BlackScholesMCEngine

Black-Scholes Monte Carlo Option Pricing

This project implements a Monte Carlo simulation for option pricing based on the Black-Scholes model. The simulation estimates the prices of European call and put options.

Project Structure

• BSM.hpp: Header file containing the class definition and constructorArgs structure.
• BSM.cpp: Source file implementing the methods of the BSM class.
• main.cpp: Main program that initializes the BSM object, runs the simulation, and prints the results.
• CMakeLists.txt: CMake configuration file for building the project.

Class Structure

BSM Class

The BSM (Black-Scholes-Merton) class represents the Monte Carlo simulation for option pricing. It includes the following methods:

• BSM(constructorArgs &args): Constructor to initialize the BSM object with the given parameters.
• ~BSM(): Destructor.
• float get_asset() const: Get the initial asset price.
• float get_strike() const: Get the strike price.
• float get_volatility() const: Get the volatility.
• float get_growth() const: Get the growth rate.
• float get_years() const: Get the time to maturity in years.
• long int get_steps() const: Get the number of time steps.
• long int get_simulations() const: Get the number of simulations.
• double get_call_price(): Get the call option price.
• double get_put_price(): Get the put option price.
• void log_random_walk(): Perform the Monte Carlo simulation.
• double rando() const: Generate a random number in the range [0, 1].

constructorArgs Structure

The constructorArgs structure holds the input parameters required for the simulation. It includes:

• float asset: Initial asset price.
• float strike: Strike price of the option.
• float growth: Growth rate of the asset.
• float volatility: Volatility of the asset.
• float years: Time to maturity in years.
• int steps: Number of time steps.
• int simulations: Number of simulation runs.

Discretized Monte Carlo Formula

The discretized Monte Carlo simulation is based on the Black-Scholes model. The key formula used for simulating the asset price path is:

S_t+1 = S_t * exp((r - (σ^2) / 2) * Δt + σ * √Δt * ε)

Where:

• S_t is the asset price at time t.
• S_t+1 is the asset price at the next time step.
• r is the risk-free interest rate.
• σ is the volatility of the asset.
• Δt is the time step size (time to maturity divided by the number of steps).
• ε is a random number drawn from a standard normal distribution.

This formula is used to update the asset price at each time step within the simulation.

Running the Program

To run the program, use the following command-line arguments: ./main asset strike growth volatility years steps simulations