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add chapter 14

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Bogumił Kamiński 2022-03-14 00:12:33 +01:00
parent 34e80b2cba
commit b5e90546e6
5 changed files with 211 additions and 88 deletions
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131
Manifest.toml
View File

@ -26,9 +26,9 @@ version = "0.2.0"
[[deps.Arrow]]
deps = ["ArrowTypes", "BitIntegers", "CodecLz4", "CodecZstd", "DataAPI", "Dates", "Mmap", "PooledArrays", "SentinelArrays", "Tables", "TimeZones", "UUIDs"]
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version = "2.2.1"
[[deps.ArrowTypes]]
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@ -78,9 +78,9 @@ version = "0.4.1"
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version = "0.10.3"
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@ -96,9 +96,9 @@ version = "0.5.1"
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@ -107,9 +107,9 @@ version = "0.4.10"
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@ -166,9 +166,9 @@ version = "1.0.2"
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@ -278,9 +278,9 @@ uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
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@ -319,9 +319,9 @@ version = "0.9.17"
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@ -389,9 +389,9 @@ version = "0.64.0+0"
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@ -452,10 +452,9 @@ uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
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@ -469,9 +468,9 @@ uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
[[deps.InverseFunctions]]
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@ -507,9 +506,9 @@ version = "0.21.3"
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@ -523,6 +522,12 @@ git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
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@ -536,9 +541,9 @@ version = "1.3.0"
[[deps.Latexify]]
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version = "0.15.13"
[[deps.LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
@ -600,10 +605,10 @@ uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"
[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
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[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@ -623,9 +628,9 @@ version = "0.5.4"
[[deps.LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
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version = "0.3.8"
[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
@ -680,9 +685,9 @@ version = "0.7.3"
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
[[deps.NaNMath]]
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[[deps.NamedArrays]]
deps = ["Combinatorics", "DataStructures", "DelimitedFiles", "InvertedIndices", "LinearAlgebra", "Random", "Requires", "SparseArrays", "Statistics"]
@ -750,15 +755,15 @@ version = "8.44.0+0"
[[deps.PDMats]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
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@ -783,10 +788,10 @@ uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.1.3"
[[deps.Plots]]
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@ -796,9 +801,9 @@ version = "1.4.0"
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@ -816,9 +821,9 @@ uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
[[deps.PyCall]]
deps = ["Conda", "Dates", "Libdl", "LinearAlgebra", "MacroTools", "Serialization", "VersionParsing"]
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@ -843,10 +848,10 @@ deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
[[deps.ROCAnalysis]]
deps = ["DataFrames", "LinearAlgebra", "Printf", "Random", "RecipesBase", "SpecialFunctions"]
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deps = ["DataFrames", "Distributions", "LinearAlgebra", "Printf", "Random", "RecipesBase", "SpecialFunctions", "StatsBase"]
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[[deps.Random]]
deps = ["SHA", "Serialization"]
@ -859,9 +864,9 @@ version = "1.2.1"
[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
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@ -958,15 +963,15 @@ uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[[deps.SpecialFunctions]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
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@ -992,9 +997,9 @@ version = "0.9.16"
[[deps.StatsModels]]
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@ -1029,10 +1034,10 @@ uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"
[[deps.Tables]]
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@ -1044,9 +1049,9 @@ uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
[[deps.TimeZones]]
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@ -1090,15 +1095,15 @@ version = "1.19.0+0"
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[[deps.WinReg]]
deps = ["Test"]

14
appB.jl
View File

@ -256,3 +256,17 @@ end
train2 = owensboro2[owensboro2.train, :]
test2 = owensboro2[.!owensboro2.train, :]
test3, train3 = groupby(owensboro2, :train, sort=true)
# Code for exercise 14.1
@time mean(x -> x < 0, -10^6:10^6)
@time mean(x -> x < 0, -10^6:10^6)
@time mean(x -> x < 0, -10^6:10^6)
@time mean(<(0), -10^6:10^6)
@time mean(<(0), -10^6:10^6)
@time mean(<(0), -10^6:10^6)
lt0(x) = x < 0
@time mean(lt0, -10^6:10^6)
@time mean(lt0, -10^6:10^6)
@time mean(lt0, -10^6:10^6)

