30,186 research outputs found
A convex duality method for optimal liquidation with participation constraints
In spite of the growing consideration for optimal execution in the financial
mathematics literature, numerical approximations of optimal trading curves are
almost never discussed. In this article, we present a numerical method to
approximate the optimal strategy of a trader willing to unwind a large
portfolio. The method we propose is very general as it can be applied to
multi-asset portfolios with any form of execution costs, including a bid-ask
spread component, even when participation constraints are imposed. Our method,
based on convex duality, only requires Hamiltonian functions to have
regularity while classical methods require additional regularity and cannot be
applied to all cases found in practice
Efficient option pricing with transaction costs
A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no-transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete-time Markov chain approximation to a continuous-time singular stochastic optimal control problem. A general definition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed
Portfolio Optimization and the Random Magnet Problem
Diversification of an investment into independently fluctuating assets
reduces its risk. In reality, movement of assets are are mutually correlated
and therefore knowledge of cross--correlations among asset price movements are
of great importance. Our results support the possibility that the problem of
finding an investment in stocks which exposes invested funds to a minimum level
of risk is analogous to the problem of finding the magnetization of a random
magnet. The interactions for this ``random magnet problem'' are given by the
cross-correlation matrix {\bf \sf C} of stock returns. We find that random
matrix theory allows us to make an estimate for {\bf \sf C} which outperforms
the standard estimate in terms of constructing an investment which carries a
minimum level of risk.Comment: 12 pages, 4 figures, revte
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GMM and present value test of the C-CAPM under transactions costs: Evidence from the UK stock market
In this paper we test for the inclusion of the bid-ask spread in the consumption
CAPM, in the UK stock market over the time period of 1980-2000. Two
econometric models are used; first, Fisher’s (1994) asset pricing model is
estimated by GMM, and secondly, the VAR approach proposed by Campbell and
Shiller is extended to include the bid-ask spread. Overall the statistical tests are
unable to reject the bid-ask spread as an independent explanatory variable in the
C-CAPM. This leads to the conclusion that transactions costs should be included
in asset pricing models
On the Exact Solution of the Multi-Period Portfolio Choice Problem for an Exponential Utility under Return Predictability
In this paper we derive the exact solution of the multi-period portfolio
choice problem for an exponential utility function under return predictability.
It is assumed that the asset returns depend on predictable variables and that
the joint random process of the asset returns and the predictable variables
follow a vector autoregressive process. We prove that the optimal portfolio
weights depend on the covariance matrices of the next two periods and the
conditional mean vector of the next period. The case without predictable
variables and the case of independent asset returns are partial cases of our
solution. Furthermore, we provide an empirical study where the cumulative
empirical distribution function of the investor's wealth is calculated using
the exact solution. It is compared with the investment strategy obtained under
the additional assumption that the asset returns are independently distributed.Comment: 16 pages, 2 figure
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