Abstract
This paper presents bootstrapped nonlinear impulse response function analyses for general step ahead mean and volatility densities. From strictly (ergodic and) stationary series and BIC optimal nonlinear model coefficients, the paper establishes step-ahead densities for both the conditional mean and volatility. For sampling variances using one thousand samples and conditioning all paths on the daily impulses -5, -3, ..., 5% all mean and volatility responses show mean reversion. For the volatility, all increases seem to arise from negative index movements suggesting strong asymmetry. Furthermore, the model coefficients for the volatility exhibit data dependence suggesting ability to predict volatility. The indices report some striking step-ahead differences for both the mean and the volatility. For the mean, only the NDX100 seems to show overreactions. For the volatility, for both positive and negative impulses the NDX100 reports higher volatility responses then FTSE100. However, asymmetry manifested for both indices suggesting that trading volatility as an asset may insure against market crashes and be an excellent diversification instrument. Finally, using a stochastic volatility model to obtain calibrated functions that give step-ahead predicted values for static predictions, enriches participants' derivative trading strategies (i.e., volatility swaps).
Highlights
IntroductionThis paper presents nonlinear impulse-response analyses for two central international equity indices
This paper presents bootstrapped nonlinear impulse response function analyses for general step ahead mean and volatility densities
Only the NDX100 seems to show overreactions. For both positive and negative impulses the NDX100 reports higher volatility responses FTSE100. Asymmetry manifested for both indices suggesting that trading volatility as an asset may insure against market crashes and be an excellent diversification instrument
Summary
This paper presents nonlinear impulse-response analyses for two central international equity indices. The impulse-response analysis report step ahead profiles with confidence intervals with associated distributions for the European and US indices for the period 2012–2021. Extending the SNP model to bootstrapped impulse-response distribution analysis is challenging but made possible using bash scripting tools in Linux and access to clusters of CPUs/GPUs and optimisation using the OpenMPI3 software. The simulations, iterations and density reports are Linux bash script unique while the SNP models calculate the mean and volatility responses using C/ C++. The hermite function expansions extend model approximation for the conditional density, which summarises the probability distribution and characterises the index movement processes.
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