Neutral and indifference pricing with stochastic correlation and volatility

Abstract

In this paper, we consider a Wishart Affine Stochastic Correlation (WASC) model which accounts for the stochastic volatilities of the assets and for the stochastic correlations not only between the underlying assets' returns but also between their volatilities. Under the assumptions of the model, we derive the neutral and indifference pricing for general European-style financial contracts. The paper shows that comparing to risk-neutral pricing, the utilitybased pricing methods are generally feasible and avoid factitiously dealing with some risk premia corresponding to the volatilities-correlations as a consequence of the incompleteness of the market.2010 Mathematics Subject Classification. Primary: 91G20; Secondary: 91G80.

Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

“…Furthermore, fractionally-integrated models were shown to provide a useful description of volatility dynamics in the presence of structural breaks because they effectively allow the unconditional variance to change slowly over time [12], and Hyung et al [20] further demonstrated that fractionally-integrated models provide the best volatility forecasts, when it is impossible to identify the volatility breaks before they occur. Very recently, a new fractional stochastic process for the volatility was proposed in [32,33], in which the general fractional stochastic models are shown to better capture dynamic volatilities of the assets and changing correlations between the returns and volatilities of the underlying assets.Considering the amount of resources spent by market participants to separate the component of the informed order flow from the uninformed one as well as the long memory property exhibited by the volatility, it is very demanding to understand how these affect the equilibrium price and liquidity, since similar to most of quantitative finance/economics area [19,34], finding an appropriate model that reflects the most characteristics of the real market is vital to perform correct analysis. To incorporate these, in this paper, the Kyle model is generalized so that the noise trading volatility is allowed to evolve under a stochastic setting, and the trading volume is governed by a fractional stochastic dynamic system perturbed by a memory noise.…”

“…Furthermore, fractionally-integrated models were shown to provide a useful description of volatility dynamics in the presence of structural breaks because they effectively allow the unconditional variance to change slowly over time [12], and Hyung et al [20] further demonstrated that fractionally-integrated models provide the best volatility forecasts, when it is impossible to identify the volatility breaks before they occur. Very recently, a new fractional stochastic process for the volatility was proposed in [32,33], in which the general fractional stochastic models are shown to better capture dynamic volatilities of the assets and changing correlations between the returns and volatilities of the underlying assets.…”