Merge pull request #2 from aleCombi/Adding-Implied-Vol-Surface-to-BlackScholesInputs

Adding implied vol surface to black scholes inputs

Author: aleCombi

.gitignore

@@ -1 +1,2 @@
 **/Manifest.toml
+**/.vscode

Project.toml

@@ -6,8 +6,10 @@ version = "1.0.0-DEV"
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Bessels = "0e736298-9ec6-45e8-9647-e4fc86a2fe38"
 DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+DiffEqGPU = "071ae1c0-96b5-11e9-1965-c90190d839ea"
 DiffEqNoiseProcess = "77a26b50-5914-5dd7-bc55-306e6241c503"
 DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
@@ -20,6 +22,7 @@ Optimization = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
 Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
+SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
@@ -28,8 +31,10 @@ Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 [compat]
 Accessors = "0.1.42"
 BenchmarkTools = "1.6.0"
+Bessels = "0.2.8"
 DataInterpolations = "7.2.0"
 Dates = "1.11.0"
+DiffEqGPU = "3.4.1"
 DiffEqNoiseProcess = "5.24.1"
 DifferentialEquations = "7.16.0"
 Distributions = "0.25"
@@ -42,6 +47,7 @@ Optimization = "4.1.2"
 Polynomials = "4.0.19"
 Random = "1.11.0"
 Roots = "2.2.6"
+SciMLBase = "2.77.2"
 SpecialFunctions = "2.5.0"
 StaticArrays = "1.9.13"
 Statistics = "1.11.1"

examples/Project.toml

@@ -1,8 +1,19 @@
 [deps]
 Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Bessels = "0e736298-9ec6-45e8-9647-e4fc86a2fe38"
 DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Hedgehog2 = "7f16798b-0e18-40de-98af-932948254698"
+Integrals = "de52edbc-65ea-441a-8357-d3a637375a31"
 NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 Optimization = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
+ProfileView = "c46f51b8-102a-5cf2-8d2c-8597cb0e0da7"
+Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
+Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

examples/black_scholes_sensi.jl

@@ -27,8 +27,8 @@ bs_method = BlackScholesAnalytic()
 # ------------------------------
 # Define lenses
 # ------------------------------
-vol_lens = @optic _.market.sigma
-spot_lens = @optic _.market.spot
+vol_lens = @optic _.market_inputs.sigma
+spot_lens = @optic _.market_inputs.spot
 
 # ------------------------------
 # Vega (1st order w.r.t. sigma)

examples/carr_madan_heston.jl

@@ -29,5 +29,5 @@ method_heston = Hedgehog2.CarrMadan(α, boundary, HestonDynamics())
 
 # Define pricer
 
-println(solve(payoff, market_inputs, method_heston).price)
+println(solve(PricingProblem(payoff, market_inputs), method_heston).price)
 

examples/lsm_binomial.jl

@@ -1,4 +1,4 @@
-using Revise, Hedgehog2, BenchmarkTools, Dates, Random, SciMLBase
+using Revise, Hedgehog2, BenchmarkTools, Dates, Random
 
 # Define payoff
 strike = 1.0
@@ -9,29 +9,41 @@ american_payoff = VanillaOption(strike, expiry, Hedgehog2.American(), Call(), Sp
 reference_date = Date(2020, 1, 1)
 rate = 0.2
 spot = 1.0
-sigma = 0.4
+sigma = 0.03
 market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
 
 # -- Wrap everything into a pricing problem
 prob = PricingProblem(american_payoff, market_inputs)
 
 # --- Cox–Ross–Rubinstein using `solve(...)` style
-steps_crr = 80
+steps_crr = 8
 crr_method = CoxRossRubinsteinMethod(steps_crr)
-crr_solution = solve(prob, crr_method)
+crr_solution = Hedgehog2.solve(prob, crr_method)
 
 println("Cox Ross Rubinstein American Price:")
 println(crr_solution.price)
 
 # --- LSM using `solve(...)` style
 dynamics = LognormalDynamics()
-trajectories = 1000
+trajectories = 10000
 steps_lsm = 100
 
-strategy = BlackScholesExact(trajectories, steps_lsm)
-degree = 3
-lsm_method = LSM(dynamics, strategy, degree)
-lsm_solution = solve(prob, lsm_method)
+strategy = BlackScholesExact()
+config = Hedgehog2.SimulationConfig(trajectories; steps=steps_lsm, variance_reduction=Hedgehog2.Antithetic())
+degree = 5
+lsm_method = LSM(dynamics, strategy, config, degree)
+lsm_solution = Hedgehog2.solve(prob, lsm_method)
 
 println("LSM American Price:")
 println(lsm_solution.price)
+
+euro_prob = PricingProblem(
+    VanillaOption(strike, expiry, Hedgehog2.European(), Call(), Spot()),
+    market_inputs,
+)
+black_scholes_method = BlackScholesAnalytic()
+bs_solution = Hedgehog2.solve(euro_prob, black_scholes_method)
+println("Black Scholes European Price:")    
+println(bs_solution.price)
+
+@btime Hedgehog2.solve(prob, lsm_method)

examples/montecarlo_seeds.jl

@@ -0,0 +1,14 @@
+using DifferentialEquations
+
+μ = 0.02
+σ = 0.04
+t0 = 0.0
+W0 = 0.0
+tspan = (0.0,1.0)
+trajectories = 100
+proc = GeometricBrownianMotionProcess(μ, σ, t0, W0, nothing)
+noise = NoiseProblem(proc, tspan)
+seeds = rand(UInt64,trajectories)
+prob_func = (prob, i, repeat) -> remake(prob; seed=seeds[i])
+problem = EnsembleProblem(noise; prob_func=prob_func)
+sol = solve(problem, EM(); trajectories=trajectories, dt=1.0)

