Jonathan Kinlay

Using the neoclassical growth model, researchers conduct a benchmark test in C++11, Fortran 2008, Java, Julia, Python, Matlab, Mathematica, and R, implementing the same algorithm, value function iteration with grid search, in each of the languages. They report the execution times of the codes in a Mac and in a Windows computer and briefly comment on the strengths and weaknesses of each language.

An example of how to apply the Kalman Filter to develop a pairs trading strategy for an ETF pair.

Discusses the application of the Kalman Filter in the development of statistical arbitrage strategies.

Discusses research procedures for developing statistical arbitrage strategies using cointegration. In such mean-reverting strategies, long positions are taken in under-performing stocks and short positions in stocks that have recently outperformed.

The Correlation Signal is a measure of the strength of the correlation as a signal, relative to the noise of random variation in the correlation process. It can be used to identify situations in which a relationship – whether a positive or negative correlation – appears to be stable or unstable, and therefore viable as a basis for inference, or not.

CrashMetrics is a simple approach to the management of extreme risk that works rather well. It can be summarized as “CAPM for crashes”. Here’s how it works.

It appears that, in 2015, we can finally look forward to dispensing with legacy programing languages and their primitive syntax and instead develop large, scalable systems that combine programming productivity and execution efficiency.

What are the benefits of using a high level language like ADL compared to programming languages like C++/C# or Java that are traditionally used for trading system development? The chief advantage is speed of development: I would say that ADL offers the potential up the development process by at least one order of magnitude.

In this article I want to discuss a slightly different version of equity curve money management, which is mean-reversion oriented. The underlying thesis is that your trading strategy has good profit characteristics, and while it suffers from the occasional, significant drawdown, it can be expected to recover from the downswings.

GP is an evolutionary-based algorithmic methodology in which a system is given a set of simple rules, some data, and a fitness function that produces desired outcomes from combining the rules and applying them to the data. The idea is that, by testing large numbers of possible combinations of rules, typically in the millions, and allowing the most successful rules to propagate, eventually we will arrive at a strategy solution that offers the required characteristics.

The Systematic Strategies Volatility ETF strategy uses mathematical models to quantify the relative value of ETF products based on the CBOE S&P500 Volatility Index (VIX) and create a positive-alpha long/short volatility portfolio. The strategy is designed to perform robustly during extreme market conditions, by utilizing the positive convexity of the underlying ETF assets. It does not rely on volatility term structure (“carry”), or statistical correlations, but generates a return derived from… Show more

The Systematic Strategies Volatility ETF strategy uses mathematical models to quantify the relative value of ETF products based on the CBOE S&P500 Volatility Index (VIX) and create a positive-alpha long/short volatility portfolio. The strategy is designed to perform robustly during extreme market conditions, by utilizing the positive convexity of the underlying ETF assets. It does not rely on volatility term structure (“carry”), or statistical correlations, but generates a return derived from the ETF pricing methodology. The net volatility exposure of the portfolio may be long, short or neutral, according to market conditions, but at all times includes an underlying volatility hedge. Portfolio holdings are adjusted daily using execution algorithms that minimize market impact to achieve the best available market prices. Show less

A high frequency version of the VIX futures alendar spread strategy.

The most recent Morningstar survey provides an interesting snapshot of the state of the alternatives market. In 2013, for the third successive year, liquid alternatives was the fastest growing category of mutual funds, drawing in flows totaling $95.6 billion. The fastest growing subcategories have been long-short stock funds (growing more than 80% in 2013), nontraditional bond funds (79%) and “multi-alternative” fund-of-alts-funds products (57%).

