Carey, Alexander (2010): Higher-order volatility: time series.
Download (9MB) | Preview
This paper presents time-series of higher-order volatilities for the S&P 500 and EURUSD. We use a 3-volatility model which accounts for non-normal skewness and kurtosis. The volatilities control the level, slope and curvature of the Black-Scholes implied volatility smile; accordingly we term them "base", "skew" and "smile" volatility. We define instantaneous skewness and kurtosis as simple ratios of the volatilities, and show that when these metrics are held constant, the model is relative sticky-delta. For the S&P 500 in 2008, skew and smile volatility are highly correlated with base volatility. Instantaneous skewness and kurtosis are remarkably stable, including over the market dislocation of the last four months of the year. Daily changes in all three volatilities are correlated with daily returns. For EURUSD in 2006, base and smile volatility are closely correlated, but in contrast to the equity case, skew volatility is independent and changes sign. This change in sign appears to provide advance warning of the two major market moves of the year. However, daily changes in the volatilities are uncorrelated with daily returns.
|Item Type:||MPRA Paper|
|Original Title:||Higher-order volatility: time series|
|Keywords:||higher-order volatility; time series; S&P 500; EURUSD|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing|
|Depositing User:||Alexander Carey|
|Date Deposited:||04. Mar 2010 14:20|
|Last Modified:||28. Feb 2015 12:13|
Abramovitz, M. and I. Stegun (1972) Handbook of Mathematical Functions, 10th printing, National Bureau of Standards, United States Department of Commerce.
Babbs, S. and M. Selby (1998) Pricing by arbitrage under arbitrary information, Mathematical Finance 8(2), 163-168.
Bates, D. (1991) The crash of ’87: Was it expected? Evidence from options markets, Journal of Finance 46(3), 1009-1044.
Black, F. and M. Scholes (1973) The pricing of options and corporate liabilities, Journal of Political Economy 81(3), 637-654.
Brody, D., L. Hughston and A. Macrina (2007) Information-based asset pricing, International Journal of Theoretical and Applied Finance 11(1), 107-142.
Carey, A. (2005) Higher-order volatility, working paper, SSRN e-library.
Carey, A. (2006) Higher-order volatility: dynamics and sensitivities, working paper, SSRN e-library.
Carr, P. and L. Wu (2007) Stochastic skew in currency options, Journal of Financial Economics 86, 213-247.
Daglish, T., J. Hull and W. Suo (2007) Volatility surfaces: theory, rules of thumb, and empirical evidence, Quantitative Finance 7(5), 507-524.
Gikhman, I. and A. Skorokhod (1972) Stochastic Differential Equations, Springer-Verlag.
Hakala, J., R. Stuart and T. Hamosfakidis (2008) FX derivatives, presentation slides, Standard Chartered Bank. http://www.mathfinance.com/workshop/2008/papers/hakala/slides.pdf
Johannes, M. (2004) The statistical and economic role of jumps in continuous-time interest rate models, Journal of Finance 59(1), 227-260.
Merton, R. (1973) Theory of rational option pricing, Bell Journal of Economics and Management Science 4(1), 141-183.
Merton, R. (1976) Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics 3(1-2), 125-144.
Reiswich, D. and U. Wystup (2009) FX volatility smile construction, working paper, Frankfurt School of Finance and Management.
Stuart, A. and K. Ord (1994) Kendall’s Advanced Theory of Statistics (Volume 1), 6th edition, Arnold.
Wystup, U. (2006) FX Options and Structured Products, Wiley.