Time-Varying Skew in VIX Derivatives Pricing

This paper proposes a new reduced-form model for the pricing of VIX derivatives that includes an independent stochastic jump intensity factor and cojumps in the level and variance of VIX, while allowing the mean of VIX variance to be time varying. I fit the model to daily prices of futures and European options from April 2007 through December 2017. The empirical results indicate that the model significantly outperforms all other nested models and improves on benchmark by 21.6% in sample and 31.2% out of sample. The model more accurately portrays the tail behavior of VIX risk-neutral distribution for both short and long maturities, as it better captures the time-varying skew found to be largely independent of the level of the VIX smile. This paper was accepted by Kay Giesecke, finance.

Conditional Probability of Jumps in Oil Prices

The objective of this research is to model the behavior of oil returns. The volatility of oil returns is described through a TGARCH process. Conditional probability jumps are incorporated through uniform, double exponential and normal jump intensity distributions. We found that the volatility of oil returns follows the stylized facts of leptokurtosis, leverage effect and volatility clustering. The abnormal information that causes the jumps, can cause another type of unexpected changes in the following period and the intensity of the jumps has a negative effect on the probability of jumps in the next period. The dynamic model proposed can be extended to other markets and to multivariate time series modeling considering the dependence among the markets’ returns. The main contribution of this work is the estimation of the conditional probability of jumps depending on the previous behavior leading to a better description of the stochastic dynamics of crude oil prices. This will be useful for making better decisions regarding oil as an underlying asset in derivatives or in the formulation of better public policies.

The Law of the Iterated Logarithm for Random Dynamical System with Jumps and State-Dependent Jump Intensity

In this paper our considerations are focused on some Markov chain associated with certain piecewise-deterministic Markov process with a state-dependent jump intensity for which the exponential ergodicity was obtained in [4]. Using the results from [3] we show that the law of iterated logarithm holds for such a model.

Jumps and Cojumps analyses of major and minor cryptocurrencies

This paper empirically examines jumps and cojumps of both major and minor cryptocurrencies. Understanding the nature of their jumps and cojumps plays an important role in risk management, asset allocation and pricing of derivatives. We find that all cryptocurrencies display significant jumps. Furthermore, minor cryptocurrencies appear to have significantly higher jump intensity and jump size than major cryptocurrencies. Finally, we find that cojumps of the Thai stock market index and minor cryptocurrencies have a greater intensity than that of major cryptocurrencies.

EQUILIBRIUM VALUATION OF CURRENCY OPTIONS UNDER A DISCONTINUOUS MODEL WITH CO-JUMPS

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.