Hyppyjen tunnistus Standard & Poor's 500-indeksissä mallivapaan implisiittisen volatiliteetin avulla

Jumps are large and fast price movements in asset prices, which cannot be explained by traditional Brownian motion in models for stock price dynamics. In equity prices, jumps are often caused for example by significant macroeconomic or company-specific announcements. Recent financial literature has immensely studied jumps and methodologies to detect them, especially in high-frequency data. An important aspect in determining whether the price has jumped or not is the market spot volatility at the moment of the large price movement. Since spot volatility is not directly observable, multiple ways in estimating it has been suggested in literature. Existing jump detection methodologies often use historical realized variation as a proxy for spot volatility. This thesis studies jumps in S&P 500 index using minute-by-minute high-frequency data. Using this data, VIX index and its corridor implied equivalent, CX index are computed from observable option prices. Jump detection test on S&P 500 price data is then run using both realized bipower variance and both implied volatility measures as a spot volatility estimators. Detailed analysis is made on the detected jumps yielded from both methodologies. The object is to identify, how the characteristics of detected jumps di er when using di erent volatility measures in jump detection. The results suggest that implied spot volatility measure is often lower than realized bipower variance, which results in total number of detected jumps being significantly higher using implied spot volatility measures. However, the implied spot volatility is more robust spot volatility measure especially when there are jumps or large shifts present in the volatility time series. Realized bipower variance often results in false detections of price jumps when upward volatility jumps occur. Similar behaviour is not visible when using implied spot volatility estimators. Implied volatility appears more robust especially during first minutes of the trading day