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Publications (10 of 17) Show all publications
Malyarenko, A., Ni, Y., Canhanga, B. & Silvestrov, S. (2018). Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities. In: Christos H Skiadas (Ed.), Proceedings : 5th Stochastic Modeling Techniques and Data Analysis International Conference withDemographics Workshop (SMTDA2018): . Paper presented at 12 -15 June 2018, Cultural Centre of Chania, Crete, Greece (pp. 409-422). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Advanced Monte Carlo pricing of European options in a market model with two stochastic volatilities
2018 (English)In: Proceedings : 5th Stochastic Modeling Techniques and Data Analysis International Conference withDemographics Workshop (SMTDA2018) / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology, 2018, p. 409-422Conference paper, Published paper (Refereed)
Abstract [en]

We consider a market model with four correlated factors and two stochastic volatilities, one of which is rapid-changing, while another one is slow-changing in time. An advanced Monte Carlo methods based on the theory of cubature in Wiener space, is used to find the no-arbitrage price of the European call option in the above model.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology: , 2018
National Category
Mathematics Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-43299 (URN)
Conference
12 -15 June 2018, Cultural Centre of Chania, Crete, Greece
Available from: 2019-05-02 Created: 2019-05-02 Last updated: 2019-10-12Bibliographically approved
Betuel, C., Malyarenko, A., Ni, Y., Rancic, M. & Silvestrov, S. (2018). Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach. In: Christos H Skiadas (Ed.), : . Paper presented at SMTDA2018 5th Stochastic Modeling Techniques and Data Analysis International Conference - SMTDA 2018, Crete, Greece. ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Calibration of Multiscale Two-Factor Stochastic Volatility Models: A Second-Order Asymptotic Expansion Approach
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2018 (English)In: / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2018Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

The development of financial markets imposes more complex models on the option pricing problems. On the previous papers by the authors, we consider a model under which the underlying asset is driven by two independent Heston-type stochastic volatility processes of multiscale (fast and slow) mean-reverting rates and we compute an approximate solution for the option pricing problem, using asymptotic expansion method. In the present paper, we aim to calibrate the model using the market prices of options on Euro Stoxx 50 index and an equity stock in the European market. Our approach is to use the market implied volatility surface for calibrating directly a set of new parameters required in our second-order asymptotic expansion pricing formula for European options. This secondorder asymptotic expansion formula provides a better approximation formula for European option prices than the first-order formula, as explained in an earlier work of the authors.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2018
Keywords
Option pricing model, asymptotic expansion of option price, stochastic volatility model, multiscale stochastic volatility, calibration
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41091 (URN)978-618-5180-27-0 (ISBN)978-618-5180-29-4 (ISBN)
Conference
SMTDA2018 5th Stochastic Modeling Techniques and Data Analysis International Conference - SMTDA 2018, Crete, Greece
Available from: 2018-09-30 Created: 2018-09-30 Last updated: 2018-10-01Bibliographically approved
Lundengård, K., Ogutu, C., Silvestrov, S., Ni, Y. & Weke, P. (2017). Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases. In: Sivasundaram, S (Ed.), AIP Conference Proceedings: . Paper presented at 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016 (pp. 020094-1-020094-7). American Institute of Physics (AIP), 1798, Article ID 020094.
Open this publication in new window or tab >>Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases
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2017 (English)In: AIP Conference Proceedings / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020094-1-020094-7, article id 020094Conference paper, Published paper (Refereed)
Abstract [en]

In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process. 

