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conversion_calculator_served.jl
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### A Pluto.jl notebook ###
# v0.20.4
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
#! format: off
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
#! format: on
end
# ╔═╡ b6aaa574-7002-42dd-b195-765bb88896c6
begin
using Revise, CSV, DataFrames, Dates, Distributions, Format, Grep, HypertextLiteral, Ipopt, JuMP, LinearAlgebra, Loess, NaNStatistics, Optim, Plots, PlutoUI, PrettyTables, Random, Revise, XLSX
include(download("https://raw.githubusercontent.com/adannenberg/PlutoExport/main/myFuncs.jl"))
Print()
end
# ╔═╡ 66f07370-1190-4f2a-a509-fb0bdc72653d
md"""
## Conversion Calculator w/ Rate Inputs
"""
# ╔═╡ 707e1bdc-e84b-4d5c-b44a-a6a61b877e85
PlutoUI.combine() do Child
md"""
**Implied Dividend Section**:
Compute implied dividend(s) that reprice market conversion price:$(@bind doImpDivs CheckBox(default = false))
"""
end
# ╔═╡ 877df67b-6950-4a5c-881c-b252c77e2707
if doImpDivs
@bind maxDiv2Px confirm(
PlutoUI.combine() do Child
md"""
Max value of divamt / px to consider:
$(Child(Slider(0:.01:.9, show_value = true, default = .1)))
"""
end
)
#maxDiv2Px = maxDiv2Px[1]
end
# ╔═╡ c1003ee9-c023-41ea-a4ef-b1493287afa3
begin
nbsp = html" "
Print()
end
# ╔═╡ bd181597-a3dc-4a15-91f0-9611a330c8db
@bind inputs confirm(
PlutoUI.combine() do Child
md"""
**Conversion Parameters**:
Stock Price: $(Child(NumberField(0:.01:10000, default=100.00)))
$nbsp Strike Price: $(Child(NumberField(5.0:1000.0,default = 120.00)))
$nbsp Volatility: $(Child(NumberField(0.0:500.0,default = 25.00)))
Expiration Date: $(Child(Select(bizDayAdjustedThirdFriday.(today()+Month.(0:60)), default = bizDayAdjustedThirdFriday(today() .+ Year(1)))))
$nbsp
Trade date: $(Child(Select(unique(bd.(today() - Day(180):Day(1):today() + Day(180))), default = bd(today()))))
Funding Rate: $(Child(NumberField(0.0:.1:10.0,default = 5.0)))
$nbsp Repo Rate: $(Child(NumberField(-500.0:.1:10.0, default = -1.0)))
Dividend amounts:$(Child(NumberField(0.0:100.0, default = 2.00)))
$(Child(NumberField(0.0:100.0, default = 2.00)))
$(Child(NumberField(0.0:100.0, default = 0.00)))
Ex-dividend Dates:
$(Child(Select(unique(bd.(today()-Day(180):Day(1):today()+Year(5))), default = bd(today()+Month(3)))))
$nbsp
$(Child(Select(unique(bd.(today():Day(1):today()+Year(5))), default = bd(today()+Month(6)))))
$nbsp
$(Child(Select(unique(bd.(today():Day(1):today()+Year(5))), default = bd(today()+Month(9)))))
Dividend Pay Dates:
$(Child(Select(unique(bd.(today():Day(1):today()+Year(5))), default = bd(today()+Month(3)+Week(1)))))
$nbsp
$(Child(Select(unique(bd.(today():Day(1):today()+Year(5))), default = bd(today()+Month(6)+Week(1)))))
$nbsp
$(Child(Select(unique(bd.(today():Day(1):today()+Year(5))), default = bd(today()+Month(9)+Week(1)))))
Tree type: $(Child(Select(["CRR","LR","Trinomial"], default = "CRR")))
$nbsp
Steps per day: $(Child(NumberField(1.0:50.0,default = 1.0)))
Market Price of Conversion: $(Child(NumberField(-50.0:.1:50.0, default = 2.0)))
"""
end
)
# ╔═╡ bde7c9cc-a124-419b-ab02-6c2273e87a26
begin
(S, K, vol_pct, dt_expiry, dt_trade, r_csa_mm_pct, r_repo_mm_pct, divamt1, divamt2, divamt3, dt_exdiv1, dt_exdiv2, dt_exdiv3, dt_divpmt1, dt_divpmt2, dt_divpmt3, treeType, stepsPerDay, mktConversionPx) = inputs
Print()
end
# ╔═╡ f5c2fd63-5fc6-40bd-9a7f-9731ea5636b8
begin
divamt = [divamt1; divamt2; divamt3]
dt_exdiv = [dt_exdiv1; dt_exdiv2; dt_exdiv3]
dt_divpmt = [dt_divpmt1; dt_divpmt2; dt_divpmt3]
local idx = findall(divamt .> 0)
if length(idx) == 0
divamt = [divamt[1]]
dt_exdiv = [dt_exdiv[1]]
dt_divpmt = [dt_divpmt[1]]
else
divamt = divamt[idx]
dt_exdiv = dt_exdiv[idx]
dt_divpmt = dt_divpmt[idx]
end
local indx = findall(dt_exdiv .<= dt_expiry)
if length(indx) > 0
