modelx Documentation#

Use Python like a spreadsheet!

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What is modelx?#

modelx is a numerical computing tool that enables you to use Python like a spreadsheet by quickly defining cached functions. modelx is best suited for implementing mathematical models expressed in a large system of recursive formulas, in such fields as actuarial science, quantitative finance and risk management.

Feature highlights#

modelx enables you to interactively develop, run and debug complex models in smart ways. modelx allows you to:

  • Define cached functions as Cells objects by writing Python functions

  • Quickly build object-oriented models, utilizing prototype-based inheritance and composition

  • Quickly parameterize a set of formulas and get results for different parameters

  • Trace formula dependency

  • Import and use any Python modules, such as Numpy, pandas, SciPy, scikit-learn, etc..

  • See formula traceback upon error and inspect local variables

  • Save models to text files and version-control with Git

  • Save data such as pandas DataFrames in Excel or CSV files within models

  • Auto-document saved models by Python documentation generators, such as Sphinx

  • Use Spyder with a plugin for modelx (spyder-modelx) to interface with modelx through GUI

modelx sites#

Who is modelx for?#

modelx is designed to be domain agnostic, so it’s useful for anyone in any field. Especially, modelx is suited for modeling in such fields such as:

  • Quantitative finance

  • Risk management

  • Actuarial science

lifelib ( is a library of actuarial and financial models that are built on top of modelx.

How modelx works#

Below is an example showing how to build a simple model using modelx. The model performs a Monte Carlo simulation to generate 10,000 stochastic paths of a stock price that follow a geometric Brownian motion and to price an European call option on the stock.

import modelx as mx
import numpy as np

model = mx.new_model()                  # Create a new Model named "Model1"
space = model.new_space("MonteCarlo")   # Create a UserSpace named "MonteCralo"

# Define names in MonteCarlo = np
space.M = 10000     # Number of scenarios
space.T = 3         # Time to maturity in years
space.N = 36        # Number of time steps
space.S0 = 100      # S(0): Stock price at t=0
space.r = 0.05      # Risk Free Rate
space.sigma = 0.2   # Volatility
space.K = 110       # Option Strike

# Define Cells objects in MonteCarlo from function definitions
def std_norm_rand():
    gen = np.random.default_rng(1234)
    return gen.standard_normal(size=(N, M))

def stock(i):
    """Stock price at time t_i"""
    dt = T/N; t = dt * i
    if i == 0:
        return np.full(shape=M, fill_value=S0)
        epsilon = std_norm_rand()[i-1]
        return stock(i-1) * np.exp((r - 0.5 * sigma**2) * dt + sigma * epsilon * dt**0.5)

def call_opt():
    """Call option price by Monte Carlo"""
    return np.average(np.maximum(stock(N) - K, 0)) * np.exp(-r*T)

Running the model from IPython is as simple as calling a function:

>>> stock(space.N)      # Stock price at i=N i.e. t=T
array([ 78.58406132,  59.01504804, 115.148291  , ..., 155.39335662,
        74.7907511 , 137.82730703])

>>> call_opt()

Changing a parameter is as simple as assigning a value to a name:

>>> space.K = 100   # Cache is cleared by this assignment

>>> call_opt()    # New option price for the updated strike

You can even dynamically create multiple copies of MonteCarlo with different combinations of r and sigma, by parameterizing MonteCarlo with r and sigma:

>>> space.parameters = ("r", "sigma")   # Parameterize MonteCarlo with r and sigma

>>> space[0.03, 0.15].call_opt()  # Dynamically create a copy of MonteCarlo with r=3% and sigma=15%

>>> space[0.06, 0.4].call_opt()   # Dynamically create another copy with r=6% and sigma=40%


Copyright 2017-2024, Fumito Hamamura

modelx is free software; you can redistribute it and/or modify it under the terms of GNU Lesser General Public License v3 (LGPLv3).

Contributions, productive comments, requests and feedback from the community are always welcome. Information on modelx development is found at Github fumitoh/modelx

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