Added montecarlo methods benchmark

Author: aleCombi

examples/montecarlo_benchmark.jl

@@ -0,0 +1,71 @@
+using Revise
+using Hedgehog
+using Dates
+using Printf
+using BenchmarkTools
+using Random 
+
+function test_eur()
+    spot = 100.0
+    strike = 100.0
+    rate = 0.05
+    sigma = 0.20
+    reference_date = Date(2023, 1, 1)
+    expiry = reference_date + Year(1)
+
+    # Create the payoff (European call option)
+    payoff = VanillaOption(strike, expiry, European(), Call(), Spot())
+
+    # Create market inputs
+    market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
+
+    # Create pricing problem
+    prob = PricingProblem(payoff, market_inputs)
+
+    trajectories = 5_000
+    mc_exact_method =
+        MonteCarlo(LognormalDynamics(), BlackScholesExact(), SimulationConfig(trajectories))
+    mc_exact_solution = solve(prob, mc_exact_method)
+    @show mc_exact_solution.price
+
+    display(@benchmark solve($prob, $mc_exact_method))
+end
+
+function test_am()
+    @show "american"
+    # Define market inputs
+    strike = 10.0
+    reference_date = Date(2020, 1, 1)
+    expiry = reference_date + Year(1)
+    rate = 0.05
+    spot = 10.0
+    sigma = 0.2
+    market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
+
+    # Define payoff
+    american_payoff = VanillaOption(strike, expiry, American(), Put(), Spot())
+
+    # -- Wrap everything into a pricing problem
+    prob = PricingProblem(american_payoff, market_inputs)
+
+    # --- LSM using `solve(...)` style
+    dynamics = LognormalDynamics()
+    trajectories = 10_000
+    steps_lsm = 100
+
+    strategy = BlackScholesExact()
+    config = Hedgehog.SimulationConfig(trajectories; steps=steps_lsm, variance_reduction=Hedgehog.Antithetic()
+    #variance_reduction=Hedgehog.NoVarianceReduction()
+    )
+    degree = 5
+    lsm_method = LSM(dynamics, strategy, config, degree)
+
+    lsm_solution = Hedgehog.solve(prob, lsm_method)
+
+    @show lsm_solution.price
+
+    display(@benchmark Hedgehog.solve($prob, $lsm_method))
+end
+
+test_eur()
+test_am()