Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

Risk Parity: A Modern Tool for Diversification

The purpose of this study is to examine how well risk parity works in terms of risk, return and diversification relative to more traditional minimum variance, 1/N and 60/40 portfolios. Risk parity portfolios were constituted of five risk sources; three common asset classes and two alternative beta investment strategies. The three common asset classes were equities, bonds and commodities, and the alternative beta investment strategies were carry trade and trend following. Risk parity portfolios were constructed using five different risk measures of which four were tail risk measures. The risk measures were standard deviation, Value-at-Risk, Expected Shortfall, modified Value-at-Risk and modified Expected Shortfall. We studied also how sensitive risk parity is to the choice of risk measure. The hypothesis is that risk parity portfolios provide better return with the same amount of risk and are better diversified than the benchmark portfolios. We used two data sets, monthly and weekly data. The monthly data was from the years 1989-2011 and the weekly data was from the years 2000-2011. Empirical studies showed that risk parity portfolios provide better diversification since the diversification is made at the risk level. Risk based portfolios provided superior return compared to the asset based portfolios. Using tail risk measures in risk parity portfolios do not necessarily provide better hedge from tail events than standard deviation.

Stochastic variability of output levels in a pulp mill

Quite often, in the construction of a pulp mill involves establishing the size of tanks which will accommodate the material from the various processes in which case estimating the right tank size a priori would be vital. Hence, simulation of the whole production process would be worthwhile. Therefore, there is need to develop mathematical models that would mimic the behavior of the output from the various production units of the pulp mill to work as simulators. Markov chain models, Autoregressive moving average (ARMA) model, Mean reversion models with ensemble interaction together with Markov regime switching models are proposed for that purpose.

Korkokäyrän mallintaminen: tarkastelussa Cox-Ingersoll-Ross -malli

Korot ovat erittäin tärkeässä osassa kaikessa taloudellisessa toiminnassa ja tästä syystä niiden kehitystä seurataan mielenkiinnolla. Yksi keino korkojen kehityksen tutkimiseen on rahoitusmarkkinoilla havaittavan korkokäyrän tarkastelu. Tämän tutkielman tarkoituksena on tarkastella Cox-Ingersoll-Ross-mallin soveltuvuutta korkokäyrän empiriseen mallintamiseen. Tässä tutkielmassa Cox-Ingersoll-Ross-malli estimoidaan pienimmän neliösumman – ja suurimman uskottavuuden –menetelmillä. Tutkimuksen datana käytetään 3 kuukauden euribor-korkojen ja Saksan valtion 3 kuukauden mittaisen joukkolainan päivätason tuottoja kolmelta eri vuoden mittaiselta periodilta. Mallin avulla estimoituja korkokäyriä verrataan samojen periodien lopussa rahoitusmarkkinoilla realisoituneisiin korkokäyriin. Estimoinnin tulosten perusteella Cox-Ingersoll- Ross-malli ei sovi varauksitta korkokäyrän mallintamiseen. Pienimmän neliösumman –menetelmän diagnostisista tarkastuksista käy ilmi, että menetelmä ei ole sopiva mallin estimoimiseen. Suurimman uskottavuuden –estimoinnin avulla estimoidut korkokäyrät eroavat kaikissa paitsi yhdessä tapauksessa melko selvästi realisoituneista korkokäyristä. Tutkielman tuloksissa on selviä yhtymäkohtia aiempien empiristen tutkimusten tuloksiin. Varsinkin mallin odotusarvohakuisuutta (mean reversion) kuvaavan parametrin estimoinnissa ilmenee epävarmuutta, mikä vaikuttaa koko mallin toimintaan. Sama tulos ilmenee myös aiemmista tutkimuksista, osassa jopa kyseenalaistetaan koko ilmiön olemassaolo. Tutkielman tuloksista voidaan päätellä, että yhden muuttujan Cox-Ingersoll-Ross-malli ei varauksitta sovellu korkokäyrän empiriseen mallintamiseen. Todennäköisiä syitä tähän ovat mallin tekemät epärealistiset taustaoletukset sekä se, että tarkasteluperiodien aikana Eurooppa kärsi velkakriisistä, mikä kevensi Euroopan keskuspankin rahapolitiikkaa ja alensi korkotasoa. Tämä seikka vaikuttaa eri periodien tulosten vertailukelpoisuuteen. Tutkielman johtopäätöksenä on, että yhden muuttujan mallien sijaan korkokäyrän mallintamisessa tulisi keskittyä 3 muuttujan malleihin. Tällöin jokaiselle korkokäyrän elementille: taso, kulmakerroin ja konveksisuus saataisiin oma muuttujansa. Tämä helpottaisi myös korkokäyrän volatiliteetin mallintamisessa, mikä osoittautuu ongelmalliseksi vain yhtä muuttujaa käytettäessä.

Do retail investors use technical analysis? Evidence from Stuttgart stock exchange.

Tutkielma käyttää automaattista kuviontunnistusalgoritmia ja yleisiä kahden liukuvan keskiarvon leikkauspiste –sääntöjä selittääkseen Stuttgartin pörssissä toimivien yksityissijoittajien myynti-osto –epätasapainoa ja siten vastatakseen kysymykseen ”käyttävätkö yksityissijoittajat teknisen analyysin menetelmiä kaupankäyntipäätöstensä perustana?” Perusolettama sijoittajien käyttäytymisestä ja teknisen analyysin tuottavuudesta tehtyjen tutkimusten perusteella oli, että yksityissijoittajat käyttäisivät teknisen analyysin metodeja. Empiirinen tutkimus, jonka aineistona on DAX30 yhtiöiden data vuosilta 2009 – 2013, ei tuottanut riittävän selkeää vastausta tutkimuskysymykseen. Heikko todistusaineisto näyttää kuitenkin osoittavan, että yksityissijoittajat muuttavat kaupankäyntikäyttäytymistänsä eräiden kuvioiden ja leikkauspistesääntöjen ohjastamaan suuntaan.