divamt = divamt[indx]
dt_exdiv = dt_exdiv[indx]
dt_divpmt = dt_divpmt[indx]
else
divamt = [0]
dt_exdiv = [bd(dt_expiry-Day(7))]
dt_divpmt = [bd(dt_expiry-Day(7))]
end
Print()
end
# ╔═╡ d48514f9-8e54-4666-a0ae-4a5a62daae2f
if doImpDivs
#px = conversion_Basic(S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_exp, stepsPerDay, dt_exdiv, dt_divpmt, divamt, dt_trade, earlyExPut, earlyExCall)[1]
impDiv = implied_dividend_from_conversion_am(mktConversionPx, treeType, S, K, r_csa_mm_pct, r_repo_mm_pct,vol_pct, dt_trade, dt_expiry, dt_exdiv, dt_divpmt, stepsPerDay, maxDiv2Px[1])
Print("implied dividend = $(round(impDiv,digits=2))")
end
# ╔═╡ 0c482b6d-cd42-4036-8cea-7582c774eef3
if doImpDivs
divrng = collect(LinRange(0,maxDiv2Px[1],10)) .* S
#divrng = collect(0:.01:maxDiv2Px[1]) .* S
divDF = DataFrame(div = divrng, conv = zeros(length(divrng)) .+ NaN)
ndiv = length(dt_exdiv)
Threads.@threads for r in 1:nrow(divDF)
divDF.conv[r] = conversion_am(treeType, S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divDF.div[r] * ones(ndiv), dt_exdiv, dt_divpmt, stepsPerDay)
end
scatter(divDF.div,divDF.conv,xlabel="dividend",ylabel="conv px", label="conv px as function of dividend", color=:blue)
plot!(divDF.div,divDF.conv,label="",color=:blue)
hline!([mktConversionPx],color=:red, label="mkt conv px = $mktConversionPx")
end
# ╔═╡ 9f048c1e-8e5c-4e78-a587-3e8566fdc098
md"""
**Misc:**:
Include value of unexercised options in pnl calcs: $(@bind includeUnexOptVals CheckBox(default = true))
Use American pricer for unexercised option values (slower): $(@bind useAmericanPricerForUnexOpts CheckBox(default = false))
Assume early exercise is possible for:
Put holder $(@bind earlyExPut CheckBox(default = true))
$nbsp $nbsp Call holder $(@bind earlyExCall CheckBox(default = true))
"""
# ╔═╡ 3046063a-0396-4e8c-a602-b9f8f17295d4
@bind graph_inputs confirm(
PlutoUI.combine() do Child
md"""
**Plot Selection**:
Plot conversion price vs repo rate:$(Child(CheckBox(default = false)))
$nbsp
for repo rng $(Child(Slider(-1000:0, show_value = true, default = -10)))
$nbsp
to $(Child(Slider(0:100, show_value = true, default = 1)))
Do delta/gamma graphs:$(Child(CheckBox(default = false)))
Do exercise boundary graphs:$(Child(CheckBox(default = false)))
Do mtm pnl contour graph (not available):$(Child(CheckBox(default = false)))
"""
end
)
# ╔═╡ 39493c2e-0870-417b-94bc-3658c1c18d34
begin
(doRepoGraph,minRate,maxRate,doRiskGraphs,doExBoundaryGraphs, doMtmPnlGraph) = graph_inputs
Print()
end
# ╔═╡ 6413cc25-ac66-4989-8307-312a35243d1f
begin
returnRangePct = LinRange(minRate,maxRate,2*Threads.nthreads()) # just for delta/gamma graphs
days = (dt_expiry - dt_trade).value
r_repo = Rmm2Rcc(r_repo_mm_pct, days) / 100
r_csa = Rmm2Rcc(r_csa_mm_pct, days) /100
vol = vol_pct / 100.0
max_totrtn = -1 + exp((r_repo - 0.5 * vol^2) * (dt_expiry - dt_trade).value / 365 + vol * sqrt((dt_expiry - dt_trade).value / 365) * 3)
min_totrtn = -1 + exp((r_repo - 0.5 * vol^2) * (dt_expiry - dt_trade).value / 365 + vol * sqrt((dt_expiry - dt_trade).value / 365) * -3)
max_rtn_pct = 10 * ceil(10 * max_totrtn)
min_rtn_pct = 10 * floor(10 * min_totrtn)
numPrices = round(Int, 1 + (max_rtn_pct - min_rtn_pct) / 10) # number of x-axis points for graph
numDates = maximum([20; round(Int, (dt_expiry - dt_trade).value / 10)]) # number of y-axis points for graph
#American model results
conv = conversion_am(treeType, S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)
p = option_am(treeType, "put", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)[1]
c = option_am(treeType, "call", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)[1]
function isbad(x)
if ismissing(x) || isnan(x)
return true
else
return false
end
end
if !isbad(mktConversionPx)
irr = implied_repo_from_conversion_am(mktConversionPx, treeType, S, K, r_csa_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)
