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Statements

Subject Item
n2:RIV%2F61989100%3A27510%2F13%3A86086865%21RIV14-GA0-27510___
rdf:type
n11:Vysledek skos:Concept
dcterms:description
During last decades the stochastic simulation approach, both via MC and QMC has been vastly applied and subsequently analyzed in almost all branches of science. Very nice applications can be found in areas that rely on modeling via stochastic processes, such as finance. However, since financial quantities as opposed to natural processes depend on human activity, their modeling is often very challenging. Many scholars therefor suggest to specify some parts of financial models by means of fuzzy set theory. Many financial problems, such as pricing and hedging of specific financial derivatives, are too complex to be solved analytically even in a crisp case, it can be efficient to apply (Quasi) Monte Carlo simulation. In this contribution a recent knowledge of fuzzy numbers and their approximation is utilized in order to suggest fuzzy-MC simulation to option price modeling in terms of fuzzy-random variables. In particular, we suggest three distinct fuzzy-random processes as an alternative to a standard crisp model. Application possibilities are shown on illustrative examples assuming a plain vanilla European put option under Brownian motion with fuzzy parameter (volatility), Brownian motion with fuzzy subordinator and Brownian motion with fuzzyfied subordinator. In each case the model result into a whole set of prices – thus, since we assume one of the input data as LU fuzzy number, we get the price in terms of the LU fuzzy number as well. The payoff function of analyzed put option can be obviously replaced by more complex payoff structure. During last decades the stochastic simulation approach, both via MC and QMC has been vastly applied and subsequently analyzed in almost all branches of science. Very nice applications can be found in areas that rely on modeling via stochastic processes, such as finance. However, since financial quantities as opposed to natural processes depend on human activity, their modeling is often very challenging. Many scholars therefor suggest to specify some parts of financial models by means of fuzzy set theory. Many financial problems, such as pricing and hedging of specific financial derivatives, are too complex to be solved analytically even in a crisp case, it can be efficient to apply (Quasi) Monte Carlo simulation. In this contribution a recent knowledge of fuzzy numbers and their approximation is utilized in order to suggest fuzzy-MC simulation to option price modeling in terms of fuzzy-random variables. In particular, we suggest three distinct fuzzy-random processes as an alternative to a standard crisp model. Application possibilities are shown on illustrative examples assuming a plain vanilla European put option under Brownian motion with fuzzy parameter (volatility), Brownian motion with fuzzy subordinator and Brownian motion with fuzzyfied subordinator. In each case the model result into a whole set of prices – thus, since we assume one of the input data as LU fuzzy number, we get the price in terms of the LU fuzzy number as well. The payoff function of analyzed put option can be obviously replaced by more complex payoff structure.
dcterms:title
Option pricing with simulation of fuzzy stochastic variables Option pricing with simulation of fuzzy stochastic variables
skos:prefLabel
Option pricing with simulation of fuzzy stochastic variables Option pricing with simulation of fuzzy stochastic variables
skos:notation
RIV/61989100:27510/13:86086865!RIV14-GA0-27510___
n11:predkladatel
n13:orjk%3A27510
n4:aktivita
n5:S n5:P
n4:aktivity
P(ED1.1.00/02.0070), P(EE2.3.20.0296), P(GA13-13142S), S
n4:dodaniDat
n18:2014
n4:domaciTvurceVysledku
n10:1733362 n10:3252833
n4:druhVysledku
n15:D
n4:duvernostUdaju
n20:S
n4:entitaPredkladatele
n14:predkladatel
n4:idSjednocenehoVysledku
94537
n4:idVysledku
RIV/61989100:27510/13:86086865
n4:jazykVysledku
n8:eng
n4:klicovaSlova
Random variable, fuzzy variable, option, simulation
n4:klicoveSlovo
n9:fuzzy%20variable n9:simulation n9:option n9:Random%20variable
n4:kontrolniKodProRIV
[9388CD8F4F09]
n4:mistoKonaniAkce
Sychrov
n4:mistoVydani
Liberec
n4:nazevZdroje
Liberec Economic Forum 2013 : proceedings of the 11th international conference : 16th-17th September, Sychrov, Czech Republic, EU
n4:obor
n12:AH
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
2
n4:projekt
n7:GA13-13142S n7:EE2.3.20.0296 n7:ED1.1.00%2F02.0070
n4:rokUplatneniVysledku
n18:2013
n4:tvurceVysledku
Tichý, Tomáš Holčapek, Michal
n4:typAkce
n17:WRD
n4:zahajeniAkce
2013-09-16+02:00
s:numberOfPages
8
n6:hasPublisher
Technická univerzita v Liberci
n21:isbn
978-80-7372-953-0
n19:organizacniJednotka
27510