Daily returns of financial assets are frequently found to exhibit positive autocorrelation at lag 1. When specifying a linear AR(l) conditional mean, one may ask how this predictability affects option prices. We investigate the dependence of option prices on autoregressive dynamics under...

Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and...

In recent years multivariate models for asset returns have received much attention, in particular this is the case for models with time varying volatility. In this paper we consider models of this class and examine their potential when it comes to option pricing. Specifically, we derive the risk...

In recent years multivariate models for asset returns have received much attention, in particular this is the case for models with time varying volatility. In this paper we consider models of this class and examine their potential when it comes to option pricing. Specifically, we derive the risk...

In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than...

Market analysts and central banks often use the implied volatility of FX options as an indicator of expected exchange rate uncertainty. The aim of our study is to investigate the limits of this statistic. We present some key factors that may deviate the value of implied volatility from the...

We consider a semi-Markov modulated market consisting of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on a semi-Markov process x. Using the martingale characterization of semi-Markov processes, we note the incompleteness of semi-Markov modulated markets and...

This paper provides several estimates of the GARCH models' parameters for the S&P500 index, based on returns and CBOE VIX. Using a daily sample collected from 2007 to 2022, we can conclude that adding the VIX information improves the estimates of the long-term volatility. By providing an...

In this paper, a detailed proof is provided for the value of compound options based on geometric Brownian motion with maturity varying yields, maturity varying volatility, and maturity varying interest rates. Most research papers focused on compound options do not address yields on the...

I propose an affine discrete-time model, called Vector Autoregressive Gamma with volatility Bursts (VARG-B) in which volatility experiences, in addition to frequent and small changes, periods of sudden and extreme movements generated by a latent factor which evolves according to the...