Author: Gary Sze Huat QuekPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Portfolio Optimisation and Option Pricing in Discrete Time with Transaction Costs
Author: Gary Sze Huat QuekModeling and Numerical Solution of Portfolio Optimization Problems with Transaction Costs: An Option Pricing Approach
Author: Zhen LiuPublisher:
ISBN: 9781109968606
Category : Asset allocation
Languages : en
Pages : 54
Book Description
Portfolio optimization problems with transaction costs have been widely studied by both financial economists and financial engineers through various approaches. In this paper, we propose the following approach. In analogy to American option pricing, we study the problem through the Finite Element Method (FEM) combined with an optimization method: We set up a buy-and-hold problem and then we find an optimal set of trades to move to an optimal portfolio whenever the current portfolio is far from the ideal. Local Discontinuous Galerkin (LDG) FEM is used to solve the partial differential equation (PDE) associated with the buy-and-hold problem. Coupled with the Runge-Kutta method for time discretization, this method is local with respect to spatial variable, can be used to achieve any order of accuracy and is explicit in the semi-discrete Ordinary Differential Equation (ODE) form. Also it is amendable to parallel computing. In this paper we give error bounds for the LDG method, with which we establish overall bounds for the portfolio optimization problem and prove the convergence of this method.
The Least Cost Super Replicating Portfolio in the Boyle-Vorst Discrete-time Option Pricing Model with Transaction Costs: the One-period Case
Author: Ken PalmerWeak Convergence of Financial Markets
Author: Jean-Luc PrigentPublisher: Springer Science & Business Media
ISBN: 3540248315
Category : Business & Economics
Languages : en
Pages : 432
Book Description
A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
Markets with Transaction Costs
Author: Yuri KabanovPublisher: Springer Science & Business Media
ISBN: 3540681213
Category : Business & Economics
Languages : en
Pages : 306
Book Description
The book is the first monograph on this highly important subject.
Optimal Portfolio Selection with Transaction Costs and 'Event Risk'
Author: Hong LiuPublisher:
ISBN:
Category :
Languages : en
Pages : 36
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.
The Least Cost Super Replicating Portfolio in the Boyle-Vorst Discrete-time Option Pricing Model with Transactions Costs
Author: Ken PalmerPublisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 21
Book Description
Working in a binomial framework, Boyle and Vorst derived self-financing strategies perfectly replicating the final payoffs to long positions in European call and put options, assuming proportional transactions costs on trades in the stocks. The initial cost of such a strategy yields, by an arbitrage argument, an upper bound for the option price. A lower bound for the option price is obtained by replicating a short position. However, even when a contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. Nevertheless, Bensaid, Lesne, Pages and Scheinkman gave conditions under which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. These results were generalised by Stettner and Rutkowski to the case of asymmetric transcations costs. Palmer gave a further slight generalisation with what seemed to be a simpler proof. It is known from these results that no super replicating portfolio for long positions in calls and puts can have a lower cost than the replicating portfolio. However, even when a short call or put has a unique replicating portfolio, there may exist super replicating portfolios of lower cost when transactions costs are sufficiently large. Then a lower bound for the call or put price would be the negative of the least possible cost of such a super replicating portfolio. So it is important to be able to calculate this cost. Now the cost of the replicating portfolio can easily be calculated by backward recursion. However, as there are possibly infinitely many super replicating portfolios, it is not immediately obvious how the least possible cost of a super replicating portfolio can be efficiently calculated. The aim of this paper is to show how this cost can be calculated in the one-period case.contemplating priv Ơ
Replicating and Super Replicating Portfolios in the Boyle-Vorst Discrete-time Option Pricing Model with Transaction Costs
Author: Ken PalmerA Disturbance Attenuatin Approach to Option Pricing with Transaction Costs
Author: Lihui ZhengPublisher:
ISBN:
Category : Investment analysis
Languages : en
Pages : 52
Book Description
Strategic Asset Allocation
Author: John Y. CampbellPublisher: OUP Oxford
ISBN: 019160691X
Category : Business & Economics
Languages : en
Pages : 272
Book Description
Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.