Author: Ajay Subramanian Aiyer
Publisher:
ISBN:
Category : Investments
Languages : en
Pages : 28

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Author: Hong Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 36

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Book Description
Models with event risk (the possibility of sudden large price movements) have proven important for option pricing (e.g., Bates (1996))and optimal portfolio selection (e.g., Liu, Longstaff and Pan(2003)). However, most of the existing studies ignore transaction costs which are prevalent in almost all of the financial markets. How investors should trade in the presence of event risks and transaction costs remains an important but unanswered question. In this paper, we consider the optimal trading strategy for a CRRA investor who derives utility from terminal wealth and can continuously trade in a riskless asset and a risky asset. The risky asset, whose price follows a jump diffusion, is subject to proportional transaction costs. We show that the optimal trading strategy is to maintain the fraction of wealth invested in the risky asset between two bounds. In contrast to the case without jump risk, this fraction can jump outside the bounds which implies a discrete transaction back to the closest boundary and thus a greater transaction cost payment. We characterize the value function and provide bounds on the trading boundaries. Somewhat surprisingly, we find that an increase in transaction costs may increase trading frequency. Our numerical results suggest that event risk significantly reduces stock holdings and decreases trading frequency. We also show that the boundaries are affected not only by jump sizes but also by the uncertainty about jump sizes. Furthermore, we examine how the optimal transaction boundaries vary through time for investors with deterministic horizons.

Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 38

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Book Description
We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs; we allow cash dividends on the risky asset. The allocation shifts toward the riskless asset relative to diffusion in varying degrees depending on parameter values. It is sensitive to the proportion of the jump component to total volatility, but also to the expected amplitude for a given proportion. The shift becomes small when the relative risk aversion increases, but it becomes major when the solvency constraint is active in the presence of jumps. We derive utility losses and risk premia due to jumps under realistic parameter values and show that even when the no transaction region is very similar between pure diffusion and the mixed process the latter corresponds to lower utility because of higher portfolio restructuring costs.

Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 31

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Book Description
We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion process in the presence of proportional transaction costs. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in earlier work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.

Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 46

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Book Description
We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

Author: Nitin Ratilal Patel
Publisher:
ISBN:
Category : Portfolio management
Languages : en
Pages : 42

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Author: Nikolay Andreev
Publisher:
ISBN:
Category :
Languages : en
Pages : 54

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Book Description
We study a worst-case scenario approach to the stochastic dynamic programming problem, presenting a general probability-based framework and some properties of the arising Bellman-Isaacs equation which allow to obtain a closed-form analytic solution. We also adapt the results for a discrete financial market and the problem of strategic portfolio selection in the presence of transaction costs and trading limits with unspecified stochastic process of market parameters. Unlike the classic stochastic programming, the approach is model-free while the solution can be easily found numerically under economically reasonable assumptions. All results hold for a general class of utility functions and several risky assets. For a special case of proportional transaction costs and CRRA utility, we present a numerical scheme which allows to reduce the dimensionality of the Bellman-Isaacs equation by a number of risky assets.

Author: Ricardo A. Rodriguez-Pedraza
Publisher:
ISBN:
Category :
Languages : en
Pages : 70

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Book Description
We study the classical problem of allocation of funds between a bank account which grows with a deterministic rate and of a risky asset such as a stock whose value follows a geometric Brownian motion with a drift. We maximize the expected rate of growth of the net wealth in the presence of proportional transaction costs when transactions are made between the two assets. Our optimal strategy keeps the ratio of the values of these assets in an interval with minimum control. Finally an application of the model to a real stock is presented.

Author: Gerson M. Goldberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 368

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Author: Phelim P. Boyle
Publisher:
ISBN:
Category : Investment analysis
Languages : en
Pages : 23

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Book Description