Time series dynamics of vega and gamma risks; evidence from S&P 500 index options

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School of Business | Master's thesis
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This thesis provides a study of vega and gamma risks in S&P 500 index options. Most financial assets have non-constant volatility, which gives rise to volatility risk premium. There is a branch in finance literature that distinguishes between pricing shocks to realized volatility i.e. large discrete outcomes (or jumps) and conditional volatility i.e. fluctuating distribution of asset’s expected future outcomes. In the Black & Scholes they are known as gamma and vega, respectively. If these risks are seen as bad by market participants, the portfolio returns that measure these premiums should be negative. I extract the premiums using at-the-money straddle portfolios due to their sensitivity to volatility shocks. Vega premium is measured with delta-gamma hedged options portfolio and gamma premium is measured with delta-vega hedged options portfolio. I find that both premiums are negative on average during the sample period 2014-2021, which is consistent with prior research and economic theory. Portfolios that use options for hedging must pay these implicit negative premiums, which can result in sub-optimal performance from portfolio management perspective. Therefore, it is vega and gamma sellers who benefit from trading volatility. The premiums also exhibit stylized facts that are common to financial time series such as skewness, leptokurtic return distribution and clustering. Because realized and conditional volatilities are jointly estimated in most models (e.g. GARCH), I study if the volatility premiums exhibit similar reciprocal dynamic in multiple econometric tests. The findings suggest that variation in the premiums is strongly linked to each other and statistically significant. Portfolios that exclusively trade vega or gamma are therefore likely to improve risk management by considering the dynamic between the premiums and its effect on portfolio hedging. I further study how shocks to realized volatility (RV) and conditional volatility (CV) estimates affect the premiums in short-term. Both volatility premiums respond positively to RV shocks, but gamma’s cumulative response then turns negative momentarily, suggesting a possible overreaction to the initial shock. CV shocks induce positive response in gamma premium. Surprisingly, vega premium responds negatively to CV shocks, which poses a puzzle. This can be related to markets perception that CV risks in relation to vega premium incorporate net positive scenarios. Other explanation is that vega hedging decreases when CV risks increase if vega is already too expensive. Therefore, distinguishing between shocks to RV and CV when pricing vega and gamma should be considered when assessing risk management for long or short options portfolios.
Thesis advisor
Ungeheuer, Michael
option pricing, volatility risk premium, vega, gamma, straddle, Black & Scholes, hedging, GARCH
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