Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a given model parameter variation range

Application of Operator Splitting Methods in Finance

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generalizations thereof. An overview of various operator splitting methods is presented for the efficient numerical solution of these problems. Splitting schemes of the Alternating Direction Implicit (ADI) type are discussed for multidimensional problems, e.g. given by stochastic volatility (SV) models. For jump models Implicit-Explicit (IMEX) methods are considered which efficiently treat the nonlocal jump operator. For American options an easy-to-implement operator splitting method is described for the resulting linear complementarity problems. Numerical experiments are presented to illustrate the actual stability and convergence of the splitting schemes. Here European and American put options are considered under four asset price models: the classical Black-Scholes model, the Merton jump-diffusion model, the Heston SV model, and the Bates SV model with jumps

Preconditioned iterative methods on sparse subspaces

AbstractWhen some rows of the system matrix and a preconditioner coincide, preconditioned iterations can be reduced to a sparse subspace. Taking advantage of this property can lead to considerable memory and computational savings. This is particularly useful with the GMRES method. We consider the iterative solution of a discretized partial differential equation on this sparse subspace. With a domain decomposition method and a fictitious domain method the subspace corresponds a small neighborhood of an interface. As numerical examples we solve the Helmholtz equation using a fictitious domain method and an elliptic equation with a jump in the diffusion coefficient using a separable preconditioner

Using Galvanic Vestibular Stimulation to Sense Abstract Data

We propose using galvanic vestibular stimulation for presenting abstract data, for instance stock market trends. Using galvanic vestibular stimulation, data is felt directly as a perturbation in the sense of balance. This work is showcased as an art performance, where stock market fluctuations cause a person to maintain or lose balance. We present the artistic and technical principles underlying the performance and describe the technical implementation of a working system. The work shows how abstract data can be presented in a way that is not limited to visual, auditory, olfactory, or tactile sensing.Peer reviewe

Asuinhuoneistojen sähköiseen hallintaan ja vaihdantaan siirtymisen taloudelliset ja muut yhteiskunnalliset vaikutukset

Hallitusohjelman Digitalisoidaan julkiset palvelut -kärkihankkeen yhtenä toimenpiteenä on Sähköinen asunto-osakerekisteri -hanke (ASREK). ASREK vauhdittaa melko perinteisenä pidettyä kiinteistöalan yleistä digitalisoitumiskehitystä ja luo edellytyksiä yrityksille digitalisoida omia prosessejaan ja palveluitaan. ASREK:in avulla voidaan saavuttaa myös merkittäviä taloudellisia hyötyjä. Syksyllä 2017 tehdyn vaikutusarvioinnin mukaan kokonaishyöty isännöitsijöille, kiinteistönvälittäjille, pankeille, rakennuttajille ja asunto-osakkeiden omistajille on 37,5-44,5M euroa. Taloudelliset hyödyt isännöitsijöille liittyvät mm. isännöitsijätodistuksiin sekä saantojen- ja omistajavaihdosten kirjaamiseen. Hyödyt kiinteistönvälittäjille liittyvät mm. kaupan kohteen ja omistuksen varmistamiseen, arvonmääritykseen, myyntitoimeksiannon toteutukseen ja itse kaupantekoon. Pankkien näkö-kulmasta osakekirjojen siirtelemisestä luopuminen tuo vuositasolla merkittävät säästöt. Lisäksi osakekirjojen painattamiskulut säästyvät, kun omistukset muuttuvat sähköisiksi. Asunto-omistajien näkökulmasta taloudelliset hyödyt muodostuvat ennen muuta heitä palvelevien yritysten eli isännöitsijöiden ja kiinteistönvälittäjien sekä pankkien toiminnan kautta. Lisäksi (jälki)panttauksen helpottuminen mahdollistaa asuntovarallisuuden parempaa hyödyntämistä muiden kuin asuntolainojen vakuutena. Taloudellisten hyötyjen lisäksi ASREK tuo monia erilaisia laadullisia hyötyjä liittyen mm. virheiden vähenemiseen, tiedon luotettavuuteen ja ajantasaisuutee

CHCHD10 mutations and motor neuron disease: the distribution in Finnish patients.

Peer reviewe

Effects of short-term sprint interval and moderate-intensity continuous training on liver fat content, lipoprotein profile, and substrate uptake: a randomized trial

Type 2 diabetes (T2D) and increased liver fat content (LFC) alter lipoprotein profile and composition and impair liver substrate uptake. Exercise training mitigates T2D and reduces LFC, but the benefits of different training intensities in terms of lipoprotein classes and liver substrate uptake are unclear. The aim of this study was to evaluate the effects of moderate-intensity continuous training (MICT) or sprint interval training (SIT) on LFC, liver substrate uptake, and lipoprotein profile in subjects with normoglycemia or prediabetes/T2D. We randomized 54 subjects (normoglycemic group, n = 28; group with prediabetes/T2D, n = 26; age = 40-55 yr) to perform either MICT or SIT for 2 wk and measured LFC with magnetic resonance spectroscopy, lipoprotein composition with NMR, and liver glucose uptake (GU) and fatty acid uptake (FAU) using PET. At baseline, the group with prediabetes/T2D had higher LFC, impaired lipoprotein profile, and lower whole body insulin sensitivity and aerobic capacity compared with the normoglycemic group. Both training modes improved aerobic capacity (P 5.6%; low LFC, NEW & NOTEWORTHY: In the short term, both sprint interval training and moderate-intensity continuous training (MICT) reduce liver fat content and improve lipoprotein profile; however, MICT seems to be preferable in improving liver insulin sensitivity.</div