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.

The Economics of Insurance: A Derivatives-Based Approach

This article revisits the economics of insurance using insights from derivatives pricing and hedging. Applying this perspective, I emphasize the following insights applicable to insurance. First, I provide a valid justification for the use of arbitrage-free insurance premiums. This justification applies in both complete and incomplete markets. Second, I demonstrate the importance of diversifiable idiosyncratic risk for the determination of insurance premiums. And third, analyzing the insurance industry using the functional approach, I show the importance of derivatives and the synthetic construction of derivatives for reducing an insurance company's insolvency risk. Expected final online publication date for the Annual Review of Financial Economics, Volume 13 is November 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Modelling of derivatives pricing using methods of spectral analysis

In this article expands the method of finding the approximate price for a wide class of derivative financial instruments. Using the spectral theory of self-adjoint operators in Hilbert space and the wave theory of singular and regular perturbations, the analytical formula of the approximate asset price is established. Methods for calculating the approximate price of options using the tools of spectral analysis, singular and regular wave theory in the case of fast and slow factors are developed. Combining methods from the spectral theory of singular and regular perturbations, it is possible to estimate the price of derivative financial instruments as a schedule by eigenfunctions. The approximate value of securities and their rate of return are calculated. Applying the theory of Sturm-Liouville, Fredholm’s alternative and analysis of singular and regular perturbations at different time scales have enabled us to obtain explicit formulas for the approximate value of securities and their yield on the basis of the development of their eigenfunctions and eigenvalues of self-adjoint operators using boundary value problems for singular and regular perturbations. The theorem of closeness estimates for bond prices approximation is proved. An algorithm for calculating the approximate price of derivatives and the accuracy of estimates has been developed, which allows to analyze and draw precautionary conclusions and suggestions to minimize the risks of pricing derivatives that arise in the stock market. A model for finding the value of derivatives corresponding to the dynamics of the stock market and the size of financial flows has been developed. This model allows you to find the prices of derivatives and their volatility, as well as minimize speculative changes in pricing, analyze the progress of stock market processes and take concrete steps to improve the situation to optimize financial strategies. The used methodology of European options pricing based on the study of volatility behavior and analysis of the yield of financial instruments allows to increase the accuracy of the forecast and make sound management strategic decisions by stock market participants.

An Alternative Approach to Measure Co-Movement between Two Time Series

The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were proposed by researchers. ARCH, GARCH or EGARCH models, among others, are very popular to model volatility autocorrelation. In this paper, a new simple method called HP is introduced to measure the co-movement between two time series. This method, based on the Hurst exponent of the product series, is designed to detect correlation, even if the relationship is weak, but it also works fine with cointegration as well as non linear correlations or more complex relationships given by a copula. This method and different variations thereaof are tested in statistical arbitrage. Results show that HP is able to detect the relationship between assets better than the traditional correlation method.