Refactor sensitivity calculation for AMC payoffs

  - Amend AMC payoffs for smooth step function
  - Add has_amc_function to identify AMC payoffs
  - Add regression re-calibration to sensitivity calculation
  - Add swaption sensitivity component test
  - Add gradient calculation via FiniteDifferences

Project.toml

@@ -7,6 +7,7 @@ version = "0.3.0"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/DiffFusion.jl

@@ -3,6 +3,7 @@ module DiffFusion
 using ChainRulesCore
 using DelimitedFiles
 using Distributions
+using FiniteDifferences
 using ForwardDiff
 using Interpolations
 using LinearAlgebra

src/analytics/Valuations.jl

@@ -79,8 +79,11 @@ function model_price_and_deltas(
     payoffs::AbstractVector,
     path_obj::Path,
     pay_time::Union{ModelTime, Nothing} = nothing,
-    discount_curve_key::Union{String,Nothing} = nothing
+    discount_curve_key::Union{String,Nothing} = nothing,
     )
+    if has_amc_payoff(payoffs)
+        @warn "Zygote cannot properly handle AMC payoffs."
+    end
     #
     pay_time = _effective_pay_time(payoffs, pay_time, discount_curve_key)
     #
@@ -97,7 +100,7 @@ function model_price_and_deltas(
         return mean( X )
     end
     # res = obj_function(path_obj.ts_dict)
-    (v, g) = _function_value_and_gradient(obj_function, path_obj.ts_dict)
+    (v, g) = _function_value_and_gradient(obj_function, path_obj.ts_dict, Zygote)
     return (v, g)
 end
 
@@ -108,7 +111,7 @@ end
         path_obj::Path,
         pay_time::Union{ModelTime, Nothing} = nothing,
         discount_curve_key::Union{String,Nothing} = nothing,
-        ad_module::Module = Zygote,
+        ad_module::Module = ForwardDiff,
         )
 
 Calculate model price and curve sensitivities. Sensitivities are
@@ -120,22 +123,35 @@ Here, payoffs is a vector of `Payoff` objects and `path_obj` is a simulated `Pat
 numeraire calculation.
 
 `ad_module` can be `Zygote` or `ForwardDiff`.
+
+For AMC payoffs we need to update the regression path and trigger a
+recalibration. For sensitivity calculation, we impose the constraint that
+regression calibration uses the same paths as valuation.
 """
 function model_price_and_deltas_vector(
     payoffs::AbstractVector,
     path_obj::Path,
     pay_time::Union{ModelTime, Nothing} = nothing,
     discount_curve_key::Union{String,Nothing} = nothing,
-    ad_module::Module = Zygote,
+    ad_module::Module = ForwardDiff,
     )
     #
+    if has_amc_payoff(payoffs) && (ad_module == Zygote)
+        @warn "Zygote cannot properly handle AMC payoffs."
+    end
+    #
     pay_time = _effective_pay_time(payoffs, pay_time, discount_curve_key)
     ts_dict = deepcopy(path_obj.ts_dict)  # maybe we don't want (or need) this
     (ts_labels, ts_values) = termstructure_values(ts_dict)
     #
     obj_function(ts_values_) = begin
         termstructure_dictionary!(ts_dict, ts_labels, ts_values_)
         path_ = path(path_obj.sim, ts_dict, path_obj.context, path_obj.interpolation)
+        # we need to update regression paths for AMC payoffs
+        for p in payoffs
+            reset_regression!(p, path_)
+        end
+        #
         X = zeros(length(path_))
         if length(payoffs) > 0
             X += sum(( p(path_) for p in payoffs ))
@@ -185,6 +201,9 @@ function model_price_and_vegas(
     pay_time::Union{ModelTime, Nothing} = nothing,
     discount_curve_key::Union{String,Nothing} = nothing
     )
+    if has_amc_payoff(payoffs)
+        @warn "Zygote cannot properly handle AMC payoffs."
+    end
     #
     pay_time = _effective_pay_time(payoffs, pay_time, discount_curve_key)
     #
@@ -220,7 +239,7 @@ function model_price_and_vegas(
         return price
     end
     # res = obj_function(param_dict)
-    (v, g) = _function_value_and_gradient(obj_function, param_dict)
+    (v, g) = _function_value_and_gradient(obj_function, param_dict, Zygote)
     return (v, g)
 end
 
@@ -234,7 +253,7 @@ end
         context::Context,
         pay_time::Union{ModelTime, Nothing} = nothing,
         discount_curve_key::Union{String,Nothing} = nothing,
-        ad_module::Module = Zygote,
+        ad_module::Module = ForwardDiff,
         )
 
 Calculate model price and model sensitivities. Sensitivities are
@@ -252,6 +271,10 @@ signature `simulation(model::Model, ch::CorrelationHolder)`.
 numeraire calculation.
 