121
ch14.jl
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@ -1 +1,120 @@
# consider showing Arrow
# Bogumił Kamiński, 2022
# Codes for chapter 14
# Codes for section 14.2
# start Julia with and additional -t4 command line switch
Threads.nthreads()
# Code for listing 14.1
function payoff_asian_sample(T, X0, K, r, s, m)::Float64
X = X0
sumX = X
d = T / m
for i in 1:m
X *= exp((r - s^2 / 2) * d + s * sqrt(d) * randn())
sumX += X
end
Y = sumX / (m + 1)
return exp(-r * T) * max(Y - K, 0)
end
# Code for checking the results of the payoff simulation
payoff_asian_sample(1.0, 50.0, 55.0, 0.05, 0.3, 200)
payoff_asian_sample(1.0, 50.0, 55.0, 0.05, 0.3, 200)
payoff_asian_sample(1.0, 50.0, 55.0, 0.05, 0.3, 200)
# Benchmarking map
using BenchmarkTools
@btime map(i -> payoff_asian_sample(1.0, 50.0, 55.0, 0.05, 0.3, 200), 1:10_000);
using ThreadsX
@btime ThreadsX.map(i -> payoff_asian_sample(1.0, 50.0, 55.0, 0.05, 0.3, 200), 1:10_000);
# Codes for section 14.3
# Code for listing 14.2
using Statistics
function asian_value(T, X0, K, r, s, m, max_time)
result = Float64[]
start_time = time()
while time() - start_time < max_time
append!(result, ThreadsX.map(_ -> payoff_asian_sample(T, X0, K, r, s, m), 1:10_000))
end
n = length(result)
mv = mean(result)
sdv = std(result)
lo95 = mv - 1.96 * sdv / sqrt(n)
hi95 = mv + 1.96 * sdv / sqrt(n)
zero = mean(==(0), result)
return (; n, mv, lo95, hi95, zero)
end
# Code for example of the mean function
mean(x -> x ^ 2, [1, 2, 3])
eq0 = ==(0)
eq0(1)
eq0(0)
# Code for shorthand NamedTuple notation
val1 = 10
val2 = "x"
(; val1, val2)
# Testing asian_value function
@time asian_value(1.0, 50.0, 55.0, 0.05, 0.3, 200, 0.25)
@time asian_value(1.0, 50.0, 55.0, 0.05, 0.3, 200, 0.25)
@time asian_value(1.0, 50.0, 55.0, 0.05, 0.3, 200, 0.25)
# Converting NamedTuple to JSON response
using Genie
Genie.Renderer.Json.json((firstname="Bogumił", lastname="Kamiński"))
# Codes for section 14.4
# Start a new Julia session
using HTTP
using JSON3
req = HTTP.request("POST", "http://127.0.0.1:8000",
["Content-Type" => "application/json"],
JSON3.write((K=55.0, max_time=0.25)))
JSON3.read(req.body)
HTTP.request("POST", "http://127.0.0.1:8000",
["Content-Type" => "application/json"],
JSON3.write((K="", max_time=0.25)))
using DataFrames
df = DataFrame(K=30:2:80, max_time=0.25)
df.data = map(df.K, df.max_time) do K, max_time
@show K
@time req = HTTP.request("POST", "http://127.0.0.1:8000",
["Content-Type" => "application/json"],
JSON3.write((;K, max_time)))
return JSON3.read(req.body)
end;
df
all(==("OK"), getproperty.(df.data, :status))
df2 = select(df, :K, :data => ByRow(x -> x.value) => AsTable)
using Plots
plot(plot(df2.K, df2.mv; legend=false,
xlabel="K", ylabel="expected value"),
plot(df2.K, df2.zero; legend=false,
xlabel="K", ylabel="probability of zero"))

18
ch14_client.jl
View File

@ -1,18 +0,0 @@
using HTTP
using JSON3
using DataFrames
using Plots
df = DataFrame(K=30:2:80, max_time=0.25)
df.data = map(df.K, df.max_time) do K, max_time
@show K
@time req = HTTP.request("POST", "http://127.0.0.1:8000",
["Content-Type" => "application/json"],
JSON3.write((;K, max_time)))
return JSON3.read(req.body)
end
@assert all(==("OK"), getproperty.(df.data, :status))
df2 = select(df, :K, :data => ByRow(x -> x.value) => AsTable)
plot(plot(df2.K, df2.mv; legend=false, xlabel="K", ylabel="expected value"),
plot(df2.K, df2.zero; legend=false, xlabel="K", ylabel="probability of zero"))

15
ch14_server.jl
View File

@ -2,22 +2,25 @@ using Genie
using Statistics
using ThreadsX
function v_asian_sample(T, X0, K, r, s, m)::Float64
function payoff_asian_sample(T, X0, K, r, s, m)::Float64
X = X0
sumX = X
d = T / m
for i in 1:m
X *= exp((r-s^2/2)*d + s*sqrt(d)*randn())
X *= exp((r - s^2 / 2) * d + s * sqrt(d) * randn())
sumX += X
end
return exp(-r*T) * max(sumX / (m + 1) - K, 0)
Y = sumX / (m + 1)
return exp(-r * T) * max(Y - K, 0)
end
function v_asian_value(T, X0, K, r, s, m, max_time)
function asian_value(T, X0, K, r, s, m, max_time)
result = Float64[]
start_time = time()
while time() - start_time < max_time
append!(result, ThreadsX.map(_ -> v_asian_sample(T, X0, K, r, s, m), 1:10_000))
append!(result,
ThreadsX.map(_ -> payoff_asian_sample(T, X0, K, r, s, m),
1:10_000))
end
n = length(result)
mv = mean(result)
@ -35,7 +38,7 @@ Genie.Router.route("/", method=POST) do
return try
K = float(message["K"])
max_time = float(message["max_time"])
value = v_asian_value(1.0, 50.0, K, 0.05, 0.3, 200, max_time)
value = asian_value(1.0, 50.0, K, 0.05, 0.3, 200, max_time)
Genie.Renderer.Json.json((status="OK", value=value))
catch
Genie.Renderer.Json.json((status="ERROR", value=""))