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Add bermudan regression based on exercise trigger #60

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Jan 4, 2024
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Add bermudan regression based on exercise trigger #60

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87 changes: 71 additions & 16 deletions src/products/BermudanSwaptionLeg.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -124,6 +124,11 @@ and `make_regression_variables` are passed on to `BermudanSwaptionLeg`.
`path` and `make_regression` are used to create an `AmcPayoffRegression`
object for `AmcPayoff`s. This data is supposed to be updated subsequent
to leg cretion.

`regression_on_exercise_trigger = true` specifies AMC regression strategy.
If `regression_on_exercise_trigger = then` then regression on regression
is used. `regression_on_exercise_trigger = true` is recommended for
accurate sensitivity calculation.
"""
function bermudan_swaption_leg(
alias::String,
Expand All @@ -133,6 +138,7 @@ function bermudan_swaption_leg(
make_regression_variables::Function,
path::Union{AbstractPath, Nothing},
make_regression::Union{Function, Nothing},
regression_on_exercise_trigger = true,
)
#
@assert length(bermudan_exercises) > 0
Expand All @@ -157,22 +163,52 @@ function bermudan_swaption_leg(
exercise_triggers = [ Cache(Hk > Uk), ]
# backward sweep
for ex in reverse(bermudan_exercises[begin:end-1])
Hk = AmcSum(
ex.exercise_time,
[hold_values[end],],
ex.make_regression_variables(ex.exercise_time),
path,
make_regression,
numeraire_curve_key,
)
Hk = Cache(Hk)
Uk = vcat([
discounted_cashflows(leg, ex.exercise_time)
for leg in ex.cashflow_legs
]...)
Uk = Cache(sum(Uk))
hold_values = vcat(hold_values, Cache(Max(Hk, Uk)))
exercise_triggers = vcat(exercise_triggers, Cache(Hk > Uk))
if regression_on_exercise_trigger
Uk = vcat([
discounted_cashflows(leg, ex.exercise_time)
for leg in ex.cashflow_legs
]...)
Uk = Cache(sum(Uk))
Hk = AmcMax(
ex.exercise_time,
[ hold_values[end], ],
[ Uk, ],
ex.make_regression_variables(ex.exercise_time),
path,
make_regression,
numeraire_curve_key,
)
Hk = Cache(Hk)
Ik = AmcOne(
ex.exercise_time,
[ hold_values[end], ],
[ Uk, ],
ex.make_regression_variables(ex.exercise_time),
path,
make_regression,
numeraire_curve_key,
)
Ik = Cache(Ik)
hold_values = vcat(hold_values, Hk)
exercise_triggers = vcat(exercise_triggers, Ik)
else
Hk = AmcSum(
ex.exercise_time,
[hold_values[end],],
ex.make_regression_variables(ex.exercise_time),
path,
make_regression,
numeraire_curve_key,
)
Hk = Cache(Hk)
Uk = vcat([
discounted_cashflows(leg, ex.exercise_time)
for leg in ex.cashflow_legs
]...)
Uk = Cache(sum(Uk))
hold_values = vcat(hold_values, Cache(Max(Hk, Uk)))
exercise_triggers = vcat(exercise_triggers, Cache(Hk > Uk))
end
end
#
return BermudanSwaptionLeg(
Expand Down Expand Up @@ -383,12 +419,30 @@ function make_bermudan_exercises(
end


"""
bermudan_swaption_leg(
alias::String,
fixed_leg::DeterministicCashFlowLeg,
float_leg::DeterministicCashFlowLeg,
exercise_times::AbstractVector,
option_long_short::ModelValue,
regression_on_exercise_trigger = false,
)

Create a `BermudanSwaptionLeg` using simplified interface.

`regression_on_exercise_trigger = true` specifies AMC regression strategy.
If `regression_on_exercise_trigger = then` then regression on regression
is used. `regression_on_exercise_trigger = true` is recommended for
accurate sensitivity calculation.
"""
function bermudan_swaption_leg(
alias::String,
fixed_leg::DeterministicCashFlowLeg,
float_leg::DeterministicCashFlowLeg,
exercise_times::AbstractVector,
option_long_short::ModelValue,
regression_on_exercise_trigger = true,
)
#
bermudan_exercises = make_bermudan_exercises(fixed_leg, float_leg, exercise_times)
Expand All @@ -409,5 +463,6 @@ function bermudan_swaption_leg(
make_regression_variables_,
path_,
make_regression_,
regression_on_exercise_trigger,
)
end
26 changes: 25 additions & 1 deletion test/componenttests/scenarios/swaptions_expected_exposure.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -191,15 +191,28 @@ using UnicodePlots
make_regression_variables,
nothing, # path
nothing, # make_regression
true, # regression_on_exercise_trigger
)


berm_2 = DiffFusion.bermudan_swaption_leg(
"berm/10-nc-2 (regr_on_regr)",
[ exercise_2y, exercise_4y, exercise_6y, exercise_8y, ],
1.0, # long option
"", # default discounting (curve key)
make_regression_variables,
nothing, # path
nothing, # make_regression
false, # regression_on_exercise_trigger
)


