Stochastics and Sentiment Analysis in Wall Street

Wall Street is not only a place of facilitating the money flow, but also a playground for scientists.

When I was young, I saw one of my uncles plotting prices for stocks to perform technical analysis. When I was in college, my friends often talked about investing in a few financial futures and options. When I was doing my graduate degree in physics, we studied John Hull’s famous textbook [Hull 2011] on quantitative finance to learn about financial modeling. A few of my classmates went to Wall Street to become quantitative analysts or financial software developers. There are ups and downs in the financial markets. But as long as we are in a capitalist society, finance is a subject we never ignore. However, scientists have not come up with a consensus about the nature of a financial market.

Agent-Based Models

Economists believe that individuals in a market are rational being who always aim at maximizing their profits. They often apply agent-based models, which employs complex system theories or game theory.

Random Processes and Statistical Physics

However, a lot of mathematicians in Wall Street (including quantitative analysts and econophysicists) see the stock prices as undergoing Brownian motion. [Hull 2011, Baaquie 2007] They employ tools in statistical physics and stochastic processes to study the pricings of various financial derivatives. Therefore, the random-process and econophysical approaches have nothing much about stock price prediction (despite the fact that they do need a “return rate” in their model.) Random processes are unpredictable.

However, some sort of predictions carry great values. For example, when there is overhypes or bubbles in the market, we want to know when it will burst. There are models that predict defaults and bubble burst in a market using the log-periodic power law (LPPL). [Wosnitza, Denz 2013] In addition, there has been research showing the leverage effect in stock markets in developed countries such as Germany (c.f. fluctuation-dissipation theorem in statistical physics), and anti-leverage effect in China (Shanghai and Shenzhen). [Qiu, Zhen, Ren, Trimper 2006]

Reconciling Intelligence and Randomness

There are some values to both views. It is hard to believe that stock prices are completely random, as the economic environment and the public opinions must affect the stock prices. People can neither be completely rational nor completely random.

There has been some study in reconciling game theory and random processes, in an attempt to bring economists and mathematicians together. In this theoretical framework, financial systems still sought to attain the maximum entropy (randomness), but the “particles” in the system behaves intelligently. [Venkatasubramanian, Luo, Sethuraman 2015] (See my another blog entry: MathAnalytics (1) – Beautiful Mind, Physical Nature and Economic Inequality) We are not sure how successful this attempt will be at this point.

Sentiment Analysis

As people are talking about big data in recent years, there have been attempts to apply machine learning algorithms in finance. However, scientists tend not to price using machine learning algorithms because these algorithms mostly perform classification. However, there are attempts, with natural language processing (NLP) techniques, to predict the stock prices by detecting the public emotions (or sentiments) in social media such as Twitter. [Bollen, Mao, Zeng 2010] It has been found that measuring the public mood in a few dimensions (including Calm, Alert, Sure, Vital, Kind, and Happy) allows scientists to accurately predict the trend of Dow Jones Industrial Average (DJIA). However, some hackers take advantage on the sentiment analysis on Twitter. In 2013, there was a rumor on Twitter saying the White House being bombed, The computers responded instantly and automatically by performing trading, causing the stock market to fall immediately. But the market restored quickly after it was discovered that the news was fake. (Fig. 1)

Fig. 1: DJIA fell because of a rumor of the White House being bombed, but recovered when discovered the news was fake (taken from

P.S.: While I was writing this, I saw an interesting statement in the paper about leverage effect. [Qiu, Zhen, Ren, Trimper 2006] The authors said that:

Why do the German and Chinese markets exhibit different return-volatility correlations? Germany is a developed country. To some extent, people show risk aversion, and therefore, may be nervous in trading as the stock price is falling. This induces a higher volatility. When the price is rising, people feel safe and are inactive in trading. Thus, the stock price tends to be stable. This should be the social origin of the leverage effect. However, China just experiences the first stage of capitalism, and people are somewhat excessive speculative in the financial markets. Therefore, people rush for trading as the stock price increases. When the price drops, people stay inactive in trading and wait for rising up of the stock price. That explains the antileverage effect.

Does this paragraph written in 2006 give a hint of what happened in China in 2015 now? (Fig. 2)

Fig. 2: The fall of Chinese stock market in 2015 (taken from

Continue reading “Stochastics and Sentiment Analysis in Wall Street”

Lyrics Generation

Eminem (taken from web)

When I saw the “standardized” style of writing written in the classic book “Elements of Style” written by William Strunk, I have been wondering if the style of writing can be programmable. And now, with artificial intelligence, people can write automated codes that generate lyrics. In a paper written by Eric Malmi and his collaborators [Malmi, Takala, Toivonen, Raiko, Gionis 2015], the system DopeLearning, which generates rap lyrics to certain complexities, was introduced. It applies two machine learning techniques, namely the RankSVM and the deep neural network. It is fascinating that automated codes can be creative to produce complex artistic things, as the abstract says:

Writing rap lyrics requires both creativity, to construct a meaningful and an interesting story, and lyrical skills, to produce complex rhyme patterns, which are the cornerstone of a good flow.

What does DopeLearning produce? See the example the paper gives:

For a chance at romance I would love to enhance (Big Daddy Kane – The Day You’re Mine)
But everything I love has turned to a tedious task (Jedi Mind Tricks – Black Winter Day)
One day we gonna have to leave our love in the past (Lil Wayne – Marvin’s Room)
I love my fans but no one ever puts a grasp (Eminem – Say Goodbye Hollywood)
I love you momma I love my momma – I love you momma (Snoop Dogg – I Love My Momma)
And I would love to have a thing like you on my team you take care (Ghostface Killah – Paragraphs Of Love)
I love it when it’s sunny Sonny girl you could be my Cher (Common – Make My Day)
I’m in a love affair I can’t share it ain’t fair (Snoop Dogg – Show Me Love)
Haha I’m just playin’ ladies you know I love you. (Eminem – Kill You)
I know my love is true and I know you love me too (Everlast – On The Edge)
Girl I’m down for whatever cause my love is true (Lil Wayne – Sean Kingston I’m At War)
This one goes to my man old dirty one love we be swigging brew (Big Daddy Kane – Entaprizin)
My brother I love you Be encouraged man And just know (Tech N9ne – Need More Angels)
When you done let me know cause my love make you be like WHOA (Missy Elliot – Dog In Heat)
If I can’t do it for the love then do it I won’t (KRS One – Take It To God)
All I know is I love you too much to walk away though (Eminem – Love The Way You Lie)

There are similar work for Chinese Mandopop, using RNN. Chinese readers can refer to this blog post:

Continue reading “Lyrics Generation”

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