examples/polished_examples/american_options.jl

@@ -0,0 +1,58 @@
+using Revise, Hedgehog2, BenchmarkTools, Dates
+using Accessors
+import Accessors: @optic
+
+# ------------------------------
+# Define payoff and pricing problem
+# ------------------------------
+strike = 1.0
+expiry = Date(2020, 1, 2)
+underlying = Hedgehog2.Forward()
+
+euro_payoff = VanillaOption(strike, expiry, European(), Put(), underlying)
+
+reference_date = Date(2020, 1, 1)
+rate = 0.03
+spot = 1.0
+sigma = 1.0
+
+market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
+euro_pricing_prob = PricingProblem(euro_payoff, market_inputs)
+
+# ------------------------------
+# Pricing method
+# ------------------------------
+bs_method = BlackScholesAnalytic()
+
+# ------------------------------
+# Define lenses
+# ------------------------------
+vol_lens = @optic _.market_inputs.sigma
+spot_lens = @optic _.market_inputs.spot
+
+# ------------------------------
+# Delta (1st order w.r.t. spot)
+# ------------------------------
+delta_prob = Hedgehog2.GreekProblem(euro_pricing_prob, spot_lens)
+fd_method = FiniteDifference(1E-4, Hedgehog2.FDForward())
+ad_method = ForwardAD()
+analytic_method = AnalyticGreek()
+pricing_method = BlackScholesAnalytic()
+
+@btime solve($euro_pricing_prob, $pricing_method)
+@btime solve($delta_prob, $fd_method, $pricing_method)
+@btime solve($delta_prob, $ad_method, $pricing_method)
+@btime solve($delta_prob, $analytic_method, $pricing_method)
+
+rate_greek_prob = GreekProblem(euro_pricing_prob, ZeroRateSpineLens(1))
+solve(rate_greek_prob, ad_method, pricing_method)
+@btime solve($rate_greek_prob, $ad_method, $pricing_method)
+@btime solve($rate_greek_prob, $fd_method, $pricing_method)
+
+vol_greek_prob = GreekProblem(euro_pricing_prob, VolLens(1,1))
+@btime solve($vol_greek_prob, $ad_method, $pricing_method)
+
+
+steps = 80
+crr = CoxRossRubinsteinMethod(steps)
+solve(euro_pricing_prob, crr)

examples/polished_examples/black_scholes.jl

@@ -20,38 +20,41 @@ method_analytic = BlackScholesAnalytic()
 method_carr_madan = CarrMadan(1.0, 16.0, LognormalDynamics())
 
 # -- Solve for prices
-sol_analytic = solve(prob, method_analytic)
-sol_carr = solve(prob, method_carr_madan)
+sol_analytic = Hedgehog2.solve(prob, method_analytic)
+sol_carr = Hedgehog2.solve(prob, method_carr_madan)
+
+@btime Hedgehog2.solve($prob, $method_analytic)
+@btime Hedgehog2.solve($prob, $method_carr_madan)
 
 println("Analytic price:   ", sol_analytic.price)
 println("Carr-Madan price: ", sol_carr.price)
 
 # --- Greeks via GreekProblem
 
 # Accessors
-spot_lens = @optic _.market.spot
-sigma_lens = @optic _.market.sigma
+spot_lens = @optic _.market_inputs.spot
+sigma_lens = Hedgehog2.VolLens(1,1)
 
 # Methods
 fd = FiniteDifference(1e-3)
 ad = ForwardAD()
 
 println("\n--- Greeks (Analytic Method) ---")
-delta_fd = solve(GreekProblem(prob, spot_lens), fd, method_analytic).greek
-vega_fd = solve(GreekProblem(prob, sigma_lens), fd, method_analytic).greek
-delta_ad = solve(GreekProblem(prob, spot_lens), ad, method_analytic).greek
-vega_ad = solve(GreekProblem(prob, sigma_lens), ad, method_analytic).greek
+delta_fd = Hedgehog2.solve(GreekProblem(prob, spot_lens), fd, method_analytic).greek
+vega_fd = Hedgehog2.solve(GreekProblem(prob, sigma_lens), fd, method_analytic).greek
+delta_ad = Hedgehog2.solve(GreekProblem(prob, spot_lens), ad, method_analytic).greek
+vega_ad = Hedgehog2.solve(GreekProblem(prob, sigma_lens), ad, method_analytic).greek
 
 println("FD Delta (analytic): ", delta_fd)
 println("AD Delta (analytic): ", delta_ad)
 println("FD Vega  (analytic): ", vega_fd)
 println("AD Vega  (analytic): ", vega_ad)
 
 println("\n--- Greeks (Carr-Madan Method) ---")
-delta_fd_cm = solve(GreekProblem(prob, spot_lens), fd, method_carr_madan).greek
-vega_fd_cm = solve(GreekProblem(prob, sigma_lens), fd, method_carr_madan).greek
-delta_ad_cm = solve(GreekProblem(prob, spot_lens), ad, method_carr_madan).greek
-vega_ad_cm = solve(GreekProblem(prob, sigma_lens), ad, method_carr_madan).greek
+delta_fd_cm = Hedgehog2.solve(GreekProblem(prob, spot_lens), fd, method_carr_madan).greek
+vega_fd_cm = Hedgehog2.solve(GreekProblem(prob, sigma_lens), fd, method_carr_madan).greek
+delta_ad_cm = Hedgehog2.solve(GreekProblem(prob, spot_lens), ad, method_carr_madan).greek
+vega_ad_cm = Hedgehog2.solve(GreekProblem(prob, sigma_lens), ad, method_carr_madan).greek
 
 println("FD Delta (Carr-Madan): ", delta_fd_cm)
 println("AD Delta (Carr-Madan): ", delta_ad_cm)