Manuscript Topics

Volatility is a key variable in derivatives pricing and optimal asset allocation models. The Black-Scholes model for pricing an option and Markowitz mean-variance approach for portfolio optimization are widely known examples that largely depends on the measure of volatility. So, a better measure of volatility would bring more accurate prices of derivatives and more efficient capital allocation. The problem with volatility is that it is not directly observable in practice. One can observe some aspects of it using the transformed data from the respective derivative prices. Otherwise, we need to rely on a suitable construction of a model to forecast volatility. This is a plausible approach because volatility has a number of characteristics observed in many asset returns. Clustering, Mean-reversion, continuous movement with rare jumps, stationary property, asymmetric reaction to price increase and decrease (leverage), multiscale property and fractional nature are some of the well-known properties. It would be desirable to formulate a volatility model reflecting many of those properties while maintaining the computational efficiency of its practical implementation.

This special topic issue of AIMS Mathematics focuses on mathematical volatility models and their applications in finance, with an emphasis on the combined structure of diverse nature of volatility itself or other factors influencing the degree of variation of a price series over time. The special issue presents recent high-quality original results related to hybrid mathematical volatility models as well as the wide range of their applications in finance from leading experts in the field. Topics of interest include, but are not limited to, derivatives pricing and portfolio optimization based on multiscale stochastic volatility models, hybrid stochastic-local volatility models, hybrid stochastic volatility and stochastic interest rate models, jump-diffusion models, fractional volatility models or multi-factor stochastic volatility models combining the existing single-factor volatility models. Novel methods are welcomed from a variety of academic areas such as mathematics, data science (machine learning) and engineering. The issue is expected to stimulate further interdisciplinary research in financial mathematics area.

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