else
irr = r_repo_mm_pct
convMkt = conv
end
#European model results
conv_bs = conversion_BS(S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt)
p_bs = BS("put", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt)
c_bs = BS("call", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt)
if !isbad(mktConversionPx)
irr2 = implied_repo_from_conversion_BS(mktConversionPx, S, K, r_csa_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt)
else
irr2 = r_repo_mm_pct
end
#=
if !ismissing(pExPx)
pExPxSynth = pExPx
local indx = findall(pExDt .>= dt_exdiv)
if length(indx) > 0
pExPxSynth = pExPxSynth + sum(divamt[indx])
end
pExRtn = log(pExPxSynth/S)
pExTime = (pExDt - dt_trade).value/365
pExSigs = (pExRtn - (r_repo - vol^2/2) * pExTime) / (vol * sqrt(pExTime))
if pExRtn > 0
pExDir = "above"
else
pExDir = "below"
end
str1 = "earliest put exercise seen by valuation is at " * string(round(pExPx, digits = 2)) * " on " * Dates.format(pExDt,"u d, Y")
if isfinite(pExSigs)
str1 = str1 * " which is " * string(abs(round(Int, pExSigs))) * "σ "* pExDir *" spot"
end
else
str1 = " "
end
if !ismissing(cExPx)
cExPxSynth = cExPx
local indx = findall(cExDt .>= dt_exdiv)
if length(indx) > 0
cExPxSynth = cExPxSynth + sum(divamt[indx])
end
cExRtn = log(cExPxSynth/S)
cExTime = (cExDt - dt_trade).value/365
cExSigs = (cExRtn - (r_repo - vol^2/2) * cExTime) / (vol * sqrt(cExTime))
if cExRtn > 0
cExDir = "above"
else
cExDir = "below"
end
str2 = "earliest call exercise seen by valuation is at " * string(round(cExPx, digits = 2)) * " on " * Dates.format(cExDt,"u d, Y")
if isfinite(cExSigs)
str2 = str2 * " which is " * string(abs(round(Int, cExSigs))) * "σ "* cExDir *" spot"
end
else
str2 = " "
end
=#
if isbad(mktConversionPx)
dum = convMkt
else
dum = mktConversionPx
end
message = string(
"** American model **\n",
"With user-input repo rate of ", round(r_repo_mm_pct,digits=2),"%,",
"\nconversion = ",
round(conv, digits = 3),
"\nput = ",
round(p, digits = 2),
"\ncall = ",
round(c, digits = 2),
"\n\nBut note that user-input conversion price of ", mktConversionPx," implies a repo rate of ", round(irr,digits = 2),"%",
)
#=,
"\n" * str1,
"\nexpected put life is " * string(round(putTau)) * " days, i.e. until " * Dates.format(dt_trade + Day(round(putTau)),"Y-m-d"),
"\n" * str2,
"\nexpected call life is " * string(round(callTau)) * " days, i.e. until " * Dates.format(dt_trade + Day(round(callTau)),"Y-m-d"),
)
=#
message = string(
message,
"\n\n** European (BS) model **\n",
"With user-input repo rate of ", round(r_repo_mm_pct,digits=2),"%,",
"\nconversion = ",
round(conv_bs, digits = 3),
"\nput = ",
round(p_bs, digits = 2),
"\ncall = ",
round(c_bs, digits = 2),
"\n\nBut note that user-input conversion price of ", mktConversionPx," implies a repo rate of ", round(irr2,digits = 2),"%",
"\n(using BS and, therefore, ignoring early exercise)"
)
#=
message = string(
message,
"\n",
"\nusing European model:",
"\nconversion = ",
round(conv_bs, digits = 4),
"\nput = ",
round(p_bs, digits = 2),
"\ncall = ",
round(c_bs, digits = 2),
"\nimplied repo rate from mkt conversion price is ",
round(irr2, digits = 2),
"%\n",
)
=#
Print()
end
# ╔═╡ 03142ff5-32f4-44a7-a11f-38d55ce06712
Print(message)
# ╔═╡ 97498b0f-b148-41e7-b16e-abb6447f0b61
if doRepoGraph
r_repo_pct_rng = LinRange(minRate,maxRate,30)
conversions = zeros(length(r_repo_pct_rng))
Threads.@threads for i = 1:length(r_repo_pct_rng)
conversions[i] = conversion_am(treeType, S, K, r_csa_mm_pct, r_repo_pct_rng[i], vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)
end
global p_repo = scatter(r_repo_pct_rng, conversions, label = "conv price as function of repo rate", xlabel = "r_repo_pct", ylabel = "conversion px", color=:blue)
plot!(r_repo_pct_rng, conversions, label = "", color=:blue)
