Author: Ken PalmerPublisher:
ISBN:
Category : Options
Languages : en
Pages : 21
Book Description
The Least Cost Super Replicating Portfolio in the Boyle-Vorst Discrete-time Option Pricing Model with Transaction Costs: the One-period Case
Author: Ken PalmerThe 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 Transactions Costs
Author: Ken PalmerPublisher:
ISBN:
Category : Transaction costs
Languages : en
Pages : 25
Book Description
Working in a binomial framework, Boyle and Vorst (1992) derive 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. The authors' first aim in this paper is to clarify the conditions under which there is a unique replicating strategy for an arbitrary contingent claim. Following Stettner (1997) and Rutkowski (1998), the authors work in the framework of asymmetric proportional transactions costs, which includes not only the model of Boyle and Vorst but also that of Bensaid, Lesne, Pages and Scheinkman (1992). The authors first clarify the conditions in the case of a one-period model and then extend them to the multi-period case, yielding a result which extends slightly a result of Rutkowski. Even when a contingent claim has a unique replicating portfolio, there may exist super replicating portfolios of lower cost. However, Bensaid, Lesne, Pages and Scheinkman gave super replicating portfolio. These results were generalised by Stettner and Rutkowski to the case of asymmetric transactions costs. Here the authors provide a further slight generalisation and give what seems to be a simpler proof. There are two results here: one gives a class of contingent claims for which the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio and the other gives conditions on the level of transactions costs such that for any contingent claim the cost of the replicating portfolio does not exceed the cost of any super replicating portfolio. Finally the authors conjecture a necessary and sufficient condition in terms of computable "terminal probabilities" for the latter to hold for a given contingent claim when the conditions on the transactions costs do not hold.
Replication and Super Replicating Portfolios in the Boyle-Vorst Discrete-time Option Pricing Model with Transactions Costs
Author: Replicating and Super Replicating Portfolios in the Boyle-Vorst Discrete-time Option Pricing Model with Transaction Costs
Author: Ken PalmerMathematical Models in Finance
Author: S.D. HowisonPublisher: CRC Press
ISBN: 9780412630705
Category : Mathematics
Languages : en
Pages : 164
Book Description
Mathematical Models in Finance compiles papers presented at the Royal Society of London discussion meeting. Topics range from the foundations of classical theory to sophisticated, up-to-date mathematical modeling and analysis. In the wake of the increased level of mathematical awareness in the financial research community, attention has focused on fundamental issues of market modelling that are not adequately allowed for in the standard analyses. Examples include market anomalies and nonlinear coupling effects, and demand new synthesis of mathematical and numerical techniques. This line of inquiry is further stimulated by ever tightening profits due to increased competition. Several papers in this volume offer pointers to future developments in this area.
Extensions to the Boyle-Vorst Discrete-time Option Pricing Model with Transactions Costs
Author: Ken PalmerPublisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 49
Book Description
Working in a binomial framework, Boyle and Vorst (1992) derive 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, for short positions, Boyle and Vorst have to impose three additional conditions. The authors' first aim in this paper is to remove Boyle and Vorst's conditions for the replication of short calls and puts. Boyle and Vorst's algorithm calculates the current holdings in stocks and bonds in terms of those at the following period. This is unlike the case of no transaction costs where the current cost of the option can be calculated directly from the costs at the following period. The authors' second aim is to show that even in the case of transactions costs the cost of replication can be directly calculated also. As a by-product, the authors are able to derive upper bounds for the cost of replication which are valid for long positions and also for short positions when two of Boyle and Vorst's additional conditions hold. The authors' third aim is to show that the time of computation using the backward recursion can be halved. This seems to to be a new observation, even in the case of no transactions costs.
Mathematics of Derivative Securities
Author: Michael A. H. DempsterPublisher: Cambridge University Press
ISBN: 9780521584241
Category : Business & Economics
Languages : en
Pages : 614
Book Description
During 1995 the Isaac Newton Institute for the Mathematical Sciences at Cambridge University hosted a six month research program on financial mathematics. During this period more than 300 scholars and financial practitioners attended to conduct research and to attend more than 150 research seminars. Many of the presented papers were on the subject of financial derivatives. The very best were selected to appear in this volume. They range from abstract financial theory to practical issues pertaining to the pricing and hedging of interest rate derivatives and exotic options in the market place. Hence this book will be of interest to both academic scholars and financial engineers.
Author: 
Author: Phelim P. Boyle