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Mc speed up (#17)
* Updated roadmap * first draft of my EnsembleSol with reuse of noiseproblem * first sketch of fast noise solvers * Benchmarking speed up for montecarlo exact * First quick solve with alloc * Best alloc free version so far * Working on Montecarlo using marginal law for exact simulation and euro payoffs * New way to do montecarlo sampling from Distributions.rand * Seeding montecarlo sampler * Added license badge * Documenting montecarlo * Consolidated montecarlo european solvers * Added docstrings * Moved heston to log space * Debugging heston exact * Correcting sampling of log_price for heston * Added heston montecarlo agreement tests and checks for seed numbers in SimulationConfig builder. * Testing LSM against binomial tree * Little corrections * more euler heston paths * Added montecarlo methods benchmark * Removed old working examples * Trigger CI * CI name change to allow PR checks succeeding
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‎.github/workflows/CI.yml

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name: CI
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on:
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push:
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branches:
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- master
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tags: ['*']
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pull_request:
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workflow_dispatch:
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concurrency:
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# Skip intermediate builds: always.
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# Cancel intermediate builds: only if it is a pull request build.
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group: ${{ github.workflow }}-${{ github.ref }}
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cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
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jobs:
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test:
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name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }}
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name: CI
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runs-on: ${{ matrix.os }}
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timeout-minutes: 60
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permissions: # needed to allow julia-actions/cache to proactively delete old caches that it has created
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permissions:
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actions: write
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contents: read
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strategy:

‎README.md

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[![Build Status](https://github.com/aleCombi/Hedgehog.jl/actions/workflows/CI.yml/badge.svg?branch=master)](https://github.com/aleCombi/Hedgehog.jl/actions/workflows/CI.yml?query=branch%3Amaster)
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[![Documentation](https://img.shields.io/badge/docs-stable-blue.svg)](https://alecombi.github.io/Hedgehog.jl/)
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[![License: MIT](https://img.shields.io/badge/License-MIT-green.svg)](LICENSE)
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## 📐 Design Overview
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‎examples/Project.toml

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DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
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DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
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Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
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DiffEqNoiseProcess = "77a26b50-5914-5dd7-bc55-306e6241c503"
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Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
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ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
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Hedgehog = "7f16798b-0e18-40de-98af-932948254698"
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Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
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PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
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Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
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ProfileView = "c46f51b8-102a-5cf2-8d2c-8597cb0e0da7"
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Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
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Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
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SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
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SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
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StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

‎examples/mc_heston_euler.jl

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# Define the vanilla option payoff
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strike = 100.0
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expiry_date = Date(2025, 12, 31)
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payoff = VanillaOption(strike, expiry_date, European(), Call(), Spot())
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# Define the Heston model market inputs using positional arguments
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reference_date = Date(2025, 1, 1)
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spot = 100.0
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rate = 0.05
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heston_inputs = HestonInputs(
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reference_date,
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rate,
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spot,
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1.5, # kappa
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0.04, # theta
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0.3, # sigma
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-0.6, # rho
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0.04 # v0
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)
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# Create the pricing problem
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problem = PricingProblem(payoff, heston_inputs)
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# Generate a vector of seeds for reproducibility
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num_paths = 10_000
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rng = MersenneTwister(42)
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seeds = rand(rng, UInt, num_paths)
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# Pricing with Broadie-Kaya (Heston Exact) using Antithetic variance reduction
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mc_exact_method = MonteCarlo(
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HestonDynamics(),
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HestonBroadieKaya(),
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SimulationConfig(num_paths; seeds=seeds)
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)
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solution_exact = solve(problem, mc_exact_method)
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price_exact = solution_exact.price
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# Pricing with Euler-Maruyama using Antithetic variance reduction
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mc_euler_method = MonteCarlo(
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HestonDynamics(),
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EulerMaruyama(),
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SimulationConfig(10*num_paths; steps=200, seeds=seeds, variance_reduction=Hedgehog.Antithetic())
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)
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solution_euler = solve(problem, mc_euler_method)
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sample_at_expiry = Hedgehog.get_final_samples(problem, mc_euler_method)
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sde_prob = Hedgehog.sde_problem(problem, mc_euler_method)
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ens = Hedgehog.simulate_paths(sde_prob, mc_euler_method, mc_euler_method.config.variance_reduction)
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config = mc_euler_method.config
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dt = sde_prob.tspan[2] / config.steps
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ensemble_prob = Hedgehog.get_ensemble_problem(sde_prob, config)
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normal_sol = StochasticDiffEq.solve(ensemble_prob, EM(); dt = dt, trajectories=config.trajectories)
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price_euler = solution_euler.price