hline!([mktConversionPx], label = "mkt conv px = $mktConversionPx")
Print()
#png(p1,"/Users/alex/Downloads/png1.png")
end
# ╔═╡ 1bd4a082-fcfb-4ae2-b435-d8ea0e926033
if doRepoGraph
try
plot(p_repo)
catch e
println("the repo graph barfed - no graph available")
end
else
Print()
end
# ╔═╡ 7a389e3c-a5d7-4780-b637-122b88d35c4c
if doRiskGraphs
if sum(divamt) > 0
title = "Conversion with strike = \$$K, vol = $(vol_pct)%, expiry = $((dt_expiry - dt_trade).value) days, \ndiv = $divamt, exdiv = $(Dates.value.(dt_exdiv .- dt_trade)) days, r_csa = $(r_csa_mm_pct)%, r_repo = $(r_repo_mm_pct)%"
else
title = "Conversion with strike = \$$K, vol = $(vol_pct)%, expiry = $((dt_expiry - dt_trade).value) days, \nr_csa = $(r_csa_mm_pct)%, r_repo = $(round(r_repo_mm_pct,digits = 2))%"
end
return_range = (100 .+ collect(-30:1:80)) ./ 100.0
n = length(return_range)
δ = Vector{Float64}(undef, n)
Γ = Vector{Float64}(undef, n)
Threads.@threads for i = 1:n
s = return_range[i] * S
putVal, putDelta, putGamma = option_am(treeType, "put", s, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)
callVal, callDelta, callGamma = option_am(treeType, "call", s, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt, stepsPerDay)
δ[i] = putDelta - callDelta + 1
Γ[i] = putGamma - callGamma
end
p1a = plot(
S .* return_range,
δ,
lw = 4,
label = "",
ylabel = "Delta",
#xlabel = "Price",
#xguidefontsize = 8,
title = title,
titlefontsize = 10,
)
vline!(p1a, [S], legend = false)
p1b = plot(
S .* return_range,
Γ,
lw = 4,
label = "",
ylabel = "Gamma",
xlabel = "Price",
xguidefontsize = 8,
#title = title,
#titlefontsize = 10
)
vline!(p1b, [S], legend = false)
Print()
end
# ╔═╡ c4fe8ad8-bbd9-490f-8509-27a3536cbc2c
if doRiskGraphs
try
plot(p1a, p1b, layout = (2, 1))
catch e
println("the code barfed - no graph available")
end
else
Print()
end
# ╔═╡ 6542d0e2-8e5f-4a06-ac97-4aca938d1594
if doExBoundaryGraphs
if treeType == "CRR"
(callpx, X_call) = crr_extra_output("call", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt,2)[1:2]
#
(putpx, X_put) = crr_extra_output("put", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt,2)[1:2]
elseif treeType == "LR"
if (dt_expiry - dt_trade).value % 2 == 0
println("Skipping LR valuation because stepsPerDay = 1 gives even number of steps -> unreliable valuation")
X =[]
else
(callpx, X_call) = lr_extra_output("call", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt,2)[1:2]
#
(putpx, X_put) = lr_extra_output("put", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt,2)[1:2]
end
elseif treeType == "Trinomial"
(callpx, X_call) = trinomial_extra_output("call", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt,2)[1:2]
#
(putpx, X_put) = trinomial_extra_output("put", S, K, r_csa_mm_pct, r_repo_mm_pct, vol_pct, dt_trade, dt_expiry, divamt, dt_exdiv, dt_divpmt,2)[1:2]
end
if sum(divamt) > 0
dates2 = dt_trade:Day(1):maximum(vcat(dt_divpmt, dt_expiry))
ndays2 = length(dates2)
divfvs = zeros(Float64,ndays2)
# we want at each slice divfv = value of all divs w/ exdiv not in the past as of that slice
dfs = exp.(-r_csa * (0:ndays2-1) / 360)
i_exdiv = zeros(Int, length(divamt))
i_divpmt = zeros(Int, length(divamt))
for i = 1:length(divamt)
i_divpmt[i] = findall(dates2 .== dt_divpmt[i])[1]
i_exdiv[i] = findall(dates2 .== dt_exdiv[i])[1]
global divfvs[1:i_exdiv[i]-1] .=divfvs[1:i_exdiv[i]-1] + (divamt[i] * dfs[i_divpmt[i]]) ./ dfs[1:i_exdiv[i]-1]
end
end
callMult = 1
putMult = -1
##
myString_call = ""
if size(X_call)[1] > 0 # i.e. when there is early exercise
ndays = nrow(X_call)
#r_csa = log(1.0 + 0.01 * r_csa_mm_pct * ndays / 360) / (ndays / 360)
#r_repo = log(1.0 + 0.01 * r_repo_mm_pct * ndays / 360) / (ndays / 360)
S0 = S
X_call.divfvs = zeros(ndays)
if sum(divamt) > 0
X_call.divfvs = divfvs[1:ndays]
S0 = S0 - divfvs[1]
end
σ = vol_pct/100 * S / S0
