Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRobust portfolio optimization with multi-factor stochastic volatility
118
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without derivative trading. To illustrate the effects of ambiguity, we compare our optimal robust strategy with some strategies that ignore the information of uncertainty, and provide the corresponding welfare analysis. The effects of derivative trading to the optimal portfolio selection are also discussed by considering alternative strategies. Our study is further extended to the cases with jump risks in asset price and correlated volatility factors, respectively. Numerical experiments are provided to demonstrate the behavior of the optimal portfolio and utility loss.
rate research
Read More
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the regime where these factors are running on both slow and fast timescales. However, the rigorous justification of the accuracy of these approximations has been limited to power utilities and a single factor. In this paper, we provide an accuracy analysis for cases with general utility functions and two timescale factors by constructing sub- and super-solutions to the fully nonlinear problem such that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.
In the present work, we propose a new multifactor stochastic volatility model in which slow factor of volatility is approximated by a parabolic arc. We retain ourselves to the perturbation technique to obtain approximate expression for European option prices. We introduce the notion of modified Black-Scholes price. We obtain a simplified expression for European option price which is perturbed around the modified Black-Scholes price and have also obtained the expression of modified price in terms of Black-Scholes price.
Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price volatility: both fast-time scale on the order of days and slow-scale on the order of months. So, it is natural to study the portfolio optimization problem under the effects of dependence behavior which we will model by fractional Brownian motions with Hurst index $H$, and in the fast or slow regimes characterized by small parameters $eps$ or $delta$. For the slowly varying volatility with $H in (0,1)$, it was shown that the first order correction to the problem value contains two terms of order $delta^H$, one random component and one deterministic function of state processes, while for the fast varying case with $H > half$, the same form holds at order $eps^{1-H}$. This paper is dedicated to the remaining case of a fast-varying rough environment ($H < half$) which exhibits a different behavior. We show that, in the expansion, only one deterministic term of order $sqrt{eps}$ appears in the first order correction.
The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the problem with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. We illustrate our result with a particular model for which we have explicit formulas. A rigorous accuracy result is also derived using a verification result for the HJB equation involved. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.
In this paper we show how to implement in a simple way some complex real-life constraints on the portfolio optimization problem, so that it becomes amenable to quantum optimization algorithms. Specifically, first we explain how to obtain the best investment portfolio with a given target risk. This is important in order to produce portfolios with different risk profiles, as typically offered by financial institutions. Second, we show how to implement individual investment bands, i.e., minimum and maximum possible investments for each asset. This is also important in order to impose diversification and avoid corner solutions. Quite remarkably, we show how to build the constrained cost function as a quadratic binary optimization (QUBO) problem, this being the natural input of quantum annealers. The validity of our implementation is proven by finding the optimal portfolios, using D-Wave Hybrid and its Advantage quantum processor, on portfolios built with all the assets from S&P100 and S&P500. Our results show how practical daily constraints found in quantitative finance can be implemented in a simple way in current NISQ quantum processors, with real data, and under realistic market conditions. In combination with clustering algorithms, our methods would allow to replicate the behaviour of more complex indexes, such as Nasdaq Composite or others, in turn being particularly useful to build and replicate Exchange Traded Funds (ETF).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