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2017
National Category
Mathematics Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-35007 (URN)10.1063/1.4972686 (DOI)000399203000094 ()2-s2.0-85013643900 (Scopus ID)9780735414648 (ISBN)
Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2017-03-09 Created: 2017-03-09 Last updated: 2017-09-01Bibliographically approved
Canhanga, B., Malyarenko, A., Murara, J.-P., Ni, Y. & Silvestrov, S. (2017). Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility. Paper presented at 15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Univ Piraeus, Piraeus, GREECE, JUN 30-JUL 04, 2015. Methodology and Computing in Applied Probability, 19(4), 1075-1087
Open this publication in new window or tab >>Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility
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2017 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, no 4, p. 1075-1087Article in journal (Refereed) Published
Abstract [en]

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. Manag Sci 55(2):1914–1932 (2009) presented a model where the underlying price is governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American option prices. In a previous research of the authors (Canhanga et al. 2014), a particular case of Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013) model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi Appl Math Comput 224:283–310 (2013).

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Financial market, Mean reversion volatility, Asymptotic expansion,  Stochastic volatilities, Regular perturbation, Singular perturbation, European option
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-36594 (URN)10.1007/s11009-017-9553-8 (DOI)000413792200005 ()2-s2.0-85016098160 (Scopus ID)
Conference
15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Univ Piraeus, Piraeus, GREECE, JUN 30-JUL 04, 2015
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2017-10-01 Created: 2017-10-01 Last updated: 2018-01-23Bibliographically approved
Malyarenko, A., Canhanga, B., Ni, Y., Silvestrov, S. & Rancic, M. (2017). Option pricing and model calibration under multifactor stochastic volatility and stochastic interest rate - an asymptotic expansion approach. In: Skiadas, Christos H. (Ed.), Proceedings ASMDA2017: . Paper presented at 17th Applied Stochastic Models and Data Analysis International Conference with Demographics Workshop (pp. 219-231). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Option pricing and model calibration under multifactor stochastic volatility and stochastic interest rate - an asymptotic expansion approach
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2017 (English)In: Proceedings ASMDA2017 / [ed] Skiadas, Christos H., ISAST: International Society for the Advancement of Science and Technology , 2017, p. 219-231-Conference paper, Published paper (Refereed)
Abstract [en]

Among other limitations, the celebrated Black--Scholes option pricingmodel assumes constant volatility and constant interest rates, which is not supportedby empirical studies on for example implied volatility surfaces. Studiesby many researchers such as Heston in 1993, Christoffersen in 2009, Fouque in2012, Chiarella--Ziveyi in 2013, and the authors' previous work removed the constantvolatility assumption from the Black--Scholes model by introducing one ortwo stochastic volatility factors with constant interest rate. In the present paperwe follow this line but generalize the model by considering also stochasticinterest rate. More specifically, the underlying asset process is governed by amean-reverting interest rate process in addition to two mean-reverting stochasticvolatility processes of fast and slow mean-reverting rates respectively. The focusis to derive an approximating formula for pricing the European option using adouble asymptotic expansion method.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2017
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-45223 (URN)
Conference
17th Applied Stochastic Models and Data Analysis International Conference with Demographics Workshop
Available from: 2019-09-16 Created: 2019-09-16 Last updated: 2019-09-24Bibliographically approved
Ni, Y., Engström, C., Malyarenko, A. & Wallin, F. (2015). Building-type classification based on measurements of energy consumption data. In: Raimondo Manca, Sally McClean, Christos H SkiadasISAST 2015 (Ed.), H. Skiadas (Ed) (Ed.), New Trends in Stochastic Modeling and Data Analysis: . Paper presented at 3rd Stochastic Modelling Techniques and Data Analysis International Conference (SMTDA 2014), 11-14 June 2014, Lisbon, Portugal (pp. 287-298). Paper presented at 3rd Stochastic Modelling Techniques and Data Analysis International Conference (SMTDA 2014), 11-14 June 2014, Lisbon, Portugal. ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Building-type classification based on measurements of energy consumption data
2015 (English)In: New Trends in Stochastic Modeling and Data Analysis / [ed] Raimondo Manca, Sally McClean, Christos H SkiadasISAST 2015, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 287-298Chapter in book (Refereed)
Abstract [en]