‎examples/montecarlo_benchmark.jl

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

‎examples/montecarlo_exact.jl

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using Revise, Hedgehog, BenchmarkTools, Dates
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using Accessors
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import Accessors: @optic
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using StochasticDiffEq
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# ------------------------------
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# Define payoff and pricing problem
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# ------------------------------
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strike = 1.0
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expiry = Date(2021, 1, 1)
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euro_payoff = VanillaOption(strike, expiry, European(), Put(), Spot())
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reference_date = Date(2020, 1, 1)
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rate = 0.03
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spot = 1.0
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sigma = 0.04
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market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
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euro_pricing_prob = PricingProblem(euro_payoff, market_inputs)
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dynamics = LognormalDynamics()
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trajectories = 10000
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config = Hedgehog.SimulationConfig(trajectories; steps=100, variance_reduction=Hedgehog.Antithetic())
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strategy = EulerMaruyama()
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montecarlo_method = MonteCarlo(dynamics, strategy, config)
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solution_analytic = Hedgehog.solve(euro_pricing_prob, BlackScholesAnalytic()).price
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solution = Hedgehog.solve(euro_pricing_prob, montecarlo_method).price
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@show Hedgehog.solve(euro_pricing_prob, montecarlo_method).price
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@show Hedgehog.solve(euro_pricing_prob, BlackScholesAnalytic()).price
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law = Hedgehog.marginal_law(euro_pricing_prob, LognormalDynamics(), expiry) #log-marginal law
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log_sample = rand(law, trajectories)
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final_sample = exp.(log_sample)
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payoff_sample = euro_payoff.(final_sample)
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discount = df(euro_pricing_prob.market_inputs.rate, euro_pricing_prob.payoff.expiry)
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price = discount * mean(payoff_sample)
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antithetic_sample = exp.(2 * mean(law) .- log_sample)
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payoff_anti_sample = (euro_payoff.(final_sample) + euro_payoff.(antithetic_sample)) / 2
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price_anti = discount * mean(payoff_anti_sample)
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montecarlo_method_exact = MonteCarlo(dynamics, BlackScholesExact(), config)
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solution_exact = Hedgehog.solve(euro_pricing_prob, montecarlo_method_exact).price
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@btime Hedgehog.solve($euro_pricing_prob, $montecarlo_method_exact).price
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@show solution_exact

