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= K₂ p₁ = European Put(expiry, Single Stock(), K₁) p₂ = European Put(expiry, Single Stock(), K₂) Both(p₁, Give(p₂)) end bear₂ = bear_put(expirydate, K₁, K₂) r,p_bear₂ = payoff_curve(bear₂, expirydate, price) blk = colorant"black" red = colorant"red" blu = colorant"blue" plot(layer( x=s, y=p_bear₂, Geom.line, Theme(default_color=blk,line_width=1.5mm)), layer( x=s₁, y= pp₁ , Geom.line, Theme(default_color=red,line_width=1.0mm)), layer( x=s₂, y=-pp₂ , Geom.line, Theme(default_color=blu,line_width=1.0mm)), Guide.manual_color_key("",["Bear Put", "call₁", "-call₂"], ["black", "red", "blue"]), Guide.title("Bear Put Payoff Curve at Expiry"), Guide.xlabel("Stock Price"), Guide.ylabel("Payoff"))# Buy a call at the low strike # Sell a call at the high strike function bull_call(expiry:: Date, K₁, K₂) @assert K₁ ! = K₂ c₁ = European Call(expiry, Single Stock(), K₁) c₂ = European Call(expiry, Single Stock(), K₂) Both(c₁, Give(c₂)) end bull₁ = bull_call(expirydate, K₁, K₂) r,p_bull₁ = payoff_curve(bull₁, expirydate, price) blk = colorant"black" red = colorant"red" blu = colorant"blue" plot(layer( x=s ,y=p_bull₁, Geom.line, Theme(default_color=blk,line_width=1.5mm)), layer( x=s₁,y= cp₁ , Geom.line, Theme(default_color=red,line_width=1.0mm)), layer( x=s₂,y=-cp₂ , Geom.line, Theme(default_color=blu,line_width=1.0mm)), Guide.manual_color_key("",["Bull Call", "call₁", "-call₂"], ["black", "red", "blue"]), Guide.title("Bull Call Payoff Curve at Expiry"), Guide.xlabel("Stock Price"), Guide.ylabel("Payoff"))# Buy a put at the high strike # Sell a put at the low strike function bull_put(expiry:: Date, K₁, K₂) @assert K₁ !

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The included plots show the payoff of the option at the middle strike, K₂.call₁ = European Call(expirydate, Single Stock(), K₁) call₂ = European Call(expirydate, Single Stock(), K₂) call₃ = European Call(expirydate, Single Stock(), K₃) s₁,cp₁ = payoff_curve(call₁, expirydate, price) s₂,cp₂ = payoff_curve(call₂, expirydate, price) s₃,cp₃ = payoff_curve(call₃, expirydate, price) plot(x = s₂, y = cp₂, Geom.line, Theme(default_color=colorant"blue", line_width = 1.0mm), Guide.title("Vanilla Call Payoff Curve at Expiry"), Guide.xlabel("Stock Price"), Guide.ylabel("Payoff"))put₁ = European Put(expirydate, Single Stock(), K₁) put₂ = European Put(expirydate, Single Stock(), K₂) put₃ = European Put(expirydate, Single Stock(), K₃) s₁,pp₁ = payoff_curve(put₁, expirydate, price) s₂,pp₂ = payoff_curve(put₂, expirydate, price) s₃,pp₃ = payoff_curve(put₃, expirydate, price) plot(x = s₂, y = pp₂, Geom.line, Theme(default_color=colorant"blue", line_width = 1.0mm), Guide.title("Vanilla Put Payoff Curve at Expiry"), Guide.xlabel("Stock Price"), Guide.ylabel("Payoff"))# Buy a call at the high strike # Sell a call at the low strike function bear_call(expiry:: Date, K₁, K₂) @assert K₁ !

= K₂ c₁ = European Call(expiry, Single Stock(), K₁) c₂ = European Call(expiry, Single Stock(), K₂) Both(Give(c₁), c₂) end bear₁ = bear_call(expirydate, K₁, K₂) s,p_bear₁ = payoff_curve(bear₁, expirydate, price) blk = colorant"black" red = colorant"red" blu = colorant"blue" plot(layer( x=s, y=p_bear₁, Geom.line, Theme(default_color=blk,line_width=1.5mm)), layer( x=s₁,y=-cp₁ , Geom.line, Theme(default_color=red,line_width=1.0mm)), layer( x=s₂,y= cp₂ , Geom.line, Theme(default_color=blu,line_width=1.0mm)), Guide.manual_color_key("",["Bear Call", "-call₁", "call₂"], ["black", "red", "blue"]), Guide.title("Bear Call Payoff Curve at Expiry"), Guide.xlabel("Stock Price"), Guide.ylabel("Payoff"))# Buy a put at the low strike # Sell a put at the high strike function bear_put(expiry:: Date, K₁, K₂) @assert K₁ ! Actual365(),0.0,: Continuous,-1,2017-02-09)),2017-02-09:1 day:2017-06-09,[100.0 100.665 …

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expirydate = Date("2016-12-25") startdate = Date("2016-12-1") interestrate = 0.05 carryrate = 0.1 volatility = 0.15 K₁ = 98.0USD K₂ = 100.0USD K₃ = 102.0USD L = 11 # Layers in the binomial lattice / Number of time stepsgbmm = Geom BMModel(startdate, K₂, interestrate, carryrate, volatility) crr = CRRModel(startdate, expirydate, L, K₂, interestrate, carryrate, volatility) mcm = Miletus.montecarlo(gbmm, startdate:expirydate, 10_000)Next let's define a function for calculating the payoff curve of each spread at expiry over a range of asset prices.

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