On Option Price Information Content and Extraction of Implied Probability Distributions

In this study we used market settlement prices of European call options on stock index futures to extract implied probability distribution function (PDF). The method used produces a PDF of returns of an underlying asset at expiration date from implied volatility smile. With this method, the assumption of lognormal distribution (Black-Scholes model) is tested. The market view of the asset price dynamics can then be used for various purposes (hedging, speculation). We used the so called smoothing approach for implied PDF extraction presented by Shimko (1993). In our analysis we obtained implied volatility smiles from index futures markets (S&P 500 and DAX indices) and standardized them. The method introduced by Breeden and Litzenberger (1978) was then used on PDF extraction. The results show significant deviations from the assumption of lognormal returns for S&P500 options while DAX options mostly fit the lognormal distribution. A deviant subjective view of PDF can be used to form a strategy as discussed in the last section.

Normaalijakaumaan perustuva mutaatio-operaatio differentiaalievoluutioalgoritmiin

Evoluutioalgoritmit ovat viime vuosina osoittautuneet tehokkaiksi menetelmiksi globaalien optimointitehtävien ratkaisuun. Niiden vahvuutena on etenkin yleiskäyttöisyys ja kyky löytää globaali ratkaisu juuttumatta optimoitavan tavoitefunktion paikallisiin optimikohtiin. Tässä työssä on tavoitteena kehittää uusi, normaalijakaumaan perustuva mutaatio-operaatio differentiaalievoluutioalgoritmiin, joka on eräs uusimmista evoluutiopohjaisista optimointialgoritmeista. Menetelmän oletetaan vähentävän entisestään sekä populaation ennenaikaisen suppenemisen, että algoritmin tilojen juuttumisen riskiä ja se on teoreettisesti osoitettavissa suppenevaksi. Tämä ei päde alkuperäisen differentiaalievoluution tapauksessa, koska on voitu osoittaa, että sen tilanmuutokset voivat pienellä todennäköisyydellä juuttua. Työssä uuden menetelmän toimintaa tarkastellaan kokeellisesti käyttäen testiongelmina monirajoiteongelmia. Rajoitefunktioiden käsittelyyn käytetään Jouni Lampisen kehittämää, Pareto-optimaalisuuden periaatteeseen perustuvaa menetelmää. Samalla saadaan kerättyä lisää kokeellista näyttöä myös tämän menetelmän toiminnasta. Kaikki käytetyt testiongelmat kyettiin ratkaisemaan sekä alkuperäisellä differentiaalievoluutiolla, että uutta mutaatio-operaatiota käyttävällä versiolla. Uusi menetelmä osoittautui kuitenkin luotettavammaksi sellaisissa tapauksissa, joissa alkuperäisellä algoritmilla oli vaikeuksia. Lisäksi useimmat ongelmat kyettiin ratkaisemaan luotettavasti pienemmällä populaation koolla kuin alkuperäistä differentiaalievoluutiota käytettäessä. Uuden menetelmän käyttö myös mahdollistaa paremmin sellaisten kontrolliparametrien käytön, joilla hausta saadaan rotaatioinvariantti. Laskennallisesti uusi menetelmä on hieman alkuperäistä differentiaalievoluutiota raskaampi ja se tarvitsee yhden kontrolliparametrin enemmän. Uusille kontrolliparametreille määritettiin kuitenkin mahdollisimman yleiskäyttöiset arvot, joita käyttämällä on mahdollista ratkaista suuri joukko erilaisia ongelmia.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Maritime transportation in the Gulf of Finland in 2007 and in 2015

