Mean-variance Hedging Strategy Research Articles

A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus

ABSTRACTWe focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models.

A General Multidimensional Monte Carlo Approach for Dynamic Hedging under Stochastic Volatility

We propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to arbitrary square-integrable claims in incomplete markets. In contrast to previous works based on PDE and BSDE methods, the main merit of our approach is the flexibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff. In particular, the methodology can be applied to multidimensional quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. In order to demonstrate that our methodology is indeed applicable, we provide a Monte Carlo study on generalized Föllmer-Schweizer decompositions, locally risk minimizing, and mean variance hedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.

Pricing and hedging basis risk under no good deal assumption

We consider the problem of explicitly pricing and hedging an option written on a non-exchangeable asset when trading in a correlated asset is possible. This is a typical case of incomplete market where it is well known that the super-replication concept provides generally too high prices. We study several prices and in particular the instantaneous no-good-deal price (see Cochrane and Saa-Requejo in J Polit Econ 108(1):79–119, 2001) and the global one. We show numerically that the global no-good-deal price can be significantly higher that the instantaneous one. We then propose several hedging strategies and show numerically that the mean-variance hedging strategy can be efficient.

The optimal value-at-risk hedging strategy under bivariate regime switching ARCH framework

Unlike the majority of other hedging literatures in which variance is taken as the risk indicator, this article uses the Value-at-Risk (VaR) as the risk management tool of the hedged portfolio. This article adopts a bivariate Markov regime Switching Autoregressive Conditional Heteroscedastic (SWARCH) model to formulate the optimal VaR hedging strategy and then compares it with the other dynamic futures hedging strategies mentioned in the literature in hedging performance. Using Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) futures data, the in-sample and out-of-sample results shows that when VaR is used as the criterion to measure the futures hedging effectiveness, the performance of the dynamic hedging strategy is superior to that of the static hedging strategy, and the performance of the optimal VaR hedging strategy is better than that of the minimum variance and mean-variance hedging strategies. Besides, from the standpoint that the volatility of hedge ratio and hedged portfolio variance decline, no matter what kind of hedging strategy is adopted, the regime switching model is better in in-sample and out-of-sample hedging effectiveness than the Generalized Autoregressive Conditional Heteroscedastic (GARCH) model.

Discrete time mean-variance analysis with singular second moment matrixes and an exogenous liability

We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonal transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.

QUADRATIC HEDGING FOR THE BATES MODEL

In the present paper we give some preliminary results for option pricing and hedging in the framework of the Bates model based on quadratic risk minimization. We provide an explicit expression of the mean-variance hedging strategy in the martingale case and study the Minimal Martingale measure in the general case.

On the structure of general mean-variance hedging strategies

We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure $P^{\star}$ which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to $P^{\star}$ coincides with the variance-optimal martingale measure relative to the original probability measure $P$.

Asymptotic analysis of utility-based hedging strategies for small number of contingent claims

We study the linear approximation of utility-based hedging strategies for small number of contingent claims. We show that this approximation is actually a mean-variance hedging strategy under an appropriate choice of a numéraire and a risk-neutral probability. In contrast to previous studies, we work in the general framework of a semimartingale financial model and a utility function defined on the positive real line.

An extension of mean-variance hedging to the discontinuous case

Our goal in this paper is to give a representation of the mean-variance hedging strategy for models whose asset price process is discontinuous as an extension of Gourieroux, Laurent and Pham (1998) and Rheinlander and Schweizer (1997). However, we have to impose some additional assumptions related to the variance-optimal martingale measure.

On the Structure of General Mean-Variance Hedging Strategies

We provide a new characterisation of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure P* which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to P* coincides with the variance-optimal martingale measure relative to the original probability measure P.

Optimal Continuous-Time Hedging with Leptokurtic Returns

We examine the behaviour of optimal mean-variance hedging strategies at high rebalancing frequencies in a model where stock prices follow a discretely sampled exponential Levy process and one hedges a European call option to maturity. Using elementary methods we show that all the attributes of a discretely rebalanced optimal hedge, i.e. the mean value, the hedge ratio and the expected squared hedging error, converge pointwise in the state space as the rebalancing interval goes to zero. The limiting formulae represent 1-D and 2-D generalized Fourier transforms which can be evaluated much faster than backward recursion schemes, with the same degree of accuracy. In the special case of a compound Poisson process we demonstrate that the convergence results hold true if instead of using an infinitely divisible distribution from the outset one models log returns by multinomial approximations thereof. This result represents an important extension of Cox, Ross and Rubinstein (1979) to markets with leptokurtic returns.

Mean-Variance Hedging for Discontinuous Semimartingales

Mean-variance hedging is well-known as one of hedging methods for incomplete markets. Our end is leading to mean-variance hedging strategy for incomplete market models whose asset price process is given by a discontinuous semimartingale and whose mean-variance trade-off process is not deterministic. In this paper, on account, we focus on this problem under the following assumptions: (1) the local martingale part of the stock price process is a process with independent increments; (2) a certain condition restricting the number and the size of jumps of the asset price process is satisfied; (3) the mean-variance trade-off process is uniformly bounded; (4) the minimal martingale measure coincides with the variance-optimal martingale measure.

MEAN-VARIANCE HEDGING FOR PARTIALLY OBSERVED DRIFT PROCESSES

We consider the mean-variance hedging when an investor observes just the stock prices. We explain how the theory developed in Gouriéroux, Laurent and Pham (1998) and Rheinländer and Schweizer (1997) can be extended to this framework. We then focus to a diffusion model when drift of stock prices are not observed directly but only through a measurement process. By using filtering techniques, we obtain explicit formulae for optimal mean-variance hedging strategies and for the associated minimal risk. Closed-form expressions are provided in the case of a Bayesian investor and when the stock drift is modelled as a linear Gaussian process.