# AMC Regression

#make_regression = (C, O) -> DiffFusion.polynomial_regression(C, O, 2)
make_regression = (C, O) -> DiffFusion.piecewise_regression(C, O, 2, [3])

DiffFusion.reset_regression!(berm, path, make_regression)
DiffFusion.reset_regression!(berm_2, path, make_regression)


# Scenario Calculation
Expand All @@ -213,13 +226,15 @@ using UnicodePlots
swaption_8y_scens = DiffFusion.scenarios([swaption_8y], times, path, "", with_progress_bar=false)

berm_scens = DiffFusion.scenarios([berm], times, path, "", with_progress_bar=false)
berm_2_scens = DiffFusion.scenarios([berm_2], times, path, "", with_progress_bar=false)

vanilla_swap_ee = DiffFusion.expected_exposure(vanilla_swap_scens)
swaption_2y_ee = DiffFusion.expected_exposure(swaption_2y_scens)
swaption_4y_ee = DiffFusion.expected_exposure(swaption_4y_scens)
swaption_6y_ee = DiffFusion.expected_exposure(swaption_6y_scens)
swaption_8y_ee = DiffFusion.expected_exposure(swaption_8y_scens)
berm_ee = DiffFusion.expected_exposure(berm_scens)
berm_2_ee = DiffFusion.expected_exposure(berm_2_scens)

portfolo = DiffFusion.join_scenarios([
vanilla_swap_ee,
Expand All @@ -230,6 +245,11 @@ using UnicodePlots
berm_ee,
])

portfolo_berms = DiffFusion.join_scenarios([
berm_ee,
berm_2_ee,
])

function plot_scens(scens, title)
plt = lineplot(scens.times, scens.X[1,:,:],
title = title,
Expand All @@ -245,8 +265,12 @@ using UnicodePlots
end

plot_scens(portfolo, "Rates Derivatives")
plot_scens(portfolo_berms, "Bermudans")

max_european_ee = maximum(portfolo.X[1,:,2:5], dims=2)[:,1]
berm_ee = portfolo.X[1,:,6]
@test berm_ee ≥ max_european_ee

rel_error_berms = (portfolo_berms.X[1,:,1] .+ 1.0e-8) ./ (portfolo_berms.X[1,:,2] .+ 1.0e-8) .- 1.0
@test maximum(abs.(rel_error_berms)) < 0.007
end
2 changes: 1 addition & 1 deletion test/componenttests/sensitivities/swaptions_delta_vega.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -267,7 +267,7 @@ using UnicodePlots
@test abs(sum(g2[5:8])/sum(g1[5:8]) - 1.0) < 7.5e-2 # berm_4y ESTR
#
@test abs(sum(g3[1:4])/sum(g1[1:4]) - 1.0) < 0.27 # berm_10nc2 EURIBOR6M Delta
@test abs(sum(g3[5:8])/sum(g1[5:8]) - 1.0) < 0.17 # berm_10nc2 ESTR
@test abs(sum(g3[5:8])/sum(g1[5:8]) - 1.0) < 0.28 # berm_10nc2 ESTR
end


Expand Down
39 changes: 39 additions & 0 deletions test/unittests/products/bermudan_swaption_leg.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -261,6 +261,30 @@ berm_35 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"}
berm_40 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"} > {"*underl_20*"})} * {(0.0000 > {"*underl_30*"})}) * "*underl_40*" @ 4.00)"
berm_45 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"} > {"*underl_20*"})} * {(0.0000 > {"*underl_30*"})}) * "*underl_45*" @ 4.50)"

