TP: Monte Carlo Option Pricing with Decorators

A hands-on practical exercise on creating a decorator that injects payoff functions into a Monte Carlo option pricing simulator, exploring advanced concepts in Python and financial modeling.

TP: Monte Carlo Option Pricing with Decorators

In this practical exercise, we’ll create a Monte Carlo simulator for option pricing and use decorators to inject different payoff functions into the simulator. This approach will allow us to easily create and price various types of options using the same underlying simulation framework.

Scenario: Flexible Option Pricing System

We want to build a system that can price different types of options using Monte Carlo simulation. The system should be flexible enough to handle various payoff structures without modifying the core simulation logic.

Step 1: Implement the Base Monte Carlo Simulator

First, let’s implement our base MonteCarloSimulator class:

Step 2: Implement the Decorator

Now, implement a decorator called option_pricer. This decorator should:

1. Take a payoff function as input
2. Create a new class that inherits from MonteCarloSimulator
3. Inject the input function as the payoff method of the new class
4. Return the new class

Here’s the skeleton for the decorator:

Step 3: Use the Decorator

Once you’ve implemented the decorator, you should be able to use it like this:

Your Task

1. Implement the option_pricer decorator to make the above code work.
2. Ensure that the new classes created by the decorator inherit from MonteCarloSimulator.
3. Make sure that the payoff method in the new classes calls the decorated function.

Hints

• You can use type() to create a new class dynamically.
• The payoff function will become a method, so it needs to take self as its first parameter.
• You can use __name__ attribute of the function to name your new class.
• You can use functools wraps to keep tracking of the base function

Bonus Challenges

1. Modify the decorator to allow for additional parameters in the payoff function, such as strike price or barrier levels.

2. Implement a more complex option type, such as an Asian option, where the payoff depends on the average stock price over the simulation period.

3. Add a method to calculate the standard error of the Monte Carlo estimate and use it to compute confidence intervals for the option prices.