WOrking on bumping montecarlo

Author: aleCombi

examples/Project.toml

@@ -3,6 +3,8 @@ Accessors = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+DiffEqNoiseProcess = "77a26b50-5914-5dd7-bc55-306e6241c503"
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 Hedgehog2 = "7f16798b-0e18-40de-98af-932948254698"

examples/bumped_montecarlo.jl

@@ -0,0 +1,33 @@
+using DifferentialEquations
+using DiffEqNoiseProcess
+using Plots
+
+# Parameters
+μ = 0.05
+σ = 0.2
+t0 = 0.0
+T = 1.0
+W0 = 100.0
+tspan = (t0, T)
+N = 250
+dt = (T - t0) / N
+
+# Step 1: Simulate base GBM and save the noise
+gbm = GeometricBrownianMotionProcess(μ, σ, t0, W0)
+gbm_noise = NoiseProblem(gbm, tspan, seed=1)
+sol = DifferentialEquations.solve(gbm_noise, dt=dt)
+
+# Step 2: Reuse the noise and simulate with bumped μ
+μ_bumped = μ
+σ_bumped = σ + 0.1
+gbm_bumped = GeometricBrownianMotionProcess(μ_bumped, σ_bumped, t0, W0)
+gbm_bumped_noise = NoiseProblem(gbm_bumped, tspan, seed=1)
+ensemble_problem_bumped = EnsembleProblem(gbm_bumped_noise)
+sol_bumped = DifferentialEquations.solve(gbm_bumped_noise, dt=dt)
+
+# Step 3: Plot both
+plot(sol.t, sol.u, label="μ = $μ", linewidth=2)
+plot!(sol_bumped.t, sol_bumped.u, label="μ = $μ_bumped", linestyle=:dash, linewidth=2)
+xlabel!("Time")
+ylabel!("GBM Value")
+title!("GBM with Drift Bump and Reused Noise")

examples/montecarlo_bs.jl

@@ -23,13 +23,13 @@ prob = PricingProblem(payoff, market_inputs)
 
 # -- Monte Carlo Method
 trajectories = 10_000
-strategy = BlackScholesExact(trajectories)
+strategy = BlackScholesExact(trajectories, seed=1)
 dynamics = LognormalDynamics()
 method_mc = MonteCarlo(dynamics, strategy)
 
 # -- Analytic Method
 method_analytic = BlackScholesAnalytic()
-
+ 
 # -- Solve Both
 solution_analytic = solve(prob, method_analytic)
 solution_mc = solve(prob, method_mc)
@@ -38,6 +38,6 @@ println("Analytic price:   ", solution_analytic.price)
 println("Monte Carlo price:", solution_mc.price)
 
 # -- Benchmark
-println("\n--- Benchmarking ---")
-@btime solve($prob, $method_analytic).price
-@btime solve($prob, $method_mc).price
+# println("\n--- Benchmarking ---")
+# @btime solve($prob, $method_analytic).price
+# @btime solve($prob, $method_mc).price