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Harbourfront Technologies
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Harbourfront Technologies
Harbourfront Technologies
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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 tradin
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 sho
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/autocorr
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 si
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 o
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-portf
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 a
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
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 a
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 f
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 us
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.
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 imp
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.harbourfron
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 rateshttp://tech.harbourfronts.com/derivative
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 valua
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 performanc
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. Oth
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 us
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
In the previous post, we introduced the Parkinson volatility estimator that takes into account the high and low prices of a stock. In this follow-up post, we present the Garman-Klass volatility estimator that uses not only the high and low but
A disadvantage of using the CCHV is that it does not take into account the information about intraday prices. The Parkinson volatility extends the CCHV by incorporating the stock’s daily high and low prices.http://tech.harbourfronts.com/tradi
In this post, we are going to discuss historical volatilities of a stock in more details. There are various types of historical volatilities such as close to close, Parkinson, Garman-KIass, Yang-Zhang, etc. Here we will discuss the close-to-clo
In finance, beta measures a stock’s volatility with respect to the overall market. It is used in many areas of financial analysis and investment, for example in the calculation of the Weighted Average Cost of Capital, in the Capital Asset Prici
The VIX index is an important market indicator that everyone is watching. VVIX, on the other hand, receives less attention. In this post, we are going to take a look at the relationship between the VIX and VVIX indices.http://blog.harbourfront
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