TAKING ADVANTAGE OF THE LOCAL ADVANTAGE? - Investment value of the analyst local advantage in the Finnish stock market in 2006–2014

An investor can either conduct independent analysis or rely on the analyses of others. Stock analysts provide markets with expectations regarding particular securities. However, analysts have different capabilities and resources, of which investors are seldom cognizant. The local advantage refers to the advantage stemming from cultural or geographical proximity to securities analyzed. The research has confirmed that local agents are generally more accurate or produce excess returns. This thesis tests the investment value of the local advantage regarding Finnish stocks via target price data. The empirical section investigates the local advantage from several aspects. It is discovered that local analysts were more focused on certain sectors generally located close to consumer markets. Market reactions to target price revisions were generally insignificant with the exception to local positive target prices. Both local and foreign target prices were overly optimistic and exhibited signs of herding. Neither group could be identified as a leader or follower of new information. Additionally, foreign price change expectations were more in line with the quantitative models and ideas such as beta or return mean reversion. The locals were more accurate than foreign analysts in 5 out of 9 sectors and vice versa in one. These sectors were somewhat in line with coverage decisions and buttressed the idea of local advantage stemming from proximity to markets, not to headquarters. The accuracy advantage was dependent on sample years and on the measure used. Local analysts ranked magnitudes of price changes more accurately in optimistic and foreign analysts in pessimistic target prices. Directional accuracy of both groups was under 50% and target prices held no linear predictive power. Investment value of target prices were tested by forming mean-variance efficient portfolios. Parallel to differing accuracies in the levels of expectations foreign portfolio performed better when short sales were allowed and local better when disallowed. Both local and non-local portfolios performed worse than a passive index fund, albeit not statistically significantly. This was in line with previously reported low overall accuracy and different accuracy profiles. Refraining from estimating individual stock returns altogether produced statistically significantly higher Sharpe ratios compared to local or foreign portfolios. The proposed method of testing the investment value of target prices of different groups suffered from some inconsistencies. Nevertheless, these results are of interest to investors seeking the advice of security analysts.

TAKING ADVANTAGE OF THE LOCAL ADVANTAGE? - Investment value of the analyst local advantage in the Finnish stock market in 2006–2014

An investor can either conduct independent analysis or rely on the analyses of others. Stock analysts provide markets with expectations regarding particular securities. However, analysts have different capabilities and resources, of which investors are seldom cognizant. The local advantage refers to the advantage stemming from cultural or geographical proximity to securities analyzed. The research has confirmed that local agents are generally more accurate or produce excess returns. This thesis tests the investment value of the local advantage regarding Finnish stocks via target price data. The empirical section investigates the local advantage from several aspects. It is discovered that local analysts were more focused on certain sectors generally located close to consumer markets. Market reactions to target price revisions were generally insignificant with the exception to local positive target prices. Both local and foreign target prices were overly optimistic and exhibited signs of herding. Neither group could be identified as a leader or follower of new information. Additionally, foreign price change expectations were more in line with the quantitative models and ideas such as beta or return mean reversion. The locals were more accurate than foreign analysts in 5 out of 9 sectors and vice versa in one. These sectors were somewhat in line with coverage decisions and buttressed the idea of local advantage stemming from proximity to markets, not to headquarters. The accuracy advantage was dependent on sample years and on the measure used. Local analysts ranked magnitudes of price changes more accurately in optimistic and foreign analysts in pessimistic target prices. Directional accuracy of both groups was under 50% and target prices held no linear predictive power. Investment value of target prices were tested by forming mean-variance efficient portfolios. Parallel to differing accuracies in the levels of expectations foreign portfolio performed better when short sales were allowed and local better when disallowed. Both local and non-local portfolios performed worse than a passive index fund, albeit not statistically significantly. This was in line with previously reported low overall accuracy and different accuracy profiles. Refraining from estimating individual stock returns altogether produced statistically significantly higher Sharpe ratios compared to local or foreign portfolios. The proposed method of testing the investment value of target prices of different groups suffered from some inconsistencies. Nevertheless, these results are of interest to investors seeking the advice of security analysts.

Kalman Filtering in Online Paper Quality Assessment

Controlling the quality variables (such as basis weight, moisture etc.) is a vital part of making top quality paper or board. In this thesis, an advanced data assimilation tool is applied to the quality control system (QCS) of a paper or board machine. The functionality of the QCS is based on quality observations that are measured with a traversing scanner making a zigzag path. The basic idea is the following: The measured quality variable has to be separated into its machine direction (MD) and cross direction (CD) variations due to the fact that the QCS works separately in MD and CD. Traditionally this is done simply by assuming one scan of the zigzag path to be the CD profile and its mean value to be one point of the MD trend. In this thesis, a more advanced method is introduced. The fundamental idea is to use the signals’ frequency components to represent the variation in both CD and MD. To be able to get to the frequency domain, the Fourier transform is utilized. The frequency domain, that is, the Fourier components are then used as a state vector in a Kalman filter. The Kalman filter is a widely used data assimilation tool to combine noisy observations with a model. The observations here refer to the quality measurements and the model to the Fourier frequency components. By implementing the two dimensional Fourier transform into the Kalman filter, we get an advanced tool for the separation of CD and MD components in total variation or, to be more general, for data assimilation. A piece of a paper roll is analyzed and this tool is applied to model the dataset. As a result, it is clear that the Kalman filter algorithm is able to reconstruct the main features of the dataset from a zigzag path. Although the results are made with a very short sample of paper roll, it seems that this method has great potential to be used later on as a part of the quality control system.