In this paper we solve the discrete time mean-variance hedging problem when asset returns follow a multivariate autoregressive hidden Markov model. Time dependent volatility and serial dependence are well established properties of financial time seri
es and our model covers both. To illustrate the relevance of our proposed methodology, we first compare the proposed model with the well-known hidden Markov model via likelihood ratio tests and a novel goodness-of-fit test on the S&P 500 daily returns. Secondly, we present out-of-sample hedging results on S&P 500 vanilla options as well as a trading strategy based on theoretical prices, which we compare to simpler models including the classical Black-Scholes delta-hedging approach.
Deheuvels [J. Multivariate Anal. 11 (1981) 102--113] and Genest and R{e}millard [Test 13 (2004) 335--369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cram{e}r--von Mises
statistics derived from a M{o}bius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting distribution of such test statistics and to compute their relative local asymptotic efficiency. Local power curves and asymptotic relative efficiencies are compared under familiar classes of copula alternatives.
In this paper, we construct a Malliavin derivative for functionals of square-integrable Levy processes and derive a Clark-Ocone formula. The Malliavin derivative is defined via chaos expansions involving stochastic integrals with respect to Brownian
motion and Poisson random measure. As an illustration, we compute the explicit martingale representation for the maximum of a Levy process.