X_call.noSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_call.sliceNum / 360 ) + X_call.divfvs
X_call.oneSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_call.sliceNum / 360 .+ σ * sqrt.(X_call.sliceNum / 360) * 1 * callMult) + X_call.divfvs
X_call.twoSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_call.sliceNum / 360 .+ σ * sqrt.(X_call.sliceNum / 360) * 2 * callMult) + X_call.divfvs
X_call.threeSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_call.sliceNum / 360 .+ σ * sqrt.(X_call.sliceNum / 360) * 3 * callMult) + X_call.divfvs
ymin_call = 0.9 * minimum(vcat(X_call.noSig, X_call.threeSig, X_call.sExPrice[isfinite.(X_call.sExPrice)]))
ymax_call = 1.1 * maximum(vcat(X_call.noSig, X_call.threeSig, X_call.sExPrice[isfinite.(X_call.sExPrice)]))
gr()
expStr = Dates.format(dt_expiry,"d-u-yy")
trdStr = Dates.format(dt_trade,"d-u-yy")
indx = findall(isfinite.(X_call.sExPrice))
if length(indx) > 0
mindx = minimum(indx)
myString_call = " (earliest call exercise boundary at $(round(X_call.sExPrice[mindx],digits=2)) on $(X_call.date[mindx]), i.e. $((X_call.date[mindx]-dt_trade).value) days from trade date)"
end
end
##put
myString_put = ""
if size(X_put)[1]>0 # in case of no early exercise
ndays = nrow(X_put)
#r_csa = log(1.0 + 0.01 * r_csa_mm_pct * ndays / 360) / (ndays / 360)
#r_repo = log(1.0 + 0.01 * r_repo_mm_pct * ndays / 360) / (ndays / 360)
S0 = S
X_put.divfvs = zeros(ndays)
if sum(divamt) > 0
X_put.divfvs = divfvs[1:ndays]
S0 = S0 - divfvs[1]
end
σ = vol_pct/100 * S / S0
X_put.noSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_put.sliceNum / 360 ) + X_put.divfvs
X_put.oneSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_put.sliceNum / 360 .+ σ * sqrt.(X_put.sliceNum / 360) * 1 * putMult) + X_put.divfvs
X_put.twoSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_put.sliceNum / 360 .+ σ * sqrt.(X_put.sliceNum / 360) * 2 * putMult) + X_put.divfvs
X_put.threeSig = S0 .* exp.((r_repo - 0.5 * σ^2) * X_put.sliceNum / 360 .+ σ * sqrt.(X_put.sliceNum / 360) * 3 * putMult) + X_put.divfvs
ymin_put = 0.9 * minimum(vcat(X_put.noSig, X_put.threeSig, X_put.sExPrice[isfinite.(X_put.sExPrice)]))
ymax_put = 1.1 * maximum(vcat(X_put.noSig, X_put.threeSig, X_put.sExPrice[isfinite.(X_put.sExPrice)]))
gr()
expStr = Dates.format(dt_expiry,"d-u-yy")
trdStr = Dates.format(dt_trade,"d-u-yy")
indx = findall(isfinite.(X_put.sExPrice))
if length(indx) > 0
mindx = minimum(indx)
myString_put = " (earliest put exercise boundary at $(round(X_put.sExPrice[mindx],digits=2)) on $(X_put.date[mindx]), i.e. $((X_put.date[mindx]-dt_trade).value) days from trade date)"
end
end
Print()
end
# ╔═╡ 07c8d43e-163d-44dd-ba31-fcf045d178b8
if doExBoundaryGraphs
gr()
if size(X_put)[1]>0 # in case of no early exercise
if false
p_exput = scatter(X_put.date, X_put.exPrice, ticks=:native, label = "", bg=:lightgray, size = (800,600), ylims = (ymin_put,ymax_put), yguide = "price", yguidefontsize = 12, yguidefontcolor = :black, ytickfontcolor=:black)
else
p_exput = scatter(X_put.date, NaN .+ X_put.exPrice, ticks=:native, label = "", bg=:lightgray, size = (800,600), ylims = (ymin_put,ymax_put), yguide = "price", yguidefontsize = 12, yguidefontcolor = :black, ytickfontcolor=:black)
end
title!(p_exput, "EE region (light blue) for S = $S, K = $K, $expStr PUT as of $trdStr with σ = $vol_pct%",titlefontsize=9)
xlabel!(p_exput, "Stock has 16%, 2%, 0.1% prob of being outside respective band")
#if lowercase(opttype)[1] == 'c'
# ribbonGapBelow = zeros(nrow(X_put))
# ribbonGapAbove = ymax_call .- X_put.sExPrice
#else
ribbonGapBelow2 = X_put.sExPrice .- ymin_put
ribbonGapAbove2 = zeros(nrow(X_put))
#end
plot!(p_exput, X_put.date, X_put.sExPrice, lw=0, color=:blue, label = "",
ribbon = (ribbonGapBelow2, ribbonGapAbove2),fillalpha=0.1
#ribbon = (X.sExPrice .- ymin,zeros(nrow(X)) ),fillalpha=0.2
)