‎examples/montecarlo_heston.jl

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using Revise, Hedgehog, BenchmarkTools, Dates
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"""Example code with benchmarks"""
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# Define market inputs
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reference_date = Date(2020, 1, 1)
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# Define Heston model parameters
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S0 = 100 # Initial stock price
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V0 = 0.010201 # Initial variance
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κ = 6.21 # Mean reversion speed
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θ = 0.019 # Long-run variance
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σ = 0.61 # Volatility of variance
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ρ = -0.7 # Correlation
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r = 0.0319 # Risk-free rate
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T = 1.0 # Time to maturity
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market_inputs = Hedgehog.HestonInputs(reference_date, r, S0, V0, κ, θ, σ, ρ)
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bs_market_inputs = BlackScholesInputs(reference_date, r, S0, sqrt(V0))
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# Define payoff
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expiry = reference_date + Day(365)
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strike = 100
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payoff =
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VanillaOption(strike, expiry, Hedgehog.European(), Hedgehog.Call(), Hedgehog.Spot())
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# Define carr madan method
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boundary = 32
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α = 1
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method_heston = Hedgehog.CarrMadan(α, boundary, HestonDynamics())
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# Define pricer
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pricing_problem = PricingProblem(payoff, market_inputs)
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analytic_sol = Hedgehog.solve(pricing_problem, method_heston)
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dynamics = HestonDynamics()
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trajectories = 10000
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config = Hedgehog.SimulationConfig(trajectories; steps=100, variance_reduction=Hedgehog.NoVarianceReduction())
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config_exact = Hedgehog.SimulationConfig(trajectories; steps=1, variance_reduction=Hedgehog.NoVarianceReduction())
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montecarlo_method = MonteCarlo(dynamics, EulerMaruyama(), config)
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montecarlo_method_exact = MonteCarlo(dynamics, HestonBroadieKaya(), config_exact)
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solution = Hedgehog.solve(pricing_problem, montecarlo_method)
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solution_exact = Hedgehog.solve(pricing_problem, montecarlo_method_exact)
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@show solution.price
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@show analytic_sol.price
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@show solution_exact.price
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@btime Hedgehog.solve($pricing_problem, $montecarlo_method_exact).price
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@btime Hedgehog.solve($pricing_problem, $montecarlo_method).price
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using Test
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using Hedgehog
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using Dates
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using Random
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@testset "Heston Exact Simulation vs Euler Maruyama" begin
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# Define the vanilla option payoff
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strike = 100.0
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expiry_date = Date(2025, 12, 31)
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payoff = VanillaOption(strike, expiry_date, European(), Call(), Spot())
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# Define the Heston model market inputs using positional arguments
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reference_date = Date(2025, 1, 1)
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spot = 100.0
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rate = 0.05
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heston_inputs = HestonInputs(
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reference_date,
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rate,
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spot,
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1.5, # kappa
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0.04, # theta
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0.3, # sigma
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-0.6, # rho
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0.04 # v0
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)
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# Create the pricing problem
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problem = PricingProblem(payoff, heston_inputs)
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# Generate a vector of seeds for reproducibility
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num_paths = 10_000
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rng = MersenneTwister(42)
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seeds = rand(rng, UInt, 10*num_paths)
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# Pricing with Broadie-Kaya (Heston Exact) using Antithetic variance reduction
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mc_exact_method = MonteCarlo(
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HestonDynamics(),
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HestonBroadieKaya(),
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SimulationConfig(num_paths; seeds=seeds)
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)
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solution_exact = solve(problem, mc_exact_method)
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price_exact = solution_exact.price
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# Pricing with Euler-Maruyama using Antithetic variance reduction
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mc_euler_method = MonteCarlo(
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HestonDynamics(),
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EulerMaruyama(),
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SimulationConfig(num_paths; steps=200, seeds=seeds, variance_reduction=Hedgehog.Antithetic())
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)
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solution_euler = solve(problem, mc_euler_method)
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price_euler = solution_euler.price
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# Pricing with Carr-Madan
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carr_madan_method = CarrMadan(1.0, 32.0, HestonDynamics())
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solution_carr_madan = solve(problem, carr_madan_method)
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price_carr_madan = solution_carr_madan.price
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# Compare the prices with a lower tolerance
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@test isapprox(price_exact, price_euler, rtol=5e-2)
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@test isapprox(price_exact, price_carr_madan, rtol=2e-2)
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end
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@testset "Heston Exact Simulation vs Carr-Madan" begin
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# Define the vanilla option payoff
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strike = 100.0
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expiry_date = Date(2025, 12, 31)
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payoff = VanillaOption(strike, expiry_date, European(), Call(), Spot())
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# Define the Heston model market inputs using positional arguments
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reference_date = Date(2025, 1, 1)
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spot = 100.0
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rate = 0.05
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heston_inputs = HestonInputs(
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reference_date,
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rate,
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spot,
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1.5, # kappa
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0.04, # theta
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0.3, # sigma
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-0.6, # rho
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0.04 # v0
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)
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# Create the pricing problem
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problem = PricingProblem(payoff, heston_inputs)
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# Generate a vector of seeds for reproducibility
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num_paths = 10_000
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rng = MersenneTwister(42)
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seeds = rand(rng, UInt, num_paths)
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# Pricing with Broadie-Kaya (Heston Exact) using Antithetic variance reduction
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mc_exact_method = MonteCarlo(
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HestonDynamics(),
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HestonBroadieKaya(),
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SimulationConfig(num_paths; seeds=seeds)
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)
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solution_exact = solve(problem, mc_exact_method)
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price_exact = solution_exact.price
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# Pricing with Carr-Madan
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carr_madan_method = CarrMadan(1.0, 32.0, HestonDynamics())
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solution_carr_madan = solve(problem, carr_madan_method)
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price_carr_madan = solution_carr_madan.price
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# Compare the prices with a lower tolerance
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@test isapprox(price_exact, price_carr_madan, rtol=2e-2)
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end

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