The Classical and Stochastic Approach to Option Pricing

D 2014

The Classical and Stochastic Approach to Option Pricing

BENADA, Luděk a Martin CUPAL

Základní údaje

Originální název

The Classical and Stochastic Approach to Option Pricing

Autoři

BENADA, Luděk a Martin CUPAL

Vydání

Brno, Proceedings of the 11th International Scientific Conference European Financial Systems 2014, od s. 49-55, 7 s. 2014

Nakladatel

Masaryk University

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

50200 5.2 Economics and Business

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14560/14:00077219

Organizační jednotka

Ekonomicko-správní fakulta

ISBN

978-80-210-7153-7

UT WoS

000350701500006

Klíčová slova anglicky

option pricing; lattices; Black-Scholes model; volatility; Geometric Brownian motion

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 2. 4. 2015 15:28, Mgr. Daniela Marcollová

Anotace

V originále

Black-Scholes model (BS) and lattices are well-known methodologies applied to option pricing, with their own specific features and properties. Briefly, lattices are discrete in the inner computing process and stochastically based, while BS is represented by a continuous functional form without single steps, but deterministic only. The strong assumption of constant volatility and the inability of application in valuing “American” options represent major disadvantages of the BS model. Its main advantage is its simplicity and ease of application. The use of Monte Carlo simulations constitutes an alternative to this model. Its main advantages include a relatively easy procedure of calculation and efficiency. Problems can arise when applied to the “American” option. Likewise, this method does not belong among highly sophisticated ones due to the requirements of prerequisites. If we were to consider a model that can work with the “American“ option, i.e. an option that may be exercised at any time before maturity, then calculation using the lattice approach is conceivable. In contrast, the disadvantage of this method lies in the lack of ability to apply continuous consistency with price development history as well as inability to work with a model that would require more underlying assets. Finally, the two approaches, Black-Scholes model and the lattice approach, considered for pricing options, derived their value from IBM stocks as an underlying asset. On individual valuations, accuracy of these valuation models will be observed in accordance with the real option price.

Návaznosti

MUNI/A/0786/2013, interní kód MU

Název: Analýza a predikce vývoje cen finančních a investičních nástrojů

Investor: Masarykova univerzita, Analýza a predikce vývoje cen finančních a investičních nástrojů, DO R. 2020_Kategorie A - Specifický výzkum - Studentské výzkumné projekty

Citovat

BENADA, Luděk a Martin CUPAL. The Classical and Stochastic Approach to Option Pricing. In Deev, O., Kajurová, V., Krajíček, J. Proceedings of the 11th International Scientific Conference European Financial Systems 2014. Brno: Masaryk University, 2014, s. 49-55. ISBN 978-80-210-7153-7.

@inproceedings{1205457,
   author = {Benada, Luděk and Cupal, Martin},
   address = {Brno},
   booktitle = {Proceedings of the 11th International Scientific Conference European Financial Systems 2014},
   editor = {Deev, O., Kajurová, V., Krajíček, J.},
   keywords = {option pricing; lattices; Black-Scholes model; volatility; Geometric Brownian motion},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Brno},
   isbn = {978-80-210-7153-7},
   pages = {49-55},
   publisher = {Masaryk University},
   title = {The Classical and Stochastic Approach to Option Pricing},
   year = {2014}
}

TY  - CONF
ID  - 1205457
AU  - Benada, Luděk - Cupal, Martin
PY  - 2014
TI  - The Classical and Stochastic Approach to Option Pricing
PB  - Masaryk University
CY  - Brno
SN  - 9788021071537
KW  - option pricing
KW  - lattices
KW  - Black-Scholes model
KW  - volatility
KW  - Geometric Brownian motion
N2  - Black-Scholes model (BS) and lattices are well-known methodologies applied to option pricing, with their own specific features and properties. Briefly, lattices are discrete in the inner computing process and stochastically based, while BS is represented by a continuous functional form without single steps, but deterministic only. The strong assumption of constant volatility and the inability of application in valuing “American” options represent major disadvantages of the BS model. Its main advantage is its simplicity and ease of application. The use of Monte Carlo simulations constitutes an alternative to this model. Its main advantages include a relatively easy procedure of calculation and efficiency. Problems can arise when applied to the “American” option. Likewise, this method does not belong among highly sophisticated ones due to the requirements of prerequisites. If we were to consider a model that can work with the “American“ option, i.e. an option that may be exercised at any time before maturity, then calculation using the lattice approach is conceivable. In contrast, the disadvantage of this method lies in the lack of ability to apply continuous consistency with price development history as well as inability to work with a model that would require more underlying assets. Finally, the two approaches, Black-Scholes model and the lattice approach, considered for pricing options, derived their value from IBM stocks as an underlying asset. On individual valuations, accuracy of these valuation models will be observed in accordance with the real option price.
ER  -

BENADA, Luděk a Martin CUPAL. The Classical and Stochastic Approach to Option Pricing. In Deev, O., Kajurová, V., Krajíček, J. \textit{Proceedings of the 11th International Scientific Conference European Financial Systems 2014}. Brno: Masaryk University, 2014, s.~49-55. ISBN~978-80-210-7153-7.

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