RCA models with correlated errors

AbstractFinancial time series data cannot be adequately modelled by a normal distribution and empirical evidence on the non-normality assumption is very well documented in the financial literature; see [R.F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica 50 (1982) 987–1008] and [T. Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics 31 (1986) 307–327] for details. The kurtosis of various classes of RCA models has been the subject of a study by Appadoo et al. [S.S. Appadoo, M. Gharahmani, A. Thavaneswaran, Moment properties of some volatility models, Math. Sci. 30 (2005) 50–63] and Thavaneswaran et al. [A. Thavaneswaran, S.S. Appadoo, M. Samanta, Random coefficient GARCH models, Math. Comput. Modelling 41 (2005) 723–733]. In this work we derive the kurtosis of the correlated RCA model as well as the normal GARCH model under the assumption that the errors are correlated

Option valuation model with adaptive fuzzy numbers

AbstractIn this paper, we consider moment properties for a class of quadratic adaptive fuzzy numbers defined in Dubois and Prade [D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980]. The corresponding moments of Trapezoidal Fuzzy Numbers (Tr.F.N’s) and Triangular Fuzzy Numbers (T.F.N’s) turn out to be special cases of the adaptive fuzzy number [S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciences 172 (2005) 73–89]. A numerical example is presented based on the Black–Scholes option pricing formula with quadratic adaptive fuzzy numbers for the characteristics such as volatility parameter, interest rate and stock price. Our approach hinges on a characterization of imprecision by means of fuzzy set theory

Option pricing for some stochastic volatility models

Purpose – To study stochastic volatility in the pricing of options. Design/methodology/approach – Random-coefficient autoregressive and generalized autoregressive conditional heteroscedastic models are studied. The option-pricing formula is viewed as a moment of a truncated normal distribution. Findings – Kurtosis for RCA and for GARCH process is derived. Application of random coefficient GARCH kurtosis in analytical approximation of option pricing is discussed. Originality/value – Findings are useful in financial modeling.Kurtosis, Pricing, Stochastic modelling

Forecasting volatility

This paper studies the problem of volatility forecasting for some financial time series models. We consider several stochastic volatility models including GARCH, Power GARCH and non-stationary GARCH for illustration. In particular, a martingale representation is used to obtain the l-steps-ahead forecast error variance for the class of GARCH models. Some closed-form expressions for the variance of l-steps-ahead forecasts errors are given in terms of [psi] weights and the kurtosis of the error distribution.Forecasting GARCH models Stochastic volatility Innovations Heteroscedasticity Random Conditional expectation