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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. http://tech.harbourfronts.com/trend-following-trading-system-quantitative-trading-in-python/

We develop a simple trading system exploiting the mean-reverting behaviour of the SP500 market index. To generate buy and sell signals, we will use simple moving averages as noise filters. Since we know that the SP500 is mean-reverting in a short term, we will use short-term moving averages. http://tech.harbourfronts.com/mean-reverting-trading-system-quantitative-trading-in-python/

We are going to examine the mean-reverting and trending properties of SP500 directly using the autocorrelation functions. We do so with the goal of designing quantitative trading systems on stock indices. http://tech.harbourfronts.com/autocorrelation-properties-of-sp500-quantitative-trading-in-python/

We discuss ways to determine the dividend yield accurately. We use traded options to determine the implied dividend yield. Specifically, if the options are of European-style exercise, then we can use the put-call parity to create a synthetic single stock future. http://tech.harbourfronts.com/how-to-determine-implied-dividend-yield-derivative-valuation-in-excel/

We use the Exponential Weighted (EW) historical volatility that assigns bigger weights to the recent returns, and smaller weights to the past ones. The EWHV is more responsive than the equally weighted historical volatility. Also, the decline of the EWHV from its peak is smoother than that of the equally weighted HV. http://tech.harbourfronts.com/exponentially-weighted-historical-volatility-in-excel-volatility-analysis-in-excel/

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 study the effect of diversification. http://tech.harbourfronts.com/modern-portfolio-theory-effect-of-diversification-on-the-optimal-portfolio-portfolio-management-in-python/

We are going to search for the optimal portfolio, i.e. one that has the highest risk-adjusted return. To do so, we will maximize the portfolio’s Sharpe ratio. The Sharpe Ratio is a financial metric that helps investors determine the return of an investment compared to its risk. The higher the Sharpe Ratio of a portfolio, the better it is in terms of risk-adjusted return. http://tech.harbourfronts.com/modern-portfolio-theory-searching-for-the-optimal-portfolio-portfolio-management-in-python/

Harry M. Markowitz is the founder of Modern Portfolio Theory (MPT) which originated from his 1952 essay on portfolio selection. In this post, we are going to provide a concrete example of implementing MPT in Python. Our portfolio consists of 3 Exchange Traded Funds (ETF): SPY, TLT, and GLD which track the S&P500, long-term Treasury bond, and gold respectively. http://tech.harbourfronts.com/trading/modern-portfolio-theory-portfolio-management-python/

Pair trading, or statistical arbitrage, is one of the oldest forms of quantitative trading. 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 good candidate for pair trading http://tech.harbourfronts.com/trading/statistical-analysis-etf-pair-quantitative-trading-python/

We are a boutique financial service firm specializing in quantitative analysis, derivative valuation and risk management. Our clients range from asset management firms to industrial, non-financial companies. Our services include: Valuation of financial derivatives such as convertible bonds, mortgage backed securities, variance swaps, credit default swaps, collateral debt obligation http://tech.harbourfronts.com/

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. http://tech.harbourfronts.com/trading/forecasting-implied-volatility-arima-model-volatility-analysis-python/

In a previous post, we presented an example of volatility analysis using Close-to-Close historical volatility. In this post, we are going to use the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to forecast volatility. http://tech.harbourfronts.com/trading/forecasting-volatility-garch-model-volatility-analysis-python/

There are two types of volatility: historical volatility and implied volatility. In a series of previous posts, we presented methods and provided Python programs for calculating historical volatilities. In this post, we are going to discuss implied volatility and provide a concrete example of implied volatility calculation in Python. http://tech.harbourfronts.com/trading/implied-volatility-options-volatility-analysis-python/

In a previous post, we presented a method for calculating a stock beta and implemented it in Python. In this follow-up post, we are going to implement the calculation in Excel. We continue to use Facebook as an example. http://tech.harbourfronts.com/trading/calculate-stock-beta-excel-replicating-yahoo-stock-beta/

We are going to discuss valuation of a callable bond. We chose the Hull-White model to describe the interest rate dynamics. We then use a Python program to build a trinomial tree for the risk-free rates http://tech.harbourfronts.com/derivatives/valuation-callable-puttable-bonds-derivative-pricing-python/

A warrant is a financial derivative instrument that is similar to a regular stock option except that when it is exercised, the company will issue more stocks and sell them to the warrant holder. The valuation of warrants is similar to the valuation of stock options except that the effect of dilution should be considered. http://tech.harbourfronts.com/derivatives/valuation-warrants-derivative-pricing-python/

Performance share units are hypothetical share units that are granted to you based mainly on corporate and/or individual performance. Structurally, they are very similar to restricted stock units except these are more focused on your performance. They are designed to mirror share ownership and you will generally be granted additional units having the same value as dividends being paid on the regular shares http://tech.harbourfronts.com/derivatives/performance-share-units-derivative-valuation-python/

Valuation of Employee Stock Options is different from regular stock options. In this post, we are going to implement the approach proposed by Hull and White. Specifically, we are going to implement the vesting and forfeiture rate features. Other features can also be implemented without difficulty http://tech.harbourfronts.com/derivatives/employee-stock-options-derivative-pricing-python/

We are going to present a method for valuing American options using Monte Carlo simulation. This method will allow us to implement more complex option payoffs with greater flexibility, even if the payoffs are path-dependent. Specifically, we use the Least-Squares Method of Longstaff and Schwartz in order to take into account the early exercise feature. The stock price is assumed to follow the Geometrical Brownian Motion. http://tech.harbourfronts.com/derivatives/valuing-american-options-using-monte-carlo-simulation-derivative-pricing-python/

We present an extension of the Garman-Klass volatility estimator that also takes into consideration overnight jumps. Garman-Klass-Yang-Zhang (GKYZ) volatility estimator consists of using the returns of open, high, low, and closing prices in its calculation. It also uses the previous day’s closing price. http://tech.harbourfronts.com/trading/garman-klass-yang-zhang-historical-volatility-calculation-volatility-analysis-python/