* In this article, I am going to look at how stock portfolios should be constructed that best meet investment objectives.
* The theoretical and practical difficulties of the widely adopted Modern Portfolio Theory approach limits its usefulness as a tool for portfolio construction.
* MPT portfolios typically produce disappointing out-of-sample results, and will often underperform a naïve, equally-weighted stock portfolio.
* The article introduces the concept of robust portfolio… Show more

* In this article, I am going to look at how stock portfolios should be constructed that best meet investment objectives.
* The theoretical and practical difficulties of the widely adopted Modern Portfolio Theory approach limits its usefulness as a tool for portfolio construction.
* MPT portfolios typically produce disappointing out-of-sample results, and will often underperform a naïve, equally-weighted stock portfolio.
* The article introduces the concept of robust portfolio construction, which leads to portfolios that have more stable performance characteristics, including during periods of high volatility or market corrections.
* The benefits of this approach include risk-adjusted returns that substantially exceed those of traditional portfolios, together with much lower drawdowns and correlations. Show less

Summary

Pattern trading rules try to identify profit opportunities, based on short term price patterns.
An exhaustive test of simple pattern trading rules was conducted for several stocks, incorporating forecasts of the Open, High, Low and Close prices.
There is clear evidence that pattern trading rules continue to work consistently for many stocks.
Almost all of the optimal pattern trading rules suggest buying the stock if the close is below the mid-range of the day.
This… Show more

Summary

Pattern trading rules try to identify profit opportunities, based on short term price patterns.
An exhaustive test of simple pattern trading rules was conducted for several stocks, incorporating forecasts of the Open, High, Low and Close prices.
There is clear evidence that pattern trading rules continue to work consistently for many stocks.
Almost all of the optimal pattern trading rules suggest buying the stock if the close is below the mid-range of the day.
This “buy the dips” approach can sometimes be improved by overlaying additional conditions, or signals from forecasting models. Show less

Below is the equity curve for an equity strategy I developed recently, implemented in WFC. The results appear outstanding: no losing years in over 20 years, profit factor of 2.76 and average win rate of 75%. Out-of-sample results (double blind) for 2013 and 2014: net returns of 27% and 16% YTD.

* In this article, I will apply market timing techniques to several popular mutual funds.

* The market timing approach produces annual rates of return that are 3% to 7% higher, with lower risk, than an equivalent buy and hold mutual fund investment.

* Investors could in some cases have earned more than double the return achieved by holding a mutual fund investment over a 10-year period.

* Hedging strategies that use market timing signals are able to sidestep market… Show more

* In this article, I will apply market timing techniques to several popular mutual funds.

* The market timing approach produces annual rates of return that are 3% to 7% higher, with lower risk, than an equivalent buy and hold mutual fund investment.

* Investors could in some cases have earned more than double the return achieved by holding a mutual fund investment over a 10-year period.

* Hedging strategies that use market timing signals are able to sidestep market corrections, volatile conditions and the ensuing equity drawdowns.

* Hedged portfolios typically employ around 12% less capital than the equivalent buy and hold strategy. Show less

* How to stay in the market and navigate the rocky terrain ahead, without risking hard won gains.
* A hedging program to get you out of trouble at the right time and step back in when skies are clear.
* Even a modest ability to time the market can produce enormous dividends over the long haul.
* Investors can benefit by using quantitative market timing techniques to strategically adjust their market exposure.
* Market timing can be a useful tool to avoid major corrections… Show more

* How to stay in the market and navigate the rocky terrain ahead, without risking hard won gains.
* A hedging program to get you out of trouble at the right time and step back in when skies are clear.
* Even a modest ability to time the market can produce enormous dividends over the long haul.
* Investors can benefit by using quantitative market timing techniques to strategically adjust their market exposure.
* Market timing can be a useful tool to avoid major corrections, increasing investment returns, while reducing volatility and drawdowns.
Show less

In his post on Multi-Market Techniques for Robust Trading Strategies (http://www.adaptrade.com/Newsletter/NL-MultiMarket.htm) Michael Bryant of Adaptrade discusses some interesting approaches to improving model robustness. One is to use data from several correlated assets to build the model, on the basis that if the algorithm works for several assets with differing price levels, that would tend to corroborate the system’s robustness. The second approach he advocates is to use data from the same… Show more

In his post on Multi-Market Techniques for Robust Trading Strategies (http://www.adaptrade.com/Newsletter/NL-MultiMarket.htm) Michael Bryant of Adaptrade discusses some interesting approaches to improving model robustness. One is to use data from several correlated assets to build the model, on the basis that if the algorithm works for several assets with differing price levels, that would tend to corroborate the system’s robustness. The second approach he advocates is to use data from the same asset series at different bars lengths. The example he uses @ES.D at 5, 7 and 9 minute bars. The argument in favor of this approach is the same as for the first, albeit in this case the underlying asset is the same. Show less

