Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model

This paper focuses on a mixed fractional version of Heston model in which the volatility Brownian and price Brownian are replaced by mixed fractional Brownian motion with the Hurst parameter $H\in(\frac{3}{4},1)$ so that the model exhibits the long range dependence. The existence and uniqueness of solution of mixed fractional Heston model is established under various non-Lipschitz condition and a related Euler discretization method is discussed. An example on the American put option price using Least Squares Monte Carlo Algorithm to produce acceptable results under the mixed fractional Heston model is presented to illustrate the applicability of the theory. The numerical result obtained proves the performanceof our results.

INFORMATION-THEORETIC ANALYSIS OF STOCHASTIC VOLATILITY MODELS

Stochastic volatility models describe asset prices [Formula: see text] as driven by an unobserved process capturing the random dynamics of volatility [Formula: see text]. We quantify how much information about [Formula: see text] can be inferred from asset prices [Formula: see text] in terms of Shannon’s mutual information in a twofold way: theoretically, by means of a thorough study of Heston’s model; from a machine learning perspective, by means of investigating a family of exponential Ornstein–Uhlenbeck (OU) processes fitted on S&P 500 data.

Stochastic volatility for utility maximizers — A martingale approach

Using Martingale methods, we study the problem of optimal consumption-investment strategies in a complete financial market characterized by stochastic volatility. With Heston’s model as the working example, we derive optimal strategies for a constant relative risk aversion (CRRA) investor with particular attention to the cases where (i) she solely seeks to optimize her utility for consumption, and (ii) she solely seeks to optimize her bequest from investing in the market. Furthermore, we test the practical utility of our work by conducting an empirical study based on real market-data from the S&P500 index. Here, we concentrate on wealth maximization and investigate the degree to which the inclusion of derivatives facilitates higher welfare gains. Our experiments show that this is indeed the case, although we do not observe realized wealth-equivalents as high as expected. Indeed, if we factor in the increased transaction costs associated with including options, the results are somewhat less convincing.