Institute of Information Theory and Automation

Publication details

No-Arbitrage Condition of Option Implied Volatility and Bandwidth Selection

Journal Article

Kopa Miloš, Tichý T.

serial: The Anthropologist: international journal of contemporary and applied studies of man vol.17, 3 (2014), p. 751-755

project(s): GA13-25911S, GA ČR

keywords: Option Pricing, Implied Volatility, DAX Index, Local polynomial smoothing

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abstract (eng):

A standard approach to option pricing is based on Black-Scholes type (BS hereafter) models utilizing the no-arbitrage argument of complete markets. However, there are several crucial assumptions, such as that the option underlying log-returns follow normal distribution, there is unique and deterministic riskless rate as well as the volatility of underlying log-returns. Since the assumptions are generally not fulfilled, the BS-type models mostly provide false results. A common market practice is therefore to invert option pricing model and using market prices of highly liquid options to get a so called implied volatility (IV). The BS model at one time moment can be related to the whole set of IVs as given by maturity/moneyness relation of tradable options. One can therefore get IV curve or surface (a so called smirk or smile). Since the moneyness and maturity of IV often do not match the data of valuated options, some sort of estimating and local smoothing is necessary.


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Institute of Information Theory and Automation