One of the frustrating aspects of research and development of trading systems is that there is never enough time to investigate all of the interesting trading ideas one would like to explore. In the early 1970’s, when a moving average crossover system was considered state of the art, it was relatively easy to develop profitable strategies using simple technical indicators. Indeed, research has shown that the profitability of simple trading rules persisted in foreign exchange and other markets… Show more

One of the frustrating aspects of research and development of trading systems is that there is never enough time to investigate all of the interesting trading ideas one would like to explore. In the early 1970’s, when a moving average crossover system was considered state of the art, it was relatively easy to develop profitable strategies using simple technical indicators. Indeed, research has shown that the profitability of simple trading rules persisted in foreign exchange and other markets for a period of decades. But, coincident with the advent of the PC in the late 1980’s, such simple strategies began to fail. The widespread availability of data, analytical tools and computing power has, arguably, contributed to the increased efficiency of financial markets and complicated the search for profitable trading ideas. We are now at a stage where is can take a team of 5-6 researchers/developers, using advanced research techniques and computing technologies, as long as 12-18 months, and hundreds of thousands of dollars, to develop a prototype strategy. And there is no guarantee that the end result will produce the required investment returns.

The lengthening lead times and rising cost and risk of strategy research has obliged trading firms to explore possibilities for accelerating the R&D process. One such approach is Genetic Programming. Show less

This is a follow up post to my post on the Mathematics of Scalping. To illustrate the scalping methodology, I coded up a simple strategy based on the techniques described in the post.

The strategy trades a single @ES contract on 1-minute bars. The attached ELD file contains the Easylanguage code for ES scalping strategy, which can be run in Tradestation or Multicharts.

This strategy makes no attempt to forecast market direction and doesn’t consider market trends at all. It simply… Show more

This is a follow up post to my post on the Mathematics of Scalping. To illustrate the scalping methodology, I coded up a simple strategy based on the techniques described in the post.

The strategy trades a single @ES contract on 1-minute bars. The attached ELD file contains the Easylanguage code for ES scalping strategy, which can be run in Tradestation or Multicharts.

This strategy makes no attempt to forecast market direction and doesn’t consider market trends at all. It simply looks at the current levels of volatility and takes a long volatility position or a short volatility position depending on whether volatility is above or below some threshold parameters. Show less

In this article I am going to explore how, starting from the assumption of a stable, Gaussian distribution in a returns process, we evolve to a system that displays all the characteristics of empirical market data, notably time-dependent moments, high levels of kurtosis and fat tails. As it turns out, the only additional assumption one needs to make is that the market is periodically disturbed by the random arrival of news.

One of the questions of interest is the optimal sampling frequency to use for extracting the alpha signal from an alpha generation function. We can use Fourier transforms to help identify the cyclical behavior of the strategy alpha and hence determine the best time-frames for sampling and trading. Typically, these spectral analysis techniques will highlight several different cycle lengths where the alpha signal is strongest.

I want to explore aspects of scalping, a type of strategy widely utilized by high frequency trading firms.

I will define a scalping strategy as one in which we seek to take small profits by posting limit orders on alternate side of the book. Scalping, as I define it, is a strategy rather like market making, except that we “lean” on one side of the book. So, at any given time, we may have a long bias and so look to enter with a limit buy order. If this is filled, we will then look to exit… Show more

I want to explore aspects of scalping, a type of strategy widely utilized by high frequency trading firms.

I will define a scalping strategy as one in which we seek to take small profits by posting limit orders on alternate side of the book. Scalping, as I define it, is a strategy rather like market making, except that we “lean” on one side of the book. So, at any given time, we may have a long bias and so look to enter with a limit buy order. If this is filled, we will then look to exit with a subsequent limit sell order, taking a profit of a few ticks. Conversely, we may enter with a limit sell order and look to exit with a limit buy order.
The strategy relies on two critical factors:

(i) the alpha signal which tells us from moment to moment whether we should prefer to be long or short
(ii) the execution strategy, or “trade expression” Show less

I want to take a look at a trading strategy in the GDX Gold ETF that has attracted quite a lot of attention, stemming from Jay Kaeppel’s article: The Greatest Gold Stock System You’ll Probably Never Use (http://www.optionetics.com/market/articles/2012/11/28/kaeppels-corner-the-greatest-gold-stock-system-youll-probably-never-use).

