Arithmetic Brownian Motion Application from Oosterlee-Grzelak Book

A financial simulation application implementing arithmetic Brownian motion (ABM) for stock price evolution, option pricing, and risk analysis.

Overview

Modeling the price evolution of a financial instrument in the presence of fluctuating market conditions is a critical task for many financial institutions. This application implements a numerical solution of the stochastic differential equation (SDE) for an arithmetic Brownian motion process, based on the implementation from the Oosterlee-Grzelak Book¹.

Traditional Monte Carlo simulations of ABM typically use thousands to hundreds of thousands of paths across multiple time steps (e.g., 252 trading days per year). When running on the Signaloid Cloud Compute Engine, the application can replace individual samples from distributions for each path with direct computation on probability distribution representations. This allows the Signaloid platform to compute the same distribution in a single pass through the time steps, achieving results equivalent to thousands of Monte Carlo iterations.

Features

This application can calculate:

• Stock price at maturity: Distribution of asset prices after simulation period (e.g., 252 trading days)
• European call option payoff: Distribution of call option values
• European put option payoff: Distribution of put option values
• Value at Risk (VaR): Risk metric at specified quantile (default: 5%)
• Simulated returns: Portfolio return distributions

Getting Started

Cloning the Repository

The correct way to clone this repository to get the submodules is:

git clone --recursive git@github.com:signaloid/Signaloid-Demo-Finance-OosterleeGrzelakBookArithmeticBrownianMotionExample.git

If you forgot to clone with --recursive and end up with empty submodule directories, you can remedy this with:

git submodule update --init

Running on Signaloid Cloud Developer Platform

To run this application on the Signaloid Cloud Developer Platform, you need a Signaloid account. You can sign up using this link.

Once you have an account, click the "add to signaloid.io" button at the top of this README to connect this repository to the platform and run the application.

Running Locally

You can compile and run this application locally as a native Monte Carlo implementation using the GNU Scientific Library² to generate samples for different input distributions.

Prerequisites

Install dependencies (on Linux):

sudo apt-get install libgsl-dev libgslcblas0

Compilation

From the repository root:

cd src/
gcc -O3 -I. -I../submodules/common -I../submodules/compat main.c utilities.c ../submodules/compat/uxhw.c arithmetic-brownian-motion.c ../submodules/common/common.c -lgsl -lgslcblas -lm -o abm

Execution

Run with Monte Carlo mode (required for local execution):

./abm -S 0 -M 10000

This runs 10,000 Monte Carlo iterations to calculate the stock price at maturity. The results are stored in data.out where the first line contains execution time in microseconds (μs), and subsequent lines contain output sample values.

View the results:

cat data.out

Command-Line Options

Common Options

Short	Long	Type	Default	Description
-o	--output	string	-	Path to output CSV file
-S	--select-output	int	5	Select specific output (0-5): 0=stock price, 1=call option, 2=put option, 3=VaR, 4=simulated returns, 5=all outputs
-M	--multiple-executions	int	1	Number of Monte Carlo iterations (only needed for local execution)
-T	--time	flag	false	Enable timing mode
-b	--benchmarking	flag	false	Enable benchmarking output format
-j	--json	flag	false	Output results in JSON format
-h	--help	flag	false	Display help message

Financial Parameters

Long Option	Type	Default	Description
--mean-return, --periodic-mean-return	double	0.05	Periodic mean return (drift coefficient)
--initial-value, --initial-portfolio-value	double	5.0	Initial portfolio/stock value
--volatility, --periodic-volatility	double	0.4	Periodic volatility
--strike, --strike-price	double	4.5	Strike price for options
--quantile, --quantile-probability	double	0.05	Quantile probability for Value at Risk
--maturity-time, --maturity-time-years	double	1.0	Simulation time horizon in years
--frequency, --frequency-index	int	0	Time step frequency: 0=daily (252 steps/year), 1=monthly (12 steps/year), 2=yearly (1 step/year)

Note: When running on Signaloid's platform, you don't need to set -M greater than 1. The platform's uncertainty tracking provides distribution results in a single execution.

Output Types

Use the -S or --select-output option to choose which output to calculate:

-S 0: Stock Price at Maturity

Calculates the distribution of asset prices after the simulation period (default: 252 trading days for 1 year).

Example output using Signaloid's C0Pro-S core:

-S 1: Call Option Payoff

Calculates the European call option payoff distribution: max(S - K, 0) where S is the stock price at maturity and K is the strike price.

Example output using Signaloid's C0Pro-S core:

-S 2: Put Option Payoff

Calculates the European put option payoff distribution: max(K - S, 0) where K is the strike price and S is the stock price at maturity.

Example output using Signaloid's C0Pro-S core:

-S 3: Value at Risk (VaR)

Calculates the Value at Risk at the specified quantile (default: 5%). VaR represents the maximum expected loss over the time horizon at a given confidence level.

-S 4: Simulated Returns

Calculates the portfolio returns: final portfolio value minus initial value.

-S 5: All Outputs (Default)

Calculates all available outputs: stock price at maturity, call option payoff, put option payoff, Value at Risk, and simulated returns.

---

References

Footnotes

1. Oosterlee, C.W. and Grzelak, L.A. 2019. Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes. World Scientific Publishing Company. https://books.google.com/books?id=TsPKDwAAQBAJ - Python Implementation ↩

2. GNU Scientific Library ↩