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1

The Concept of Black and Scholes Model and the Analysis of WIG20 Implied Volatility

100%
Koronkiewicz G.
Optimum. Studia Ekonomiczne
|
2012
|
issue 5(59)
30-47
EN
The purpose of this article is to present the concept of Black and Scholes option pric-ing formula, with special emphasis on the three key economic and mathematical ideas that made it possible to develop the framework. An additional aim is to conduct an analysis of the WIG20 index implied volatility in order to determine whether the polish financial options market functions accordingly to the assumptions of Black and Scholes model or rather in a way that has been observed on a bigger, more liquid derivatives market. The article describes the classical way of deriving the Black and Scholes partial differential equation and presents some possible applications of the Black Scholes model outside of straightforward option pricing. In the empirical part of the article, an estimation of WIG20 index implied volatility for a three - year period ranging from 2009 to 2011 is conducted based on the daily quotes of options, futures and the index itself. The results suggest that WIG20 implied volatility follows patterns observed on other markets, what indicates that the assumptions of the model are not fully met on the Warsaw Stock Exchange.
2

BAYESIAN ANALYSIS OF EUROPEAN CALL OPTION AND DELTA-NEUTRAL HEDGE USING GARCH AND CSV PROCESSES

100%
Pipien M., Pajor A.
Przegląd Statystyczny
|
2005
|
vol. 52
|
issue 3
37-63
EN
The main goal of this article was to present an application of GARCH (Generalised Auto Regressive Conditionally Heteroscedastic) and CSV (Correlated Stochastic Volatility) processes in modelling the volatility of the daily returns of PLN/USD exchange rate and pricing the European call option for this exchange rate. The authors offer the Bayesian interpretation of commonly used methods of volatility assessment as well as predictive consequences of different volatility models. They also consider Bayesian estimation of the delta coefficient for the European call option. From the Bayesian point of view posterior distribution of delta enables to predict the cost of so called delta-neutral hedging strategy. They show the predictive distributions of the cost of this strategy as well as the cost of its managing.
3

ASSESSMENT OF MODEL RISK IN FINANCIAL MARKETS

100%
Jajuga K.
Optimum. Studia Ekonomiczne
|
2010
|
issue 4 (48)
35-43
EN
The paper presents the problem of assessment of risk in financial models. This is important from practical point of view since inappropriate use of models in financial markets may cause large losses. The paper describes the sources of model risk and the methods of measuring and handling this risk. Two types of measures are proposed: distribution based measures and sensitivity measures. The remaining part of the paper contains two examples. The first one concerns risk of optimal two-stock selection related to estimation of the correlation coefficient, the second one concerns the risk of option pricing related to estimation of the volatility parameter.
4

Target-zone rearrangement and exchange-rate behaviour in an options-based model

88%
Naszodi A.
Kozgazdasagi Szemle (Economic Review)
|
2004
|
vol. 51
|
issue 7/8
638-658
EN
This paper sets up an options-based model of the exchange rate in a target-zone system, according to which the observed exchange rate is equivalent to a floating exchange rate adjusted to the value of two options. The strike prices of the options are the limits of the band, but the two options are interrelated, which complicates valuation of them. Within that framework, the direct effect of the band rearrangement on the exchange rate can be measured by the change of the option prices caused by the change of the strike prices. The author applies this options-based model to analyse depreciation of the forint in the summer of 2003. Depreciation is decomposed into (a) the direct effect of the band shift; (b) changing expectations relating to the final conversation rate in the EMU, and (c) changing uncertainty.
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