In this paper we apply data-mining techniques to a classication problemon actual electricity consumption data from 350 Swedish households. Morespecically we use measurements of hourly electricity consumption during one monthand t classication models to the given data. The goal is to classify and later predict whether the building type of a specic household is an apartmentor a detached house. This classication/prediction problem becomes important ifone has a consumption time series for a household with unknown building type. Tocharacterise each household, we compute from the data some selected statistical attributesand also the load prole throughout the day for that household. The most important task here is to select a good representative set of feature variables, whichis solved by ranking the variable importance using technique of random forest. Wethen classify the data using classication tree method and linear discriminant analysis.The predictive power of the chosen classication models is plausible.

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2015
Keywords
data-mining, energy consumption data, classication of energy customers, clustering of energy customers
National Category
Mathematics Building Technologies
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-26110 (URN)978-618-5180-10-2 (ISBN)978-618-5180-06-5 (ISBN)
Conference
3rd Stochastic Modelling Techniques and Data Analysis International Conference (SMTDA 2014), 11-14 June 2014, Lisbon, Portugal
Available from: 2014-10-24 Created: 2014-10-15 Last updated: 2019-04-12
Canhanga, B., Malyarenko, A., Murara, J.-P., Ni, Y. & Silvestrov, S. (2015). Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility. In: Christos H Skiadas (Ed.), ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop. Paper presented at 16th Applied Stochastic Models and Data Analysis International Conference (ASMDA2015) with Demographics 2015 Workshop, 30 June – 4 July 2015, University of Piraeus, Greece (pp. 53-66). ISAST: International Society for the Advancement of Science and Technology
Open this publication in new window or tab >>Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility
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2015 (English)In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 53-66Conference paper, Published paper (Refereed)
Abstract [en]

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such model can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. [3] presented a model where the underlying priceis governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi [2] transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American options prices. In a previous research of the authors (Canhanga et al. [1]), a particular case of Chiarella and Ziveyi [2] model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi [2].

1. Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. Perturbation methods for pricing European options in a model with two stochastic volatilities. 3rd SMTDA Conference Proceedings. 11-14 June 2014, Lisbon Porturgal, C. H. Skiadas (Ed.) 489-500 (2014).

2. Chiarella, C, and Ziveyi, J. American option pricing under two stochastic volatility processes. J. Appl. Math. Comput. 224:283–310 (2013).

3. Christoffersen, P.; Heston, S.; Jacobs, K. The shape and term structure of the index option smirk: why multifactor stochastic volatility models work so well. Manage. Sci. 55 (2) 1914-1932; (2009).

Place, publisher, year, edition, pages
ISAST: International Society for the Advancement of Science and Technology, 2015
Keywords
financial market, mean reversion volatility, asymptotic expansion, stochastic volatilities, regular perturbation, singular perturbation, European option.
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-29936 (URN)978-618-5180-05-8 (ISBN)
Conference
16th Applied Stochastic Models and Data Analysis International Conference (ASMDA2015) with Demographics 2015 Workshop, 30 June – 4 July 2015, University of Piraeus, Greece
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2015-12-15 Created: 2015-12-15 Last updated: 2016-10-28Bibliographically approved
Ni, Y. (2014). Exponential asymptotical expansions for ruin probability in a classical risk process with non-polynomial perturbations. In: Silvestrov, D., Martin-Löf, A. (eds) (Ed.), Modern Problems in Insurance Mathematics: (pp. 69-94). Springer
Open this publication in new window or tab >>Exponential asymptotical expansions for ruin probability in a classical risk process with non-polynomial perturbations
2014 (English)In: Modern Problems in Insurance Mathematics / [ed] Silvestrov, D., Martin-Löf, A. (eds), Springer, 2014, p. 69-94Chapter in book (Refereed)
Abstract [en]

In this paper we investigate the asymptotical behaviour of ruin probability in a classical compound Poisson risk process associated with perturbations in the claim size distributions and/or other parameters of the risk process. The novelty of this study is that we consider non-polynomial perturbations which include the polynomial perturbations as particular cases. The aim of the study is to develop exponential asymptotical expansions for the ruin probability as the initial capital goesto infinity and the perturbation parameter goes to zero, simultaneously but in a balanced manner. Numerical examples of risk processes with such type of perturbations are also given for illustrative purposes.

