Author: Harbourfront Technologies

The Binomial tree is a standard method for pricing American style options. Recall that, The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an…

Read More The Willow Tree Method, an Advanced Option Pricing Model

Previously, we elaborated on why hedging is an important tool for risk management. We illustrated the importance of hedging with examples from the commodity, mortgage back securities, and foreign exchange markets. A recent paper [1] evaluated the hedging effectiveness of various range-based volatility estimators. Among them, we can find the commonly used GARCH model. Generalized…

Read More Hedging Market Risks Using Volatility Estimators-Are Sophisticated Methods Better?

Convertible bonds are complex, hybrid securities. In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or…

Read More Convertible Bond Arbitrage Using the Volatility Surface

Modern Portfolio Theory (MPT) is a theory developed by Harry Markowitz in 1952, which later earned him a Nobel Prize in Economics. The theory states that investors can create an ideal portfolio of investments that can provide them with maximum returns while also taking an optimal amount of risk. The theory helps risk-averse investors select…

Read More Modern Portfolio Theory-The Efficient Frontier

In a previous post, we presented statistical tests for the Australia/Canada country ETF pair. Specifically, we calculated the return correlation and performed cointegration tests using a training set consisted of 8 years of data. The high correlation and the fact that the pair spread passed 2 cointegration tests made this pair a good candidate for…

Read More Trading Performance of an ETF Pair Strategy-Quantitative Trading In Python

Harry M. Markowitz is the founder of Modern Portfolio Theory (MPT) which originated from his 1952 essay on portfolio selection. He was later awarded a Nobel Prize in Economics. His work founded the concept of an efficient frontier, and it allows for the determination of portfolio mixes that provide an optimal return for the least…

Read More Modern Portfolio Theory-Portfolio Management in Python

Pair trading, or statistical arbitrage, is one of the oldest forms of quantitative trading. In this post, we are going to present some relevant statistical tests for analyzing the Australia/Canada pair. We chose this pair because these countries’ economies are tied strongly to the commodity sector, therefore they share similar characteristics and could be a…

Read More Statistical Analysis of an ETF Pair-Quantitative Trading In Python

A recent podcast on Bloomberg offers some interesting perspectives on quantitative investing. Interest in quantitative investing strategies continues to grow; however, as the space gets more competitive, making money and winning gets harder and harder. Computation costs alone can be prohibitive. On the latest episode, we speak with Columbia Business School professor Ciamac Moallemi about…

Read More What It Takes to Win at Quantitative Investing

In a previous post, we presented theory and a practical example of calculating implied volatility for a given stock option. In this post, we are going to implement a model for forecasting the implied volatility. Specifically, we are going to use the Autoregressive Integrated Moving Average (ARIMA) model to forecast the volatility index, VIX. In…

Read More Forecasting Implied Volatility with ARIMA Model-Volatility Analysis in Python