The essence of the approach is that GDX has reliably tended to trade off during the day session, after making gains in the overnight session. One possible… Show more

I want to take a look at a trading strategy in the GDX Gold ETF that has attracted quite a lot of attention, stemming from Jay Kaeppel’s article: The Greatest Gold Stock System You’ll Probably Never Use (http://www.optionetics.com/market/articles/2012/11/28/kaeppels-corner-the-greatest-gold-stock-system-youll-probably-never-use).

The essence of the approach is that GDX has reliably tended to trade off during the day session, after making gains in the overnight session. One possible explanation for the phenomenon is offer by Adrian Douglas in his article Gold Market is not “Fixed”, it’s Rigged (see https://marketforceanalysis.com/articles/latest_article_081310.html) in which he takes issue with the London Fixing mechanism used to set the daily price of gold Show less

The “implied volatility” corresponding to an option price is the value of the volatility parameter for which the Black-Scholes model gives the same price. A well-known phenomenon in market option prices is the “volatility smile”, in which the implied volatility increases for strike values away from the spot price. The jump diffusion model is a generalization of Black\[Dash]Scholes in which the stock price has randomly occurring jumps in addition to the random walk behavior. One of the… Show more

The “implied volatility” corresponding to an option price is the value of the volatility parameter for which the Black-Scholes model gives the same price. A well-known phenomenon in market option prices is the “volatility smile”, in which the implied volatility increases for strike values away from the spot price. The jump diffusion model is a generalization of Black\[Dash]Scholes in which the stock price has randomly occurring jumps in addition to the random walk behavior. One of the interesting properties of this model is that it displays the volatility smile effect. In this Demonstration, we explore the Black-Scholes implied volatility of option prices (equal for both put and call options) in the jump diffusion model. The implied volatility is modeled as a function of the ratio of option strike price to spot price. Show less

A common theme of microstructure modeling is that trade flow is often predictive of market direction. One concept in particular that has gained traction is flow toxicity, i.e. flow where resting orders tend to be filled more quickly than expected, while aggressive orders rarely get filled at all, due to the participation of informed traders trading against uninformed traders. The fundamental insight from microstructure research is that the order arrival process is informative of subsequent… Show more

A common theme of microstructure modeling is that trade flow is often predictive of market direction. One concept in particular that has gained traction is flow toxicity, i.e. flow where resting orders tend to be filled more quickly than expected, while aggressive orders rarely get filled at all, due to the participation of informed traders trading against uninformed traders. The fundamental insight from microstructure research is that the order arrival process is informative of subsequent price moves in general and toxic flow in particular. This is turn has led researchers to try to measure the probability of informed trading (PIN). One recent attempt to model flow toxicity, the Volume-Synchronized Probability of Informed Trading (VPIN)metric, seeks to estimate PIN based on volume imbalance and trade intensity. A major advantage of this approach is that it does not require the estimation of unobservable parameters and, additionally, updating VPIN in trade time rather than clock time improves its predictive power. VPIN has potential applications both in high frequency trading strategies, but also in risk management, since highly toxic flow is likely to lead to the withdrawal of liquidity providers, setting up the conditions for a flash-crash” type of market breakdown. Show less

Linear regression is one of the most useful applications in the financial engineer’s tool-kit, but it suffers from a rather restrictive set of assumptions that limit its applicability in areas of research that are characterized by their focus on highly non-linear or correlated variables. The latter problem, referred to as colinearity (or multicolinearity) arises very frequently in financial research, because asset processes are often somewhat (or even highly) correlated. In a colinear system,… Show more

Linear regression is one of the most useful applications in the financial engineer’s tool-kit, but it suffers from a rather restrictive set of assumptions that limit its applicability in areas of research that are characterized by their focus on highly non-linear or correlated variables. The latter problem, referred to as colinearity (or multicolinearity) arises very frequently in financial research, because asset processes are often somewhat (or even highly) correlated. In a colinear system, one can test for the overall significant of the regression relationship, but one is unable to distinguish which of the explanatory variables is individually significant. Furthermore, the estimates of the model parameters, the weights applied to each explanatory variable, tend to be biased. Show less

This note summarizes some of the key research in the field of market microstructure and considers some of the models proposed by the researchers. Many of the ideas presented here have become widely adopted by high frequency trading firms and incorporated into their trading systems.

