DiffFusion.asset_variance(asset_model, nothing, nothing, ch, 1.0, 8.0)
+        @test DiffFusion.asset_variance(m, nothing, "USD", "EUR", 1.0, 8.0, SX) == DiffFusion.asset_variance(nothing, hjm_model_dom, hjm_model_for, ch, 1.0, 8.0)
+        @test DiffFusion.asset_variance(m, nothing, nothing, nothing, 1.0, 8.0, SX) == 0.0
+        #
         @test_throws KeyError DiffFusion.log_asset(m, "WrongAlias", 1.0, SX)
         @test_throws KeyError DiffFusion.log_bank_account(m, "WrongAlias", 1.0, SX)
         @test_throws KeyError DiffFusion.log_zero_bond(m, "WrongAlias", 4.0, 8.0, SX)