AbritrageTheoryInContinuousTime-Implemented

An implementation of the models presented in the text, "Arbitrage Theory In Continuous Time (fourth edition)" by Tomas Bjork.

Currently, only the discrete time models (up to, but not including, Chapter 4) have been implemented. Continuous time models, including the Black Scholes model are in progress.

Discret Time Models

The Binomial Model

Functionality: Performs all computations for a Binomial Model with one asset with interest rate R (ie. a bank account or bond) and one stochastic asset (ie. stock) that either goes up a predetermined amount, u, or down a predetermined amount, d, with probability p_u and p_d, respecively. The asset price process, martingale measures, value process and hedging portfolio for a given contract, completeness, and arbitrage freeness of the model can all be computed.

Step 1. - Import the model and contingent claim module (if needed)

import binomial_model as bm
import contingent_claim as cc

Step 2. - Consruct the model with the desired parameter values.

market_model = bm.BinomialModel(3, 1.5, 0.5, 80, 0, pu=0.6, pd=0.4)

This creates the model, and automatically computes the price process for the asset.

Step 3. - Define a derivative contract.

call_contract = partial(cc.call_option, strike_price=80)

Step 4. - Example use case (find a hedging porfolio for the above call contract).

hedging_portfolio = market_model.compute_all_hedging_portfolios(call_contract)

The General One Period Model

Functionality: Can compute, given a D bar matrix, model completeness and arbitrage-free-ness. Addition contingent claims coming soon...

Step 1. - Import the model and contingent claim module (if needed)

import numpy as np
import general_one_period_model as gopm

Step 2. - Consruct the model with the desired D_bar matrix.

# Create a boring D_bar matrix with 3 states of the world and 3 stocks. 
D_bar = np.ones((3, 4))

# Create the model.
market_model = gopm.GeneralOnePeriodModel(D_bar)

Step 3. - Example use case (compute arbitrage-free-ness and completeness).

complete = market_model.is_complete()
arbitrage_free = market_model.is_arbitrage_free()