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.

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.

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.

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Commodity Price Driven Risk Management from Viewpoint of High Grade Steel Alloys

The study of price risk management concerning high grade steel alloys and their components was conducted. This study was focused in metal commodities, of which nickel, chrome and molybdenum were in a central role. Also possible hedging instruments and strategies for referred metals were studied. In the literature part main themes are price formation of Ni, Cr and Mo, the functioning of metal exchanges and main hedging instruments for metal commodities. This section also covers how micro and macro variables may affect metal prices from the viewpoint of short as well as longer time period. The experimental part consists of three sections. In the first part, multiple regression model with seven explanatory variables was constructed to describe price behavior of nickel. Results were compared after this with information created with comparable simple regression model. Additionally, long time mean price reversion of nickel was studied. In the second part, theoretical price of CF8M alloy was studied by using nickel, ferro-chrome and ferro-molybdenum as explanatory variables. In the last section, cross hedging possibilities for illiquid FeCr -metal was studied with five LME futures. Also this section covers new information concerning possible forthcoming molybdenum future contracts as well. The results of this study confirm, that linear regression models which are based on the assumption of market rationality, are not able to reliably describe price development of metals at issue. Models fulfilling assumptions for linear regression may though include useful information of statistical significant variables which have effect on metal prices. According to the experimental part, short futures were found to incorporate the most accurate information concerning the price movements in the future. However, not even 3M futures were able to predict turning point in the market before the faced slump. Cross hedging seemed to be very doubtful risk management strategy for illiquid metals, because correlations coefficients were found to be very sensitive for the chosen time span.

Modelling mean above and below ground litter production based on yield tables

Selective papers of the workshop on "Development of models and forest soil surveys for monitoring of soil carbon", Koli, Finland, April 5-9 2006.

A comparison of electricity spot prices simulation using ARMA-GARCH and mean-reverting models

The aim of this work is to compare two families of mathematical models for their respective capability to capture the statistical properties of real electricity spot market time series. The first model family is ARMA-GARCH models and the second model family is mean-reverting Ornstein-Uhlenbeck models. These two models have been applied to two price series of Nordic Nord Pool spot market for electricity namely to the System prices and to the DenmarkW prices. The parameters of both models were calibrated from the real time series. After carrying out simulation with optimal models from both families we conclude that neither ARMA-GARCH models, nor conventional mean-reverting Ornstein-Uhlenbeck models, even when calibrated optimally with real electricity spot market price or return series, capture the statistical characteristics of the real series. But in the case of less spiky behavior (System prices), the mean-reverting Ornstein-Uhlenbeck model could be seen to partially succeeded in this task.

Comprehensive digital preservation repositories: gaps, and what do we mean by “repository” anyway?

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Simulation of the Interaction Mean Free Path between Neutrons and TRISO Particles

The interaction mean free path between neutrons and TRISO particles is simulated using scripts written in MATLAB to solve the increasing error present with an increase in the packing factor in the reactor physics code Serpent. Their movement is tracked both in an unbounded and in a bounded space. Their track is calculated, depending on the program, linearly directly using the position vectors of the neutrons and the surface equations of all the fuel particles; by dividing the space in multiple subspaces, each of which contain a fraction of the total number of particles, and choosing the particles from those subspaces through which the neutron passes through; or by choosing the particles that lie within an infinite cylinder formed on the movement axis of the neutron. The estimate from the current analytical model, based on an exponential distribution, for the mean free path, utilized by Serpent, is used as a reference result. The results from the implicit model in Serpent imply a too long mean free path with high packing factors. The received results support this observation by producing, with a packing factor of 17 %, approximately 2.46 % shorter mean free path compared to the reference model. This is supported by the packing factor experienced by the neutron, the simulation of which resulted in a 17.29 % packing factor. It was also observed that the neutrons leaving from the surfaces of the fuel particles, in contrast to those starting inside the moderator, do not follow the exponential distribution. The current model, as it is, is thus not valid in the determination of the free path lengths of the neutrons.