Implied volatility smile dynamics in the presence of jumps
Bärholm, Perttu (2017)
Bärholm, Perttu
2017
Tuotantotalouden koulutusohjelma
Talouden ja rakentamisen tiedekunta - Faculty of Business and Built Environment
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Hyväksymispäivämäärä
2017-03-08
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:tty-201702081105
https://urn.fi/URN:NBN:fi:tty-201702081105
Tiivistelmä
The objective of this study is to examine if jumps in index prices affect the implied volatility smile. This is accomplished by characterizing the volatility smile by principal component analysis, and studying the variation and level of three retained components around jumps and in the absence of jumps. The analysis is conducted for changes in volatility smiles as well as smiles as such.
Implied volatility has been established as the industry standard in quoting option prices due to its comparability across different maturities and strike prices. More importantly, understanding implied volatility and implied volatility surface dynamics has been considered a prerequisite for applying extensions to the classical Black-Scholes model to price and hedge exotic and illiquid options. One category of such extensions are jump models that allow the frequently observed jumps in modelling the price of the underlying asset of an option. The central role of these two concepts and deepening our understanding of them partly motivates also this thesis. This study uses price data for the SPX index between 2006-2010 to detect jumps in the underlying and price data for options on SPX for the same time period to infer Black-Scholes implied volatility smiles and study their dynamics around the detected jumps.
The study finds that the variation of both volatility smiles and changes in volatility smiles is higher around jumps than in the absence of jumps, regardless of maturity or moneyness of the option. However, when studying levels it was found that the volatility smile is higher around jumps than normal, but the level of changes in implied volatility around jumps is higher only for at-the-money and out-of-the-money options. This finding was deemed to be in line with previous literature on sensitivity of implied volatility changes to underlying price changes. Moreover, these results suggest a linkage between jumps in the underlying spot price and implied volatility dynamics.
Implied volatility has been established as the industry standard in quoting option prices due to its comparability across different maturities and strike prices. More importantly, understanding implied volatility and implied volatility surface dynamics has been considered a prerequisite for applying extensions to the classical Black-Scholes model to price and hedge exotic and illiquid options. One category of such extensions are jump models that allow the frequently observed jumps in modelling the price of the underlying asset of an option. The central role of these two concepts and deepening our understanding of them partly motivates also this thesis. This study uses price data for the SPX index between 2006-2010 to detect jumps in the underlying and price data for options on SPX for the same time period to infer Black-Scholes implied volatility smiles and study their dynamics around the detected jumps.
The study finds that the variation of both volatility smiles and changes in volatility smiles is higher around jumps than in the absence of jumps, regardless of maturity or moneyness of the option. However, when studying levels it was found that the volatility smile is higher around jumps than normal, but the level of changes in implied volatility around jumps is higher only for at-the-money and out-of-the-money options. This finding was deemed to be in line with previous literature on sensitivity of implied volatility changes to underlying price changes. Moreover, these results suggest a linkage between jumps in the underlying spot price and implied volatility dynamics.