Jump Risk, Stock Returns, and Slope of Implied Volatility Smile

Impact of macroeconomic announcements on implied volatility slope of SPX options and VIX

“…Similarly, a put option with D put = À0.5 is treated as an ATM put option. Although these options are not exactly ATM, they are very close to being ATM (Yan, 2011).…”

An analysis of implied volatility jump dynamics: Novel functional data representation in crude oil markets

“…Firstly, what is the link between the shape of the implied volatility smile and underlying economic events in crude oil markets? Secondly, does the implied volatility slope contain information useful in specifying the average jump amplitude for crude oil options, in a similar manner to what Yan (2011) has shown to be the case for stock returns? 3 Thirdly, can information contained in the implied volatility smile slope be exploited to improve portfolio hedging techniques?…”

“…Yan (2011) note that it can be extended to incorporate multi-dimensional Brownian motions and Poisson processes. Under the Merton (1976) jump diffusion (JD) framework, Poisson jumps are combined with a continuous Black and Scholes (1973) diffusion model.…”

“…4 Askari and Krichene (2008) find that 2002-2006 WTI oil price dynamics are dominated by jumps; the variance due the fitted model's diffusion component is high and significant, but the variance due to the jump component is even higher. In line with Yan (2011), we adopt the Merton (1976) jump diffusion framework ("Merton model"henceforth), which augments the Black-Scholes diffusion model with a jump process in order to model continuous price innovation and discontinuous price shock movements simultaneously. The model has two elements: a Black-Scholes drift for capturing regular price movements and a jump component for capturing large irregular and infrequent price shifts.…”

“…The relationship between the volatility smile shape and the parameters of the Merton jump diffusion model is assessed both theoretically and empirically. As in Yan (2011), this one-dimensional Brownian motion and Poisson process model is adopted for tractability. Using a 2007-2013 sample period, strong evidence is found of converse jump dynamics during periods of demand and supply side weakness.…”