plot!(p_exput, X_put.date, X_put.noSig,label="", color = :black, lw = 2)
plot!(p_exput, X_put.date, X_put.oneSig,label="",ls=:dash, color = :darkgray)
plot!(p_exput, X_put.date, X_put.twoSig,label="",ls=:dash, color = :darkgray)
plot!(p_exput, X_put.date, X_put.threeSig,label="",ls=:dash, color = :darkgray)
bar!(twinx(),X_put.date, X_put.cumExProb,ylims=(0,1),color=:red,alpha=0.25,label="", yguide = "cumulative prob of early exercise", yguidefontsize = 12, yguidefontcolor = :red, ytickfontcolor=:red)#yguidefont = font(:red),ytickfont = font(:red, 8),)
end
Print()
end
# ╔═╡ 18d602fd-5041-4d08-82f3-74b3efd3b7e5
if doExBoundaryGraphs && earlyExPut
try
plot(p_exput)
catch e
println("the code barfed - no graph available")
end
else
Print()
end
# ╔═╡ fa50e635-ded6-40b3-9a70-b1efd3abaa7c
if doExBoundaryGraphs
gr()
if size(X_call)[1]>0 # in case of no early exercise
if false
p_excall = scatter(X_call.date, X_call.exPrice, ticks=:native, label = "", bg=:lightgray, size = (800,600), ylims = (ymin_call,ymax_call), yguide = "price", yguidefontsize = 12, yguidefontcolor = :black, ytickfontcolor=:black)
else
p_excall = scatter(X_call.date, NaN .+ X_call.exPrice, ticks=:native, label = "", bg=:lightgray, size = (800,600), ylims = (ymin_call,ymax_call), yguide = "price", yguidefontsize = 12, yguidefontcolor = :black, ytickfontcolor=:black)
end
title!(p_excall, "EE region (light blue) for S = $S, K = $K, $expStr CALL as of $trdStr with σ = $vol_pct%",titlefontsize=9)
xlabel!(p_excall, "Stock has 16%, 2%, 0.1% prob of being outside respective band")
#if lowercase(opttype)[1] == 'c'
ribbonGapBelow = zeros(nrow(X_call))
ribbonGapAbove = ymax_call .- X_call.sExPrice
#else
# ribbonGapBelow = X_call.sExPrice .- ymin
# ribbonGapAbove = zeros(nrow(X))
#end
plot!(p_excall, X_call.date, X_call.sExPrice, lw=0, color=:blue, label = "",
ribbon = (ribbonGapBelow, ribbonGapAbove),fillalpha=0.1
#ribbon = (X.sExPrice .- ymin,zeros(nrow(X)) ),fillalpha=0.2
)
plot!(p_excall, X_call.date, X_call.noSig,label="", color = :black, lw = 2)
plot!(p_excall, X_call.date, X_call.oneSig,label="",ls=:dash, color = :darkgray)
plot!(p_excall, X_call.date, X_call.twoSig,label="",ls=:dash, color = :darkgray)
plot!(p_excall, X_call.date, X_call.threeSig,label="",ls=:dash, color = :darkgray)
bar!(twinx(),X_call.date, X_call.cumExProb,ylims=(0,1),color=:red,alpha=0.25,label="", yguide = "cumulative prob of early exercise", yguidefontsize = 12, yguidefontcolor = :red, ytickfontcolor=:red)#yguidefont = font(:red),ytickfont = font(:red, 8),)
Print()
end
end
# ╔═╡ e45dcbae-bcb0-4e33-9f0d-94519c47fd04
if doExBoundaryGraphs && earlyExCall
try
plot(p_excall)
catch e
println("the code barfed - no graph available")
end
else
Print()
end
# ╔═╡ 1e467d1d-4b5d-45a1-a6f5-043245a4d728
begin
if doMtmPnlGraph
#tic = Sys.time()
convPxAtTradeDate = mktConversionPx
if isbad(convPxAtTradeDate)
convPxAtTradeDate = conversion_Basic(
S,
K,
r_csa_mm_pct,
r_repo_mm_pct,
vol_pct,
dt_exp,
stepsPerDay,
dt_exdiv,
dt_divpmt,
divamt,
dt_trade,
frac_of_trading_day_remaining,
earlyExPut,
earlyExCall
)[1]
end
rtnVector = collect(LinRange(min_rtn_pct, max_rtn_pct, numPrices))
synthPxVector = (100 .+ rtnVector) ./ 100 * S
t_exp = (dt_expiry - dt_trade).value
dateVector = unique(
dt_trade +
Day.(
round.(
Int32,
#collect(LinRange(0, (dt_exp - dt_trade).value, numDates)),
collect(LinRange(1, (dt_expiry - dt_trade).value, numDates)),
),
),
)
v1 = repeat(dateVector, outer = length(synthPxVector)) # dates
v2 = [(v1[i] - v1[1]).value for i = 1:length(v1)] # days from trade date
v3 = repeat(rtnVector, inner = length(dateVector)) # returns
v4 = repeat(synthPxVector, inner = length(dateVector)) # synthetic pxs
v5 = copy(v4)
for i=1:length(divamt)
local indx = findall(v1 .>= dt_exdiv[i])
if length(indx) > 0
v5[indx] = v5[indx] .- divamt[i]
end
end
