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The arbitrage inconsistencies of implied volatility extraction in connection to calendar bandwidth
Vitali, Sebastiano ; Tichý, Tomáš ; Kopa, Miloš
Options are often priced by Black and Scholes model by using artificial (and unobserved) volatility implied by option market prices. Since many options do not have their traded counterparts with the same maturity and moneyness, it is often needed to interpolate the volatility values. The general procedure of implied volatility extraction from market prices and subsequent smoothing can, however, lead to inconsistent values or even arbitrage opportunities. In this paper, a potential arbitrage area is studied in connection with the calendar bandwidth construction.
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Estimation of risk-neutral probability density functions from option prices
Krejčí, Kateřina ; Málek, Jiří (advisor) ; Diviš, Martin (referee)
The thesis deals with the estimation of risk-neutral probability density functions from option prices. It focuses on smoothing techniques that are applied to volatility smile. Theoretical part describes the estimation principle and presents some solutions for problems that occur while estimating the risk-neutral distribution. The findings from the theoretical part are used in the practical part and applied to real data. An analysis of the influence of the selection of particular smoothing function on the final distribution is performed. At the end of the thesis a stability test of estimations is performed and the analysis of dynamics of risk neutral distribution is shown on a small data sample.
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Implied volatility and higher risk neutral moments: predictive ability
Hanzal, Martin ; Černý, Michal (advisor) ; Málek, Jiří (referee)
Implied volatility obtained from market option prices is widely regarded as an efficient predictor of future realised volatility. Implied volatility can be thought of as market's expectation of future realised volatility. We distinguish between volatility-changing events with respect to expectations - scheduled events (such as information releases) and unscheduled events. We propose a method of testing the information content of option-implied risk-neutral moments prior to volatility-changing events. Using the method introduced by Bakshi, Kapadia & Madan (2003) we extract implied volatility, skewness and kurtosis from S&P 500 options market prices and apply the proposed method in four case studies. Two are concerned with scheduled events - United Kingdom European Union membership referendum, 2016 and United States presidential election, 2016, two are concerned with unscheduled events - flash crash of August 24, 2015 and flash crash of October 15, 2014. Implied volatility indicates a rise in future realised volatility prior to both scheduled events. We find a significant rise in implied kurtosis during the last three days prior to the presidential election of 2016. Prior to unscheduled events, we find no evidence of implied moments indicating a rise in future realised volatility.
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Implied volatility modelling of options
Jahn, Daniel ; Kopa, Miloš (advisor) ; Hendrych, Radek (referee)
This text presents an analysis of constrained local polynomial estimation used to extract the implied volatility smile from options data. The optimization constraint derived from the state price density ensures the no arbitrage condition. The analysis contains an evaluation of the role of different parameters, such as the degree of the polynomial, kernel type and bandwidth, on the resulting IV smile. Two main approaches are suggested, one attempting to reflect the problematic case of the out-of-the- money options, the other focusing on producing a smooth state price density and a well-fitting IV smile. Powered by TCPDF (www.tcpdf.org)
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The Bandwidth Selection in Connection to Option Implied Volatility Extraction
Tichý, T. ; Kopa, Miloš ; Vitali, S.
Among various kinds of options we can found at the market, some are traded at organized exchanges and therefore are quite liquid, while others are traded only between particular parties. Whereas there is no need to look for a model to price liquid exchange traded options, since their price is generally accepted by the demand and supply, for illiquid or even exotic options new efficient models are still developed. The current market practice is to obtain the implied volatility of liquid options as based on Black-Scholes type (BS hereafter) models. The focus of this paper is to study the behavior of IV and SPD for several kernel functions and with respect to different choices of bandwidth parameter h. Specifically, we show several interesting implications of the change of h on the violation of no arbitrage condition and the total area of SPD under zero.
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Option strategies and currency options pricing
Coufalík, Jan ; Sedláček, Jiří (advisor) ; Brázdil, Jiří (referee)
The aim of this diploma thesis is to analyze and implement selected option pricing models using statistical software. The first chapter introduces theoretical basics of options as financial instruments ideal for hedging and speculation. The second chapter constitutes the core part of this thesis since it unveils theoretical concepts of risk-neutral pricing and at the same time analyze some basic, as well as highly sophisticated option pricing models. In addition, each model is accompanied by a practical example of their effective implementation. The final chapter characterize the most widely used option trading strategies and defines the ideal expected market development linked to each strategy.
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Option strategies
Foukal, Viktor ; Witzany, Jiří (advisor) ; Baran, Jaroslav (referee)
The main objective of this thesis is to acquaint the reader with the main types of option strategies, with the principles of functioning, with the methods of creating and analyzing these strategies. The practical part focus on valuation of tested option strategies, determination of the conditions for entry into strategies, prediction of future development of index S&P 500 by Monte Carlo simulation and finding relation between implied volatility of options and underlying asset itself.
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Price of Volatility of Financials Assets
Gříšek, Lukáš ; Černý, Michal (advisor) ; Chrobok, Viktor (referee)
This diploma thesis describes problem of change-points in volatility of the time-series and their impact on price of nancial assets. Those change-points are estimated by using statistical methods and tests. Change-point estimation was tested on simulated datas and real world driven datas. Simulation helped to discover signi cant characteristics of change-point test, those data were simulated with using stochastic calculus. Google share prices and prices of call options were chosen to analyse impact of volatility change on those prices. Also implied volatility and its impact to call option price was analysed.
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