In the previous post I outlined some of the available techniques used for modeling market states. The following is an illustration of how these techniques can be applied in practice. You can download this post in pdf format here.

The chart below shows the daily compounded returns for a single pair in an ETF statistical arbitrage strategy, back-tested over a 1-year period from April 2010 to March 2011.

Market state models are amongst the most useful analytical techniques that can be helpful in developing alpha-signal generators. That term covers a great deal of ground, with ideas drawn from statistics, econometrics, physics and bioinformatics. The purpose of this short note is to provide an introduction to some of the key ideas and suggest ways in which they might usefully applied in the context of researching and developing trading systems.

The great majority of empirical studies have focused on asset markets in the US and other developed economies. The purpose of this research is to determine to what extent the findings of other researchers in relation to the characteristics of asset volatility in developed economies applies also to emerging markets. The important characteristics observed in asset volatility that we wish to identify and examine in emerging markets include clustering, (the tendency for periodic regimes of high… Show more

The great majority of empirical studies have focused on asset markets in the US and other developed economies. The purpose of this research is to determine to what extent the findings of other researchers in relation to the characteristics of asset volatility in developed economies applies also to emerging markets. The important characteristics observed in asset volatility that we wish to identify and examine in emerging markets include clustering, (the tendency for periodic regimes of high or low volatility) long memory, asymmetry, and correlation with the underlying returns process. The extent to which such behaviors are present in emerging markets will serve to confirm or refute the conjecture that they are universal and not just the product of some factors specific to the intensely scrutinized, and widely traded developed markets. Show less

During the 1990′s the advent of Neural Networks unleashed a torrent of research on their applications in financial markets, accompanied by some rather extravagant claims about their predicative abilities. Sadly, much of the research proved to be sub-standard and the results illusionary, following which the topic was largely relegated to the bleachers, at least in the field of financial market research.

With the advent of new machine learning techniques such as Random Forests, Support… Show more

During the 1990′s the advent of Neural Networks unleashed a torrent of research on their applications in financial markets, accompanied by some rather extravagant claims about their predicative abilities. Sadly, much of the research proved to be sub-standard and the results illusionary, following which the topic was largely relegated to the bleachers, at least in the field of financial market research.

With the advent of new machine learning techniques such as Random Forests, Support Vector Machines and Nearest Neighbor Classification, there has been a resurgence of interest in non-linear modeling techniques and a flood of new research, a fair amount of it supportive of their potential for forecasting financial markets. Once again, however, doubts about the quality of some of the research bring the results into question. Show less

The research in this article and the related paper on Range Based EGARCH Option pricing Models is focused on the innovative range-based volatility models introduced in Alizadeh, Brandt, and Diebold (2002) (hereafter ABD). We develop new option pricing models using multi-factor diffusion approximations couched within this theoretical framework and examine their properties in comparison with the traditional Black-Scholes model.

The two-factor version of the model, which I have applied… Show more

The research in this article and the related paper on Range Based EGARCH Option pricing Models is focused on the innovative range-based volatility models introduced in Alizadeh, Brandt, and Diebold (2002) (hereafter ABD). We develop new option pricing models using multi-factor diffusion approximations couched within this theoretical framework and examine their properties in comparison with the traditional Black-Scholes model.