numEval = numPrices * length(dateVector)
pnl_array = zeros(length(dateVector), numPrices)
data = DataFrame(
date = v1,
days_out = v2,
pct_move = v3,
px_synth = v4,
px_act = v5,
convPx = zeros(numEval),
call_ex = (zeros(numEval) .> 1), #just a way of saying false
call_ex_days_out = zeros(numEval) .+ NaN, #just a way of saying NaN
call_ex_px = zeros(numEval) .+ NaN,
unex_put_px = zeros(numEval) .+ NaN,
put_ex = (zeros(numEval) .> 1),
put_ex_days_out = zeros(numEval) .+ NaN,
put_ex_px = zeros(numEval) .+ NaN,
unex_call_px = zeros(numEval) .+ NaN,
accruedInterest = zeros(numEval),
pnl = zeros(numEval),
)
#=(call, put, exInfo) = conversion(
S,
K,
r_csa,
r_repo,
vol,
dt_exp,
steps_per_day,
dt_exdiv,
dt_divpmt,
divamt,
dt_trade,
true,
frac_of_trading_day_remaining,
)=#
allDates = exInfo.date#dt_trade .+ Day.(0:(dt_exp-dt_trade).value)
cb = NaN .+ zeros(length(allDates))
pb = NaN .+ zeros(length(allDates))
indx1 = round.(Int32, myMatch(allDates, exInfo.date))
for i = 1:length(indx1)
j = indx1[i]
cb[j] = exInfo.cb[i]
pb[j] = exInfo.pb[i]
end
# fill data dataframe with exercise info for linear px evolutions
t_exdiv_vec = Dates.value.(dt_exdiv .- dt_trade)
Threads.@threads for i = 1:numEval
#println(i)
if data.days_out[i] > 0
#global px = collect(LinRange(S, data.px_synth[i], 1 + data.days_out[i]))
#global N = length(px)
px = collect(LinRange(S, data.px_synth[i], 1 + data.days_out[i]))
N = length(px)
# adjust p for divs
for j=1:length(t_exdiv_vec)
if N >= 1 + t_exdiv_vec[j]
px[1+t_exdiv_vec[j]:N] = px[1+t_exdiv_vec[j]:N] .- divamt[j]
end
end
#global pindx = findall(px .<= pb[1:N])
pindx = findall(px .<= pb[1:N])
if length(pindx) > 0
pindx = minimum(pindx)
data.put_ex[i] = true
data.put_ex_px[i] = px[pindx]
data.put_ex_days_out[i] = pindx - 1
if useAmericanPricerForUnexOpts
data.unex_call_px[i] = option_am(
"call",
data.put_ex_px[i],
K,
r_csa_mm_pct,
r_repo_mm_pct,
vol_pct,
dt_exp,
5,
dt_exdiv,
dt_divpmt,
divamt,
dt_trade + Day(data.put_ex_days_out[i]),
frac_of_trading_day_remaining,
)
else
data.unex_call_px[i] = BS(
"call",
data.put_ex_px[i],
K,
r_csa_mm_pct,
r_repo_mm_pct,
vol_pct,
dt_exp,
dt_exdiv,
dt_divpmt,
divamt,
dt_trade + Day(data.put_ex_days_out[i]),
)
end
end
#global cindx = findall(px .>= cb[1:N])
cindx = findall(px .>= cb[1:N])
if length(cindx) > 0
cindx = minimum(cindx)
data.call_ex[i] = true
data.call_ex_px[i] = px[cindx]
data.call_ex_days_out[i] = cindx - 1
if useAmericanPricerForUnexOpts
data.unex_put_px[i] = option_am(
"put",
data.call_ex_px[i],
K,
r_csa_mm_pct,
r_repo_mm_pct,
vol_pct,
dt_exp,
5,
dt_exdiv,
dt_divpmt,
divamt,
dt_trade + Day(data.call_ex_days_out[i]),
frac_of_trading_day_remaining,
)
else
data.unex_put_px[i] = BS(
"put",
data.call_ex_px[i],
K,
r_csa_mm_pct,
r_repo_mm_pct,
vol_pct,
dt_exp,
dt_exdiv,
dt_divpmt,
divamt,
dt_trade + Day(data.call_ex_days_out[i]),
)
end
end
end
end
Threads.@threads for i = 1:numEval
#println(i)
a = findfirst(dateVector .== data.date[i])
b = findfirst(rtnVector .== data.pct_move[i])
if data.date[i] == dt_exp
data.convPx[i] = 0
S_avg = (S + data.px_synth[i]) / 2
data.accruedInterest[i] =
-(S_avg * r_repo_mm_pct/100 + (K - S_avg + convPxAtTradeDate) * r_csa_mm_pct/100) *
data.days_out[i] / 360
data.pnl[i] =
-convPxAtTradeDate +
+data.accruedInterest[i] +
sum(divamt .* (data.days_out[i] .>= t_exdiv_vec))
elseif data.date[i] < dt_exp
data.convPx[i] = conversion_Basic(
data.px_act[i],
K,
r_csa_mm_pct,
r_repo_mm_pct,
vol_pct,
dt_exp,
stepsPerDay,
dt_exdiv,
dt_divpmt,
divamt,
data.date[i],
)[1]
## assumes interest calc'd on avg px
if !(data.put_ex[i] | data.call_ex[i])
# pay K + convPx for conversion bundle
# repo out the stock and use proceeds of S to defray borrowing of K + convPx
# therefore pay r_csa on K-S + convPx and pay r_repo on S
S_avg = (data.px_synth[i] + S) / 2
data.accruedInterest[i] =
-(
