Pricing of Warrants with Stock Price Dependent Threshold Conditions

Warrants with stock price dependent threshold conditions give the right to buy specially issued stocks, if the performance of the stock price satisfies some requirements. Existence of these derivatives changes the price process of the underlying. We show that in the presence of such warrants one cannot assume that the stock market is arbitrage free and that the stock is tradeable at every time moment with the same price for buying and selling. This means that the usual methods for deriving fair prices for such warrants cannot be used. We start from a simple model for the firm's value process and discuss some ways to specify a related model for the stock price process in the presence of warrants with threshold conditions. We also discuss how indifference pricing approach can be used for pricing such warrants

Computational Finance

Course "Computational Finance" gives an overview different partial differential equations arising in mathematical finance, their derivation procedures and numerical solution methods. In the computer labs students acquire practical skills for computing the prices of various financial options.BeSt programmi toetusel loodud e-kursuse "Computational Finance" õppematerjalid. Kursuse sisuks on finantsoptsioonide hindu kirjeldavate võrrandite tuletamine, nende lahendamiseks erinevate numbriliste meetodite konstrueerimine ning arvutiprogrammina realiseerimine. Materjalid sisaldavad loengukonspekti, praktikumide juhendeid ning näitelahendusi programmeerimiskeeles Python

Simulation Methods in Financial Mathematics

Course gives an overview of and practical experiece in the different aspects of applying Monte-Carlo methods for pricing various derivative securities.BeSt programmi toetusel valminud e-kursuse "Simulation Methods in Financial Mathematics " materjalid

On the stability of piecewise polynomial collocation methods for solving weakly singular integral equations of the second kind

Piecewise polynomial collocation methods on special nonuniform grids are efficient methods for solving weakly singular Fredholm and Volterra integral equations but there is a widespread belief that those methods are numerically unstable in the case of large values of the nonuniformity parameter r. We show that this method by itself is stable and discuss some implementation problems that may lead to unstable behavior of numerical results. First Published Online: 14 Oct 201

Aegridade analüüs

BeSt programmi raames loodud e-kursuse "Aegridade analüüs" õppematerjalid

On estimation of insurance risk parameters by combining local regression and distribution fitting ideas

The problem of premium estimation is an essential part of the insurance mathematics. Often the problem is divided into two parts: estimation of claim number (or frequency) and the estimation of individual claim amounts (severities). In this paper, we will focus on the former. More precisely, we are looking for certain semiparametric dynamic regression type model to avoid the "price shock" issue of static classication. We apply locally the regression method, use local maximum likelihood estimation for the parameters of the model and cross-validation techniques to determine the optimal size of a neighborhood. A case study with real vehicle casco insurance dataset is included, the results obtained by proposed method are compared by the ones obtained by global regression and the classification and regression trees (C&RT) approach

On fully discrete collocation methods for solving weakly singular integro‐differential equations

In order to find approximate solutions of Volterra and Fredholm integro‐differential equations by collocation methods it is necessary to compute certain integrals that determine the required algebraic systems. Those integrals usually can not be computed exactly and if the kernels of the integral operators are not smooth, simple quadrature formula approximations of the integrals do not preserve the convergence rate of the collocation method. In the present paper fully discrete analogs of collocation methods where non‐smooth integrals are replaced by appropriate quadrature formulas approximations, are considered and corresponding error estimates are derived. Presented numerical examples display that theoretical results are in a good accordance with the actual convergence rates of the proposed algorithms. First published online: 09 Jun 201

Uimastite tarvitamine Eesti noorte ja täisealiste seas. AAA-uuringu esmased tulemused

Taust ja eesmärk. Alkoholi, tubakatoodete ja illegaalsete uimastite tarvitamine on üha suurenev üleilmne probleem. Artikli eesmärk on anda ülevaade Eesti noorte inimeste uimastite kasutamise levimusuuringu „Ained ja arenevad ajud“ (AAA-uuring) esmastest tulemustest. Metoodika. Uuringus osales 4922 isikut, kelle keskmine vanus oli 21,4 ± 6,8 aastat (vahemik 16–45 a). Elu jooksul ja viimase 3 kuu jooksul tarvitatud uimastite määr tuvastati mõõtevahendi ASSIST (Alcohol, Smoking and Substance use Involvement Screening Test) abil. Andmete kogumiseks kasutati veebiplatvormi REDCap. Tulemused. Uuringus osalejatest oli elu jooksul vähemalt korra tarvitanud alkoholi 86,1% ja tubakatooteid 60,5%. Kanep oli kõige sagedamini (43,0%) proovitud illegaalne uimasti. Amfetamiinitüüpi stimulante oli vähemalt korra elus proovinud 15,2%, hallutsinogeene 12,5%, inhalante 8,1%, kokaiini 7,7% ja opioide 3,7% küsimustikule vastanutest. Kolme viimase kuu jooksul oli 77,6% uuringus osalenutest pruukinud alkoholi, sageduselt järgnesid tubaka (43,0%) ja kanepi (24,5%) tarvitamine. Esitatud on ka andmed erinevaid uimasteid elu jooksul vähemalt korra tarvitanud isikute jaotuse kohta maakonniti ning piirkonniti. Arutelu. Uuring kinnitab varasemaid tulemusi, et noorte hulgas on uimastite tarvitamise levimus suur. Nii legaalsete kui ka illegaalsete uimastite tarvitamine on sagedasem kui arvatud, eriti noorte hulgas. Seetõttu on soovitatav tõhustada alkoholi, tubaka ja illegaalsete ainete tarvitamise vähendamisele suunatud ennetuse ja sekkumisega seotud tegevusi Eesti noorte hulgas

Usage based insurance

There is a need to shift into more customer-centric model, as more insurance companies light up telematics technology. Imagine being able to predict an incident before it happens. Merging data analytics together with driver behavior is a game changing reality companies are just beginning to realize the benefits of. If actuaries can see patterns and trends, that’s where the magic begins to happen