The two-factor version of the model, which I have applied successfully in various option arbitrage strategies, encapsulates the intuively appealing idea of a trending long term mean volatility process, around which oscillates a mean-reverting, transient volatility process. The option pricing model also incorporates asymmetry/leverage effects and well as correlation effects between the asset return and volatility processes, which results in a volatility skew. Show less

As regards the question of forecasting accuracy discussed in the paper on Forecasting Volatility in the S&P 500 Index, there are two possible misunderstandings here that need to be cleared up. These arise from remarks by one commentator as follows:

“An above 50% vol direction forecast looks good,.. but “direction” is biased when working with highly skewed distributions! ..so it would be nice if you could benchmark it against a simple naive predictors to get a feel for significance… Show more

As regards the question of forecasting accuracy discussed in the paper on Forecasting Volatility in the S&P 500 Index, there are two possible misunderstandings here that need to be cleared up. These arise from remarks by one commentator as follows:

“An above 50% vol direction forecast looks good,.. but “direction” is biased when working with highly skewed distributions! ..so it would be nice if you could benchmark it against a simple naive predictors to get a feel for significance, -or- benchmark it with a trading strategy and see how the risk/return performs.” Show less

Perhaps the most important feature of volatility is that it is stochastic rather than constant, as envisioned in the Black Scholes framework. The presentation addresses this issue by identifying some of the chief stylized facts about volatility processes and how they can be modelled. Certain characteristics of volatility are well known to most analysts, such as, for instance, its tendency to “cluster” in periods of higher and lower volatility. However, there are many other typical features… Show more

Perhaps the most important feature of volatility is that it is stochastic rather than constant, as envisioned in the Black Scholes framework. The presentation addresses this issue by identifying some of the chief stylized facts about volatility processes and how they can be modelled. Certain characteristics of volatility are well known to most analysts, such as, for instance, its tendency to “cluster” in periods of higher and lower volatility. However, there are many other typical features that are less often rehearsed and these too are examined in the presentation. Show less

There has been a good deal of interest in the market timing ideas discussed in my earlier blog post Using Volatility to Predict Market Direction, which discusses the research of Diebold and Christoffersen into the sign predictability induced by volatility dynamics. The ideas are thoroughly explored in a QuantNotes article from 2006, which you can download here.

There is a follow-up article from 2006 in which Christoffersen, Diebold, Mariano and Tay develop the ideas further to consider… Show more

There has been a good deal of interest in the market timing ideas discussed in my earlier blog post Using Volatility to Predict Market Direction, which discusses the research of Diebold and Christoffersen into the sign predictability induced by volatility dynamics. The ideas are thoroughly explored in a QuantNotes article from 2006, which you can download here.

There is a follow-up article from 2006 in which Christoffersen, Diebold, Mariano and Tay develop the ideas further to consider the impact of higher moments of the asset return distribution on sign predictability and the potential for market timing in international markets (download here). Show less

Several people have asked me for copies of this research article, which develops a new theoretical framework, the ARFIMA-GARCH model as a basis for forecasting volatility in the S&P 500 Index. I am in the process of updating the research, but in the meantime a copy of the original paper is available here


Forecast vs Actual Realized Volatility

In this analysis we are concerned with the issue of whether market forecasts of volatility, as expressed in the Black-Scholes implied… Show more

Several people have asked me for copies of this research article, which develops a new theoretical framework, the ARFIMA-GARCH model as a basis for forecasting volatility in the S&P 500 Index. I am in the process of updating the research, but in the meantime a copy of the original paper is available here


Forecast vs Actual Realized Volatility

In this analysis we are concerned with the issue of whether market forecasts of volatility, as expressed in the Black-Scholes implied volatilities of at-the-money European options on the S&P500 Index, are superior to those produced by a new forecasting model in the GARCH framework which incorporates long-memory effects. The ARFIMA-GARCH model, which uses high frequency data comprising 5-minute returns, makes volatility the subject process of interest, to which innovations are introduced via a volatility-of-volatility (kurtosis) process. Despite performing robustly in- and out-of-sample, an encompassing regression indicates that the model is unable to add to the information already contained in market forecasts. Show less

Yield curve models are used to price a wide variety of interest rate-contingent claims. The existence of several different competing methods of curve construction available and there is no single standard method for constructing yield curves and alternate procedures are adopted in different business areas to suit local requirements and market conditions. This fragmentation has often led to confusion amongst some users of the models as to their precise functionality and uncertainty as to which… Show more

Yield curve models are used to price a wide variety of interest rate-contingent claims. The existence of several different competing methods of curve construction available and there is no single standard method for constructing yield curves and alternate procedures are adopted in different business areas to suit local requirements and market conditions. This fragmentation has often led to confusion amongst some users of the models as to their precise functionality and uncertainty as to which is the most appropriate modeling technique. In addition, recent market conditions, which inter-alia have seen elevated levels of LIBOR basis volatility, have served to heighten concerns amongst some risk managers and other model users about the output of the models and the validity of the underlying modeling methods. Show less

The LNVM model is a mixture of lognormal models and the model density is a linear combination of the underlying densities, for instance, log-normal densities. The resulting density of this mixture is no longer log-normal and the model can thereby better fit skew and smile observed in the market. The model is becoming increasingly widely used for interest rate/commodity hybrids.

