We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, capture the time-varying higher moments observed in financial series. Three desirable results are obtained. First, we have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for option prices as in Heston and Nandi (Rev Financ Stud 13(3):585–625, 2000). Second, we reproduce some features of the VIX Index. Finally, we derive a simple formula for the VIX index and use it for option pricing.
Hitaj, A., Mercuri, L., Rroji, E. (2018). VIX computation based on affine stochastic volatility models in discrete time. In G. Consigli, S. Stefani, G. Zambruno (a cura di), Handbook of Recent Advances in Commodity and Financial Modeling Quantitative Methods in Banking, Finance, Insurance, Energy and Commodity Markets (pp. 141-164). Springer [10.1007/978-3-319-61320-8_7].
VIX computation based on affine stochastic volatility models in discrete time
Hitaj, A.
Primo
;Rroji, E.Ultimo
2018
Abstract
We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, capture the time-varying higher moments observed in financial series. Three desirable results are obtained. First, we have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for option prices as in Heston and Nandi (Rev Financ Stud 13(3):585–625, 2000). Second, we reproduce some features of the VIX Index. Finally, we derive a simple formula for the VIX index and use it for option pricing.
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