The Gulf of Finland is said to be one of the densest operated sea areas in the world. It is a shallow and economically vulnerable sea area with dense passenger and cargo traffic of which petroleum transports have a share of over 50 %. The winter conditions add to the risks of maritime traffic in the Gulf of Finland. It is widely believed that the growth of maritime transportation will continue also in the future. The Gulf of Finland is surrounded by three very different national economies with, different maritime transportation structures. Finland is a country of high GDP/per capita with a diversified economic structure. The number of ports is large and the maritime transportation consists of many types of cargoes: raw materials, industrial products, consumer goods, coal and petroleum products, and the Russian transit traffic of e.g. new cars and consumer goods. Russia is a large country with huge growth potential; in recent years, the expansion of petroleum exports has lead to a strong economic growth, which is also apparent in the growth of maritime transports. Russia has been expanding its port activities in the Gulf of Finland and it is officially aiming to transport its own imports and exports through the Russian ports in the future; now they are being transported to great extend through the Finnish, Estonian and other Baltic ports. Russia has five ports in the Gulf of Finland. Estonia has also experienced fast economic growth, but the growth has been slowing down already during the past couples of years. The size of its economy is small compared to Russia, which means the transported tonnes cannot be very massive. However, relatively large amounts of the Russian petroleum exports have been transported through the Estonian ports. The future of the Russian transit traffic in Estonia looks nevertheless uncertain and it remains to be seen how it will develop and if Estonia is able to find replacing cargoes if the Russian transit traffic will come to an end in the Estonian ports. Estonia’s own import and export consists of forestry products, metals or other raw materials and consumer goods. Estonia has many ports on the shores of the Gulf of Finland, but the port of Tallinn dominates the cargo volumes. In 2007, 263 M tonnes of cargoes were transported in the maritime traffic in the Gulf of Finland, of which the share of petroleum products was 56 %. 23 % of the cargoes were loaded or unloaded in the Finnish ports, 60 % in the Russian ports and 17 % in the Estonian ports. The largest ports were Primorsk (74.2 M tonnes) St. Petersburg (59.5 M tonnes), Tallinn (35.9 M tonnes), Sköldvik (19.8 M tonnes), Vysotsk (16.5 M tonnes) and Helsinki (13.4 M) tonnes. Approximately 53 600 ship calls were made in the ports of the Gulf of Finland. The densest traffic was found in the ports of St. Petersburg (14 651 ship calls), Helsinki (11 727 ship calls) and Tallinn (10 614 ship calls) in 2007. The transportation scenarios are usually based on the assumption that the amount of transports follows the development of the economy, although also other factors influence the development of transportation, e.g. government policy, environmental aspects, and social and behavioural trends. The relationship between the development of transportation and the economy is usually analyzed in terms of the development of GDP and trade. When the GDP grows to a certain level, especially the international transports increase because countries of high GDP produce, consume and thus transport more. An effective transportation system is also a precondition for the economic development. In this study, the following factors were taken into consideration when formulating the future scenarios: maritime transportation in the Gulf of Finland 2007, economic development, development of key industries, development of infrastructure and environmental aspects in relation to maritime transportation. The basic starting points for the three alternative scenarios were: • the slow growth scenario: economic recession • the average growth scenario: economy will recover quickly from current instability • the strong growth scenario: the most optimistic views on development will realize According to the slow growth scenario, the total tonnes for the maritime transportation in the Gulf of Finland would be 322.4 M tonnes in 2015, which would mean a growth of 23 % compared to 2007. In the average growth scenario, the total tonnes were estimated to be 431.6 M tonnes – a growth of 64 %, and in the strong growth scenario 507.2 M tonnes – a growth of 93%. These tonnes were further divided into petroleum products and other cargoes by country, into export, import and domestic traffic by country, and between the ports. For petroleum products, the share of crude oil and oil products was estimated and the number of tanker calls in 2015 was calculated for each scenario. However, the future development of maritime transportation in the GoF is dependent on so many societal and economic variables that it is not realistic to predict one exact point estimate value for the cargo tonnes for a certain scenario. Plenty of uncertainty is related both to the degree in which the scenario will come true as well as to the cause-effect relations between the different variables. For these reasons, probability distributions for each scenario were formulated by an expert group. As a result, a range for the total tonnes of each scenario was formulated and they are as follows: the slow growth scenario: 280.8 – 363 M tonnes (expectation value 322.4 M tonnes)

Hygro-elasto-plastic behavior of planar orthotropic material

The mechanical and hygroscopic properties of paper and board are factors affecting the whole lifecycle of a product, including paper/board quality, production, converting, and material and energy savings. The progress of shrinkage profiles, loose edges of web, baggy web causing wrinkling and misregistration in printing are examples of factors affecting runnability and end product quality in the drying section and converting processes, where paper or board is treated as a moving web. The structural properties and internal stresses or plastic strain differences built up during production also cause the end-product defects related to distortion of the shape of the product such as sheet or box. The objective of this work was to construct a model capable of capturing the characteristic behavior of hygroscopic orthotropic material under moisture change, during different external in-plane stretch or stress conditions. Two independent experimental models were constructed: the elasto-plastic material model and the hygroexpansivity-shrinkage model. Both describe the structural properties of the sheet with a fiber orientation probability distribution, and both are functions of the dry solids content and fiber orientation anisotropy index. The anisotropy index, introduced in this work, simplifies the procedure of determining the constitutive parameters of the material model and the hygroexpansion coefficients in different in-plane directions of the orthotropic sheet. The mathematically consistent elasto-plastic material model and the dry solids content dependent hygroexpansivity have been constructed over the entire range from wet to dry. The presented elastoplastic and hygroexpansivity-shrinkage models can be used in an analytical approach to estimate the plastic strain and shrinkage in simple one-dimensional cases. For studies of the combined and more complicated effects of hygro-elasto-plastic behavior, both models were implemented in a finite element program for a numerical solution. The finite element approach also offered possibilities for studying different structural variations of orthotropic planar material, as well as local buckling behavior and internal stress situations of the sheet or web generated by local strain differences. A comparison of the simulation examples presented in this work to results published earlier confirms that the hygro-elasto-plastic model provides at least qualitatively reasonable estimates. The application potential of the hygro-elasto-plastic model is versatile, including several phenomena and defects appearing in the drying, converting and end-use conditions of the paper or board webs and products, or in other corresponding complex planar materials.