In this review of the model, I examine the mathematical framework of the model in order to gain an… Show more

The LNVM model is a mixture of lognormal models and the model density is a linear combination of the underlying densities, for instance, log-normal densities. The resulting density of this mixture is no longer log-normal and the model can thereby better fit skew and smile observed in the market. The model is becoming increasingly widely used for interest rate/commodity hybrids.

In this review of the model, I examine the mathematical framework of the model in order to gain an understanding of its key features and characteristics. Show less

Although asset returns are essentially unforecastable, the same is not true for asset return signs (i.e. the direction-of-change). As long as expected returns are nonzero, one should expect sign dependence, given the overwhelming evidence of volatility dependence. Even in assets where expected returns are zero, sign dependence may be induced by skewness in the asset returns process. Hence market timing ability is a very real possibility, depending on the relationship between the mean of the… Show more

Although asset returns are essentially unforecastable, the same is not true for asset return signs (i.e. the direction-of-change). As long as expected returns are nonzero, one should expect sign dependence, given the overwhelming evidence of volatility dependence. Even in assets where expected returns are zero, sign dependence may be induced by skewness in the asset returns process. Hence market timing ability is a very real possibility, depending on the relationship between the mean of the asset returns process and its higher moments. The highly nonlinear nature of the relationship means that conditional sign dependence is not likely to be found by traditional measures such as signs autocorrelations, runs tests or traditional market timing tests. Sign dependence is likely to be strongest at intermediate horizons of 1-3 months, and unlikely to be important at very low or high frequencies. Empirical tests demonstrate that sign dependence is very much present in actual US equity returns, with probabilities of positive returns rising to 65% or higher at various points over the last 20 years. A simple logit regression model captures the essentials of the relationship very successfully. Show less

For a very long time analysts were content to accept the standard deviation of returns as the norm for estimating volatility, even though theoretical research and empirical evidence dating from as long ago as 1980 suggested that superior estimators existed.
Part of the reason was that the claimed efficiency improvements of the Parkinson, Garman-Klass and other estimators failed to translate into practice when applied to real data. Or, at least, no one could quite be sure whether such… Show more

For a very long time analysts were content to accept the standard deviation of returns as the norm for estimating volatility, even though theoretical research and empirical evidence dating from as long ago as 1980 suggested that superior estimators existed.
Part of the reason was that the claimed efficiency improvements of the Parkinson, Garman-Klass and other estimators failed to translate into practice when applied to real data. Or, at least, no one could quite be sure whether such estimators really were superior when applied to empirical data since volatility, the second moment of the returns distribution, is inherently unknowable. You can say for sure what the return on a particular stock in a particular month was simply by taking the log of the ratio of the stock price at the month end and beginning. But the same cannot be said of volatility: the standard deviation of daily returns during the month, often naively assumed to represent the asset volatility, is in fact only an estimate of it. Show less

Reviews new techniques for forecasting volatility processes and modeling changes in market regime.

Analyzes methods for detecting changes in market regime

Explores applications of long memory models in financial market forecasting

Investigates methods for estimating the forward term structure of interest rates

Explores the latest research on volatility modeling with GARCH models

Looks at the latest research in forecasting equity returns and market timing strategies

I have been working on developing some high frequency spread strategies using Trading Technologies’ Algo Strategy Engine, which is extremely impressive (more on this in a later post). I decided to take a time out to experiment with a slower version of one of the trades, a calendar spread in VIX futures that trades the spread on the front two contracts. The strategy applies a variety of trend-following and mean-reversion indicators to trade the spread on a daily basis.