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  • 1.
    Canhanga, Betuel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Malyarenko, Anatoliy
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Murara, Jean-Paul
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ni, Ying
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Numerical Studies on Asymptotics of European Option under Multiscale Stochastic Volatility2015Ingår i: 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, s. 53-66Konferensbidrag (Refereegranskat)
    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).

  • 2.
    Canhanga, Betuel
    et al.
    DMI, Eduardo Mondlane University, Maputo, Mozambique.
    Malyarenko, Anatoliy
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Murara, Jean-Paul
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Ni, Ying
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Numerical Studies on Asymptotics of European Option Under Multiscale Stochastic Volatility2017Ingår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, nr 4, s. 1075-1087Artikel i tidskrift (Refereegranskat)
    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).

  • 3.
    Canhanga, Betuel
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Malyarenko, Anatoliy
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Murara, Jean-Paul
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Pricing European Options Under Stochastic Volatilities Models2016Ingår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 315-338Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Interested by the volatility behavior, different models have been developed for option pricing. Starting from constant volatility model which did not succeed on capturing the effects of volatility smiles and skews; stochastic volatility models appearas a response to the weakness of the constant volatility models. Constant elasticity of volatility, Heston, Hull and White, Schöbel-Zhu, Schöbel-Zhu-Hull-Whiteand many others are examples of models where the volatility is itself a random process. Along the chapter we deal with this class of models and we present the techniques of pricing European options. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. Christoffersen et al. in [4] proposed a model with two-factor stochastic volatilities where the correlation between the underlying asset price and the volatilities varies randomly. In the last section of this chapter we introduce a variation of Chiarella and Ziveyi model, which is a subclass of the model presented in [4] and we use the first order asymptotic expansion methods to determine the price of European options.

  • 4.
    Murara, Jean-Paul
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Asset Pricing Models with Stochastic Volatility2016Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Asset pricing modeling is a wide range area of research in Financial Engineering. In this thesis, which consists of an introduction, three papers and appendices; we deal with asset pricing models with stochastic volatility. Here stochastic volatility modeling includes diffusion models and regime-switching models. Stochastic volatility models appear as a response to the weakness of the constant volatility models. In Paper A , we present a survey on popular diffusion models where the volatility is itself a random process and we present the techniques of pricing European options under each model. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. We consider Chiarella and Ziveyi model, which is a subclass of the model presented in Christoffersen and in paper A, we also explain a multi-factor stochastic volatility model presented in Chiarella and Ziveyi. We review the first-order asymptotic expansion method for determining European option price in such model. Multiscale stochastic volatilities models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. In paper B, we provide 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. In paper C, we implement and analyze the Regime-Switching GARCH model using real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justified by the so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price di_erence criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coe_cient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model.

  • 5.
    Murara, Jean-Paul
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Market Models with Stochastic Volatility2019Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Financial Markets is an interesting wide range area of research in Financial Engineering. In this thesis, which consists of an introduction, six papers and appendices, we deal with market models with stochastic volatility in order to understand some financial derivatives, mainly European options. Stochastic volatility models appear as a response to the weakness of the constant volatility models. Paper A is presented as a survey of different models where the volatility is itself a stochastic process and we present the techniques of pricing European options. Comparing single factor stochastic volatility models to constant factor volatility models, it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large fluctuations in the volatility levels and slope. We propose also a new model which is a variation of the Chiarella and Ziveyi model and we use the first order asymptotic expansion methods to determine the price of European options. Multiscale stochastic volatility models can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. In paper B , we present an asymptotic expansion for the option price. We provide 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 are compared to the approximation obtained by Chiarella and Ziveyi. In paper C , we implement and analyze the Regime-Switching GARCH model using real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justified by the so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price difference criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coefficient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model. In paper D , we consider a market model with four correlated factors and two stochastic volatilities which is the same model as the one introduced in paper A and used in paper B . An advanced Monte Carlo method is used to find the no-arbitrage price of the European call option in the considered model. In paper E , we forecast the stochastic volatility for exchange rates using Exponential Weighted Moving Average (EWMA) model and study the effect of the out-of-sample periods and also the effect of the decay factor on the forecasts. In Paper F , considering a two-dimensional Black-Scholes equation, we compare the performances between the Crank-Nicolson scheme and the lognormality condition when pricing the European options. We do this by studying the effects of different parameters.

  • 6.
    Murara, Jean-Paul
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Malyarenko, Anatoliy
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Modelling electricity price series using regime-switching GARCH model2015Ingår i: 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, s. 713-725Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper implements and analyzes the Regime-Switching GARCH modelusing real NordPool Electricity spot data. We allow the model parameters to switch between a regular regime and a non-regular regime, which is justied by a so-called structural break behaviour of electricity price series. In splitting the two regimes we consider three criteria, namely the intercountry price difference criterion, the capacity/flow difference criterion and the spikes-in-Finland criterion. We study the correlation relationships among these criteria using the mean-square contingency coefficient and the co-occurrence measure. We also estimate our model parameters and present empirical validity of the model.

1 - 6 av 6
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