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Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Oct 11
A paper forthcoming in The Econometrics Journal by Qu and Perron, worth to read carefully.

This paper proposes a framework for the modeling, inference and forecasting of volatility in the presence of level shifts of unknown timing, magnitude and frequency. First, we consider a stochastic volatility model comprising both a level shift and a short-memory component, with the former modeled as a compound binomial process and the latter as an AR(1). Next, we adopt a Bayesian approach for inference and develop algorithms to obtain posterior distributions of the parameters and the two latent components. Then, we apply the model to daily S&P 500 and NASDAQ returns over the period 1980.1–2010.12. The results show that although the occurrence of a level shift is rare, about once every two years, this component clearly contributes most to the variation in the volatility. The half-life of a typical shock from the AR(1) component is short, on average between 9 and 15 days. Interestingly, isolating the level shift component from the overall volatility reveals a stronger relationship between volatility and business cycle movements. Although the paper focuses on daily index returns, the methods developed can potentially be used to study the low frequency variation in realized volatility or the volatility of other financial or macroeconomic variables.


Journal paper, Working paper in PDF
Jun 13
I am contacted by a reader to post this announcement, just in case you are interested, some good speakers.

Institute of Mathematics of the National Academy of Sciences in association with Yerevan State University and American University of Armenia is organizing a Workshop on Stochastic and PDE Methods in Financial Mathematics in September 7 - 12, 2012 to be held in Yerevan, Armenia.

The program of the workshop will consist of invited 50 minutes plenary lectures and contributed 20 minutes talks, poster sessions as well as short presentations.

Scientific Committee: Rama Cont (Universite Paris VI-VII, France), Levon Goukasian (Pepperdine University, USA), Walter Schachermayer (University of Vienna, Austria), Henrik Shahgholian (KTH, Sweden), Johan Tysk (Uppsala University, Sweden)

Organizing Committee: A. Hakobyan (YSU, Armenia), M. Poghosyan (YSU, Armenia), R. Barkhudaryan (Institute of Mathematics, Armenia), A. Hajian (AUA, Armenia)

Main Speakers: Amel Bentata (Universite Pierre et Marie Curie (P6), France),  Rama Cont (Universite Paris VI-VII, France), Boualem Djehiche (KTH, Sweden), Diogo Gomes (Instituto Superior Tecnico, Portugal), Dmitry Kramkov (Carnegie Mellon University, USA), Michael Mania (A. Razmadze Mathematical Institute, Georgia), Peter Markowich (University of Cambridge, UK and University of Vienna, Austria), Aleksandar Mijatovic (University of Warwick, UK), George Papanicolaou (Stanford University, USA), Andrea Pascucci (Universita di Bologna, Italia), Huyen Pham (University Paris Diderot (Paris 7), IUF, France), Camelia Pop (Rutgers University, USA), Walter Schachermayer (University of Vienna, Austria), Henrik Shahgholian (KTH, Sweden), Halil Mete Soner (ETH Zürich, Switzerland), Josef Teichmann (ETH Zurich, Switzerland), Nizar Touzi (Ecole Polytechnique, France), Thaleia Zariphopoulou (Oxford-Man Institute of Quantitative Finance, UK)
Apr 18
Developed by George Lane in the 1950s, the Stochastic Oscillator is one of the most popular stock trading indicators, that provide good signals in many Forex pairs, stocks and commodities. In this article we will describe how to profit with it and catching bottoms and tops.

First of all it is important to understand the formula of the Stochastic Oscillator:

Main Stochastic (%K) = 100 * (Closing Price - Lowest Close of Last 5 Bars) / (Highest High of Last 5 Bars - Lowest Close of Last 5 Bars)
Signal Stochastic (%D) = 3-Period Exponential Moving Average of the Main Stochastic

From the formula we can derive that the main stochastic is showing us the relative location of current price in relation to the range of last 5 bars. Low readings indicate that price is near a support level (the lowest point of the range) and high readings indicate that price is near a resistance level (the highest point of the range).

Most traders enter trades when the main stochastic crosses the signal stochastic line - when a cross is from below it is a long signal, and when the cross is from below it is a short signal.



Another trading method is to enter trades when the Stochastic Oscillator crosses the 60 level (long trade), and when it crosses the 40 level (for shotr trade). It is a trend-following approach that works well in stock charts with strong trends.



It is remarkable that an indicator that was developed 60 years ago is still useful and still generates powerful signals to this day, on many stocks and commodities.

One can also improve the formula of the Stochastic to take into account ranges that are shifting: Channels instead of parallel trends. The improved formula would show the location of price in relation to the boundaries of regression channel, giving much more accurate signals that take into account the trend as well, and not just flat high and low.

We highly recommend getting to know this indicator and mastering the trading systems presented here. It can provide very accurate signals, both trend-following and reversal signals, and can provide you with trading edge.
Feb 17
Stochastic Volatility Models and the Pricing of VIX Options:  this paper examines and compares the performance of a variety of continuous-time volatility models in their ability to capture the behavior of the VIX.

Finding the best distribution that fits the data: the title tells, select a best fitted distribution among dozens candidates for a given data series.

No-Hype Options Trading: Myths, Realities, and Strategies That Really Work realistic strategies to consistently generate income every month, while debunking many myths about options trading that tend to lead retail traders astray.

RStudio in the cloud, for dummies: run cloud computing version of R with RStudio, cool!
Feb 14
Stochastic Volatility Models and the Pricing of VIX Options is written by Joanna Goard, Mathew Mazur and published in Mathematical Finance. It examines and compares the performance of several volatility models to estimate the VIX, a measure of the implied volatility of S&P 500 index options. You can get access to the paper here.

An accurate estimation of VIX is obviously important given its special role as the fear gauge, there is extensive literature trying to do so, among them, mean-reverting models are especially popular. The authors compare eight different mean-reverting models, with each having different mean reversion speed or diffusion term, specifically, they can be summarized as follows in table 2.1:
volatility mean reversion models
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