S_avg * r_repo_mm_pct/100 +
(K - S_avg + convPxAtTradeDate) * r_csa_mm_pct/100
) * data.days_out[i] / 360
data.pnl[i] =
(data.convPx[i] - convPxAtTradeDate) +
data.accruedInterest[i] +
sum(divamt .* (data.days_out[i] .>= t_exdiv_vec))
else
if data.put_ex[i]
t_early = data.put_ex_days_out[i]
S_ex = data.put_ex_px[i]
else
t_early = data.call_ex_days_out[i]
S_ex = data.call_ex_px[i]
end
S_avg = (S + S_ex) / 2
data.accruedInterest[i] =
-(
S_avg * r_repo_mm_pct/100 +
(K - S_avg + convPxAtTradeDate) * r_csa_mm_pct/100
) * t_early / 360
# we ignore any residual value in the unexercised option
data.pnl[i] =
-convPxAtTradeDate +
+data.accruedInterest[i] +
sum(divamt .* (t_early .>= t_exdiv_vec))
if data.put_ex[i] &
includeUnexOptVals &
(data.unex_call_px[i] > 0)
data.pnl[i] = data.pnl[i] - data.unex_call_px[i]
end
if data.call_ex[i] &
includeUnexOptVals &
(data.unex_put_px[i] > 0)
data.pnl[i] = data.pnl[i] + data.unex_put_px[i]
end
end
end
pnl_array[a, b] = data.pnl[i]
end
T = zeros(length(dateVector))
for i = 1:length(T)
T[i] = (dateVector[i] - dateVector[1]).value
end
up1 =
100 .* (exp.((r_repo - 0.5 * vol^2) .* T / 365 .+ vol .* sqrt.(T ./ 365) * 1) .- 1)
up2 =
100 .* (exp.((r_repo - 0.5 * vol^2) .* T / 365 .+ vol .* sqrt.(T ./ 365) * 2) .- 1)
up3 =
100 .* (exp.((r_repo - 0.5 * vol^2) .* T / 365 .+ vol .* sqrt.(T ./ 365) * 3) .- 1)
down1 =
100 .* (exp.((r_repo - 0.5 * vol^2) .* T / 365 .+ vol .* sqrt.(T ./ 365) * -1) .- 1)
down2 =
100 .* (exp.((r_repo - 0.5 * vol^2) .* T / 365 .+ vol .* sqrt.(T ./ 365) * -2) .- 1)
down3 =
100 .* (exp.((r_repo - 0.5 * vol^2) .* T / 365 .+ vol .* sqrt.(T ./ 365) * -3) .- 1)
centerLine = zeros(length(T))
if sum(divamt) > 0
xlabel6 = "expiry = $dt_exp, K = $K, div = $divamt, exdiv_dt = $dt_exdiv, r_csa = $r_csa_mm_pct%, rebate = $r_repo_mm_pct%"
else
xlabel6 = "expiry = $dt_exp, K = $K, r_csa = $r_csa_mm_pct%, rebate = $r_repo_mm_pct%"
end
amax = maximum(abs.(pnl_array))
p_contour = contour(
dateVector,
rtnVector,
transpose(pnl_array),
fill = (true, cgrad(:RdYlBu_11)),
clims = (-amax, amax),
)
plot!(dateVector, up1, color = :black, legend = false, linestyle = :dot)
plot!(dateVector, up2, color = :black, legend = false, linestyle = :dot)
plot!(dateVector, up3, color = :black, legend = false, linestyle = :dot)
plot!(dateVector, down1, color = :black, legend = false, linestyle = :dot)
plot!(dateVector, down2, color = :black, legend = false, linestyle = :dot)
plot!(dateVector, down3, color = :black, legend = false, linestyle = :dot)
plot!(
dateVector,
centerLine,
color = :black,
legend = false,
linestyle = :solid,
)
#xlabel!("Date")
ylabel!("Percentage Move")
xlabel!(xlabel6, guidefontsize = 7)
title!(
"Conversion MTM PNL Heatmap with 1σ, 2σ, 3σ bands \n(stock has 16%, 2%, 0.1% prob of being outside band)",
titlefontsize = 10,
)
#=
if do3dGraph
r1 = round(100 * r_csa, digits = 2)
r2 = round(100 * r_repo, digits = 2)
if divamt > 0
myTitle = "$graphTitle<br>convPx = $(round(convPxAtTradeDate,digits=2)) S = $S K = $K expiry = $dt_exp r_csa = $r1% rebate = $r2%<br> div = $divamt exdiv_dt = $dt_exdiv dt_divpmt = $dt_divpmt"
else
myTitle = "$graphTitle<br>convPx = $(round(convPxAtTradeDate,digits=2)) S = $S K = $K expiry = $dt_exp r_csa = $r1% rebate = $r2%"
end
plotly()
p7 = plot(dateVector, rtnVector, transpose(pnl_array), size = (1000,700),st = :surface,title = myTitle)
end
Print()
=#
#toc = Sys.time()
#println("done with the mtmContourGraph section in $(round(toc-tic,digits =1)) seconds")
end
Print()
end
# ╔═╡ 3049b048-2929-401d-8687-1e80ca2b8f48
if doMtmPnlGraph
try
plot(p_contour)
catch e
Print("the code barfed - no graph available")
end
else
Print()
end
# ╔═╡ a784bc70-4b47-4154-a2c2-56b676ed91e8
html"""
<style>
div.edit_or_run {
display: none !important;
visibility: hidden !important;
width: 0 !important;
height: 0 !important;