Higher-order volatility

Carey, Alexander (2005): Higher-order volatility.

Abstract

An important purpose of derivatives modelling is to provide practitioners with actionable measures of risk. The Black and Scholes volatility remains a favourite on trading floors in spite of well-known biases. One popular extension is to make volatility a function of time and the underlying asset price, as in local volatility models. This paper presents an alternative extension, which produces volatility-like quantities to address the skews and smiles found in most derivatives markets.

• Item Type: MPRA Paper
• Language: English
• Keywords: higher-order volatility; higher-order moments; volatility smile; S&P 500
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

References

Bates, D. (1991) The crash of ’87: Was it expected? The 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.

Derman, E. and I. Kani (1994) Riding on a smile, Risk 7(2), 32-39.

Dupire, B. (1994) Pricing with a smile, Risk 7(1), 18-20.

Jarrow, R. and A. Rudd (1982) Approximate option valuation for arbitrary stochastic processes, Journal of Financial Economics 10(3), 347-369.

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.

Rubinstein, M. (1994) Implied binomial trees, Journal of Finance 49(3), 771-818.