# Author: Harbourfront Technologies

In a previous post, we demonstrated the mean-reverting and trending properties of SP500. We subsequently developed a trading system based on the mean-reverting behavior of the index. In this installment, we will develop a trend-following trading strategy. Trend following or trend trading is a trading strategy according to which one should buy an asset when…

## Can the SP500 Index be Predicted?

In a previous post, we presented a time series analysis of the SP500 index and demonstrated its mean-reverting and trending behaviour. Subsequently, we designed trading strategies exploiting these mean-reverting and trending properties of SP500. Does this mean that the SP500, and stock market indices in general, can be predicted? In a recent publication [1], the…

Read More Can the SP500 Index be Predicted?

In a previous post, we demonstrated the mean-reverting and trending properties of SP500. In this follow-up post, we will develop a simple trading system exploiting the mean-reverting behaviour of this market index. To generate buy and sell signals, we will use simple moving averages as noise filters. The simple moving average takes an average value…

## Autocorrelation Properties of SP500-Quantitative Trading in Python

A technical or quantitative trading system on a linear (i.e. delta 1) instrument is basically a bet on the autocorrelation of the underlying. The autocorrelation properties of the underlying can be examined directly through autocorrelation functions or indirectly through the Hurst exponent. In this post, we are going to examine the mean-reverting and trending properties…

## Pricing of Weather Derivatives Using Monte Carlo Simulations

Derivatives are financial products whose values are determined by the current price of the underlying asset or portfolio. Weather derivatives are a particular class of financial instruments that individuals or companies can use in support of risk management in relation to unpredictable or adverse weather conditions. While some may see them as an exciting innovation,…

Read More Pricing of Weather Derivatives Using Monte Carlo Simulations

## How to Determine Implied Dividend Yield-Derivative Valuation in Excel

Dividend yield is an input into the option valuation model that often receives little attention from practitioners. This is probably because the majority of companies do not pay dividends. And for those that pay, an inaccuracy in the estimation of the dividend yield often has a small impact on the fair value of the financial…

Read More How to Determine Implied Dividend Yield-Derivative Valuation in Excel

## Exponentially Weighted Historical Volatility in Excel-Volatility Analysis in Excel

Historical volatility (HV) is a useful measure to gauge market uncertainty. Recall that, In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices… Investors care about volatility…

Read More Exponentially Weighted Historical Volatility in Excel-Volatility Analysis in Excel

## Modern Portfolio Theory-Effect of Diversification on the Optimal Portfolio-Portfolio Management in Python

In the previous installments, we presented the concept of Modern Portfolio Theory. We also provided an optimization algorithm, written in Python, for searching for the optimal portfolio. To continue, we are going to perform some numerical experiments. Specifically, we are going to use the portfolio optimization program developed in the previous post in order to…

Read More Modern Portfolio Theory-Effect of Diversification on the Optimal Portfolio-Portfolio Management in Python

## Modern Portfolio Theory-Searching For the Optimal Portfolio-Portfolio Management in Python

In the previous installment, we presented a description of the Model Portfolio Theory and provided a concrete example in Python. We also explained the concept of an Efficient Frontier and provided a visual presentation of it. Recall that, … the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the “efficient” parts of…

Read More Modern Portfolio Theory-Searching For the Optimal Portfolio-Portfolio Management in Python

## The Willow Tree Method, an Advanced Option Pricing Model

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…