Implied volatility and state price density estimation: arbitrage analysis

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10384550" target="_blank" >RIV/00216208:11320/17:10384550 - isvavai.cz</a>

Alternative codes found

RIV/61989100:27510/17:10236823

Result on the web

<a href="https://doi.org/10.1007/s10287-017-0283-8" target="_blank" >https://doi.org/10.1007/s10287-017-0283-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10287-017-0283-8" target="_blank" >10.1007/s10287-017-0283-8</a>

Result language

angličtina

Original language name

Implied volatility and state price density estimation: arbitrage analysis

Original language description

This paper deals with implied volatility (IV) estimation using no-arbitrage techniques. The current market practice is to obtain IV of liquid options as based on Black-Scholes (BS type hereafter) models. Such volatility is subsequently used to price illiquid or even exotic options. Therefore, it follows that the BS model can be related simultaneously to thewhole set of IVs as given by maturity/moneyness relation of tradable options. Then, it is possible to get IV curve or surface (a so called smile or smirk). 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. However, it can lead to arbitrage opportunity if no-arbitrage conditions on state price density (SPD) are ignored. In this paper, using option data on DAX index, we aim to analyse the behavior of IV and SPD with respect to different choices of bandwidth parameter h, time to maturity and kernel function. A set of bandwidths which violates no-arbitrage conditions is identified. We document that the change of h implies interesting changes in the violation interval of moneyness. We also perform the analysis after removing outliers, in order to show that not only outliers cause the violation of no-arbitrage conditions. Moreover, we propose a newmeasure of arbitrage which can be considered either for the SPD curve (arbitrage area measure) or for the SPD surface (arbitrage volume measure). We highlight the impact of h on the proposed measures considering the options on a German stock index. Finally, we propose an extension of the IV and SPD estimation for the case of options on a dividend-paying stock.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/GBP402%2F12%2FG097" target="_blank" >GBP402/12/G097: DYME-Dynamic Models in Economics</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Computational Management Science

ISSN

1619-697X

e-ISSN

—

Volume of the periodical

14

Issue of the periodical within the volume

4

Country of publishing house

DE - GERMANY

Number of pages

25

Pages from-to

559-583

UT code for WoS article

000424442700006

EID of the result in the Scopus database

2-s2.0-85021989737