Place, publisher, year, edition, pages
Springer, 2014
Series
EAA Series, ISSN 1869-6929
Keywords
Ruin probability, perturbed risk process, perturbed renewal equation, non-linear perturbation, non-polynomial perturbation
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-23044 (URN)10.1007/978-3-319-06653-0_6 (DOI)978-3-319-06652-3 (ISBN)978-3-319-06653-0 (ISBN)
Available from: 2013-11-30 Created: 2013-11-30 Last updated: 2019-05-10
Ni, Y., Engström, C., Malyarenko, A. & Wallin, F. (2014). Investigating the added values of high frequency energy consumption data using data mining techniques. In: Seenith Sivasundaram (Ed.), AIP Conference Proceedings 1637 (2014): Volume number: 1637; Published: 10 december 2014. Paper presented at 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway (pp. 734-743). AIP Publishing
Open this publication in new window or tab >>Investigating the added values of high frequency energy consumption data using data mining techniques
2014 (English)In: AIP Conference Proceedings 1637 (2014): Volume number: 1637; Published: 10 december 2014 / [ed] Seenith Sivasundaram, AIP Publishing , 2014, p. 734-743Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we apply data-mining techniques to customer classification and clustering tasks on actual electricity consumption data from 350 Swedish households. For the classification task we classify households into different categories based on some statistical attributes of their energy consumption measurements. For the clustering task, we use average daily load diagrams to partition electricity-consuming households into distinct groups. The data contains electricity consumption measurements on each 10-minute time interval for each light source and electrical appliance. We perform the classification and clustering tasks using four variants of processeddata sets corresponding to the 10-minute total electricity consumption aggregated from all electrical sources, the hourly total consumption aggregated over all 10-minute intervals during that clock hour, the total consumption over each four-hour intervals and finally the daily total consumption. The goal is to see if there are any differences in using data sets of various frequency levels. We present the comparison results and investigate the added value of the high-frequency measurements, for example 10-minute measurements, in terms of its influence on customer clustering and classification.

Place, publisher, year, edition, pages
AIP Publishing, 2014
National Category
Computational Mathematics Computer and Information Sciences
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-26917 (URN)10.1063/1.4904645 (DOI)000347812200088 ()2-s2.0-85031862344 (Scopus ID)978-0-7354-1276-7 (ISBN)
Conference
10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway
Available from: 2014-12-15 Created: 2014-12-15 Last updated: 2019-01-16Bibliographically approved
Ni, Y. (2012). NONLINEARLY PERTURBED RENEWAL EQUATIONS: THE NON-POLYNOMIAL CASE. Theory of Probability and Mathematical Statistics, 84, 117-129
Open this publication in new window or tab >>NONLINEARLY PERTURBED RENEWAL EQUATIONS: THE NON-POLYNOMIAL CASE
2012 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 84, p. 117-129Article in journal (Refereed) Published
Abstract [en]

Models of nonlinearly perturbed renewal equations with non-polynomial perturbations are studied. Exponential asymptotic expansions are given for the solutions to the perturbed renewal equations under consideration. An application to perturbed M/G/1/ queues is presented.

Place, publisher, year, edition, pages
Kiev, Ukraine: Kiev University (English translation by American Mathematical Society), 2012
Keywords
Perturbed renewal equation, non-polynomial perturbation
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-12913 (URN)10.1090/S0094-9000-2012-00865-X (DOI)2-s2.0-84865087490 (Scopus ID)
Available from: 2011-08-25 Created: 2011-08-25 Last updated: 2015-06-29Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-0835-7536

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