berm_2_00 =
"AmcSum(0.00, [{AmcMax(1.00, [{AmcMax(2.00, [{Max(0.0000, {(((" *
"(P(EUR:OIS, 3.00, 4.00) * 1.0000 * 0.0300 * 1.0000 @ 3.00) + " *
"(P(EUR:OIS, 3.00, 5.00) * 1.0000 * 0.0300 * 1.0000 @ 3.00)) + " *
"(P(EUR:OIS, 3.00, 4.00) * -1.0000 * L(EURIBOR12M, 3.00; 3.00, 4.00) * 1.0000 @ 3.00)) + " *
"(P(EUR:OIS, 3.00, 5.00) * -1.0000 * L(EURIBOR12M, 3.00; 4.00, 5.00) * 1.0000 @ 3.00))})}], [{(((((" *
"(P(EUR:OIS, 2.00, 3.00) * 1.0000 * 0.0300 * 1.0000 @ 2.00) + " *
"(P(EUR:OIS, 2.00, 4.00) * 1.0000 * 0.0300 * 1.0000 @ 2.00)) + " *
"(P(EUR:OIS, 2.00, 5.00) * 1.0000 * 0.0300 * 1.0000 @ 2.00)) + " *
"(P(EUR:OIS, 2.00, 3.00) * -1.0000 * L(EURIBOR12M, 2.00; 2.00, 3.00) * 1.0000 @ 2.00)) + " *
"(P(EUR:OIS, 2.00, 4.00) * -1.0000 * L(EURIBOR12M, 2.00; 3.00, 4.00) * 1.0000 @ 2.00)) + " *
"(P(EUR:OIS, 2.00, 5.00) * -1.0000 * L(EURIBOR12M, 2.00; 4.00, 5.00) * 1.0000 @ 2.00))}], " *
"[L(EURIBOR12M, 2.00; 2.00, 5.00)])}], [{(((((((" *
"(P(EUR:OIS, 1.00, 2.00) * 1.0000 * 0.0300 * 1.0000 @ 1.00) + " *
"(P(EUR:OIS, 1.00, 3.00) * 1.0000 * 0.0300 * 1.0000 @ 1.00)) + " *
"(P(EUR:OIS, 1.00, 4.00) * 1.0000 * 0.0300 * 1.0000 @ 1.00)) + " *
"(P(EUR:OIS, 1.00, 5.00) * 1.0000 * 0.0300 * 1.0000 @ 1.00)) + " *
"(P(EUR:OIS, 1.00, 2.00) * -1.0000 * L(EURIBOR12M, 1.00; 1.00, 2.00) * 1.0000 @ 1.00)) + " *
"(P(EUR:OIS, 1.00, 3.00) * -1.0000 * L(EURIBOR12M, 1.00; 2.00, 3.00) * 1.0000 @ 1.00)) + " *
"(P(EUR:OIS, 1.00, 4.00) * -1.0000 * L(EURIBOR12M, 1.00; 3.00, 4.00) * 1.0000 @ 1.00)) + " *
"(P(EUR:OIS, 1.00, 5.00) * -1.0000 * L(EURIBOR12M, 1.00; 4.00, 5.00) * 1.0000 @ 1.00))}], " *
"[L(EURIBOR12M, 1.00; 1.00, 5.00)])}], [], [L(EURIBOR12M, 0.00; 0.00, 5.00)])"


@testset "Test discounted_cashflows" begin
berm = DiffFusion.bermudan_swaption_leg(
"berm",
Expand All @@ -270,6 +294,7 @@ berm_45 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"}
make_regression_variables,
nothing, # path
nothing, # make_regression
false, # regression_on_exercise_trigger
)
@test isa(berm, DiffFusion.BermudanSwaptionLeg)
cfs = DiffFusion.discounted_cashflows(berm, 0.0)
Expand All @@ -287,6 +312,18 @@ berm_45 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"}

@test length(DiffFusion.discounted_cashflows(berm, 5.0)) == 0
@test length(DiffFusion.discounted_cashflows(berm, 5.5)) == 0

berm_2 = DiffFusion.bermudan_swaption_leg(
"berm",
[ exercise_1, exercise_2, exercise_3,],
1.0, # long option
"OIS", # default discounting (curve key)
make_regression_variables,
nothing, # path
nothing, # make_regression
true, # regression_on_exercise_trigger
)
@test string(DiffFusion.discounted_cashflows(berm_2, 0.0)[1]) == berm_2_00
end

@testset "Test regression details setup" begin
Expand All @@ -302,6 +339,7 @@ berm_45 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"}
make_regression_variables,
NoPath(), # path
no_make_regression, # make_regression
false, # regression_on_exercise_trigger
)
@test isa(berm, DiffFusion.BermudanSwaptionLeg)
@test berm.regression_data.path == NoPath()
Expand All @@ -319,6 +357,7 @@ berm_45 = "((1.0000 - {({"*option_10*"} > {"*underl_10*"})} * {({"*option_20*"}
make_regression_variables,
nothing, # path
nothing, # make_regression
false, # regression_on_exercise_trigger
)
@test isa(berm, DiffFusion.BermudanSwaptionLeg)
@test isnothing(berm.regression_data.path)
Expand Down