 `ad_module` can be `Zygote` or `ForwardDiff`.
+
+For AMC payoffs we need to update the regression path and trigger a
+recalibration. For sensitivity calculation, we impose the constraint that
+regression calibration uses the same paths as valuation.
 """
 function model_price_and_vegas_vector(
     payoffs::AbstractVector,
@@ -261,9 +284,13 @@ function model_price_and_vegas_vector(
     context::Context,
     pay_time::Union{ModelTime, Nothing} = nothing,
     discount_curve_key::Union{String,Nothing} = nothing,
-    ad_module::Module = Zygote,
+    ad_module::Module = ForwardDiff,
     )
     #
+    if has_amc_payoff(payoffs) && (ad_module == Zygote)
+        @warn "Zygote cannot properly handle AMC payoffs."
+    end
+    #
     pay_time = _effective_pay_time(payoffs, pay_time, discount_curve_key)
     #
     param_dict = model_parameters(model)
@@ -287,6 +314,10 @@ function model_price_and_vegas_vector(
         end
         sim = simulation(mdl, ch)
         path_ = path(sim, ts_list, context, LinearPathInterpolation)
+        # we need to update regression paths for AMC payoffs
+        for p in payoffs
+            reset_regression!(p, path_)
+        end
         #
         X = zeros(length(path_))
         if length(payoffs) > 0

src/payoffs/AmcPayoffs.jl

@@ -206,6 +206,58 @@ function obs_times(p::AmcPayoff)
     return times
 end
 
+
+"""
+    has_amc_payoff(p::AmcPayoff)
+
+Determine whether a payoff is or contains an AMC payoff.
+
+AMC payoffs require special treatment e.g. for sensitivity calculation.
+"""
+has_amc_payoff(p::AmcPayoff) = true
+
+
+"""
+    has_amc_payoff(p::UnaryNode)
+
+Determine whether a payoff is or contains an AMC payoff.
+"""
+has_amc_payoff(p::UnaryNode) = has_amc_payoff(p.x)
+
+"""
+    has_amc_payoff(p::BinaryNode)
+
+Determine whether a payoff is or contains an AMC payoff.
+"""
+has_amc_payoff(p::BinaryNode) = has_amc_payoff(p.x) || has_amc_payoff(p.y)
+
+"""
+    has_amc_payoff(p::Union{Leaf, CompoundedRate, Optionlet, Swaption})
+
+Determine whether a payoff is or contains an AMC payoff.
+"""
+has_amc_payoff(p::Union{Leaf, CompoundedRate, Optionlet, Swaption}) = false
+
+"""
+    has_amc_payoff(p::Payoff)
+
+Determine whether a payoff is or contains an AMC payoff.
+"""
+has_amc_payoff(p::Payoff) = begin
+    error("Payoff " * string(typeof(p)) *  " needs to implement has_amc_payoff method.")
+    return false
+end
+
+"""
+    has_amc_payoff(payoffs::AbstractVector)
+
+Determine whether any payoff is or contains an AMC payoff.
+"""
+has_amc_payoff(payoffs::AbstractVector) = begin
+    return any([ has_amc_payoff(p) for p in payoffs ])
+end
+
+
 """
     reset_regression!(
         p::AmcPayoff,
@@ -269,7 +321,7 @@ end
 
 """
     reset_regression!(
-        p::Leaf,
+        p::Union{Leaf, CompoundedRate, Optionlet, Swaption},
         path::Union{AbstractPath, Nothing} = nothing,
         make_regression::Union{Function, Nothing}  = nothing,
         )
@@ -304,6 +356,17 @@ function reset_regression!(
 end
 
 
+"""
+    _is_larger_zero(T::AbstractArray)
+
+Implement a differentiable version of the indicator (T>0).
+"""
+function _is_larger_zero(T::AbstractArray)
+    # return 1.0 * (T .> 0.0)
+    scaling = 1.0e+8
+    return 0.5 .+ 0.5 .* tanh.(scaling .* T)
+end
+
 """
     struct AmcMax <: AmcPayoff
         links::AmcPayoffLinks
@@ -370,8 +433,8 @@ function at(p::AmcMax, path::AbstractPath)
         end
         Y = Y .* N
     end
-    use_X = (T .> 0.0)
-    return use_X .* X + (.!use_X) .* Y
+    use_X = _is_larger_zero(T)
+    return use_X .* X .+ (1.0 .- use_X) .* Y
 end
 
 """
@@ -450,8 +513,8 @@ function at(p::AmcMin, path::AbstractPath)
         end
         Y = Y .* N
     end
-    use_X = (T .<= 0.0)
-    return use_X .* X + (.!use_X) .* Y
+    use_Y = _is_larger_zero(T)
+    return (1.0 .- use_Y) .* X .+ use_Y .* Y
 end
 
 """
@@ -516,7 +579,7 @@ Evaluate an AmcOne payoff at a given path.
 """
 function at(p::AmcOne, path::AbstractPath)
     (X, Y, T) = at(p.links, p.regr, path)
-    return (T .> 0.0)
+    return _is_larger_zero(T)
 end
 
 """

src/utils/Gradients.jl

@@ -12,26 +12,32 @@ tuning AD routines.
     _function_value_and_gradient(
         f::Function,
         x::Any,
-        m::Module = Zygote,
+        m::Module = ForwardDiff,
         )
 
 Calculate the function value and gradient of a function.
 """
 function _function_value_and_gradient(
     f::Function,
     x::Any,
-    m::Module = Zygote,
+    m::Module = ForwardDiff,
     )
     #
+    if m == ForwardDiff
+        v = f(x)
+        g = ForwardDiff.gradient(f, x)
+        return (v, g)
+    end
     if m == Zygote
         (v, g) = withgradient(f, x)
         @assert length(g) == 1
         return (v, g[1])
     end
-    if m == ForwardDiff
+    if m == FiniteDifferences
         v = f(x)
-        g = ForwardDiff.gradient(f, x)
-        return (v, g)
+        m = central_fdm(3, 1)
+        g = grad(m, f, x)
+        return (v, g[1])
     end
     error("Unknown module " * string(m) * ".")
 end

test/componenttests/componenttests.jl

@@ -16,6 +16,7 @@ using Test
     include("sensitivities/option_deltas.jl")
     include("sensitivities/swap_deltas.jl")
     include("sensitivities/option_vegas.jl")
+    include("sensitivities/swaptions_delta_vega.jl")
 
 
 end