Abstract
The implied volatility is a key component in determining option prices, and consequently a model of VIX shocks in stress testing plays a crucial role in quantifying market risk of derivative portfolios. Based on hypothetical moves of SPX spot price, we first apply the “sticky strike” rule to the existing SPX volatility surface and shock the implied volatility level by an additional relative amount, which would be determined by the analysis of historical VIX fluctuations. Then, we calculate the after-shock VIX index level according to the CBOE VIX White paper, and finally determine the daily VIX shocks. Our backtesting results show that the model could generate realistic VIX shocks in mimicking historical financial crises. A simple application of our model generates stress testing scenarios of VIX shocks comparable with the scenarios from a leading financial institution in the United States. Our model has practical implications for the Basel stress testing.
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