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Essays in efficient option pricing.

Gao, Bin.

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Essays in efficient option pricing.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Essays in efficient option pricing./
作者:	Gao, Bin.
面頁冊數:	95 p.
附註:	Chair: Stephen Figlewski.
Contained By:	Dissertation Abstracts International58-01A.
標題:	Economics, Finance. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9718698
ISBN:	0591270277

Essays in efficient option pricing.
Gao, Bin.

Essays in efficient option pricing. - 95 p.

Chair: Stephen Figlewski.

Thesis (Ph.D.)--New York University, Graduate School of Business Administration, 1996.

The dissertation consists of three essays on the methodology of option valuation. Each one presents a new approach that greatly enhances the accuracy of the approximation for a broad class of derivatives. In the first essay we discuss the general pricing errors inherited in a lattice pricing framework. We identify two sources of errors, the distribution approximation error and the truncation error. We look at the binomial and the trinomial model from a viewpoint that each model has certain degrees of freedom which can be used to deal with different feature of options. For a standard option, a binomial model can match two moments of its probability distribution with those of a continuous distribution, while a trinomial model can match higher moments, thus reduces the distribution approximation error. Numerical results show that the high order matching trinomial model significantly outperforms low order models. The second essay develops an Adaptive Mesh Method (AMM), which is a general procedure for increasing the "fineness" of a pricing lattice in the regions that are particularly critical for valuation, while maintaining a coarse grid elsewhere. For example, using the AMM to improve the resolution of the grid near the "out" strike for a "down and out" option can easily produce values that are orders of magnitude more accurate in the same computation time as the standard binomial approach. Possible AMM applications cover a very wide range, including many exotic options but also ordinary American and European calls and puts. We also show how to extend the procedure to higher dimensions, with still greater improvements in relative performance. The AMM can produce such a large increase in efficiency that new classes of problems that were previously computationally infeasible can now be explored. The third essay considers the efficient valuation of barrier options. Closed form valuation equations exist when the critical barrier is continuously observed, but for real-world contracts, it is only examined at discrete intervals, e.g., once a day. This seemingly small difference actually has quite a large effect on option value, but interaction between the discreteness of the barrier and discreteness in the approximation lattice can create major problems for standard valuation methods. We show how to overcome these problems using a suitably modified trinomial model.

ISBN: 0591270277Subjects--Topical Terms:

626650
Economics, Finance.

Essays in efficient option pricing.
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520 $a The dissertation consists of three essays on the methodology of option valuation. Each one presents a new approach that greatly enhances the accuracy of the approximation for a broad class of derivatives. In the first essay we discuss the general pricing errors inherited in a lattice pricing framework. We identify two sources of errors, the distribution approximation error and the truncation error. We look at the binomial and the trinomial model from a viewpoint that each model has certain degrees of freedom which can be used to deal with different feature of options. For a standard option, a binomial model can match two moments of its probability distribution with those of a continuous distribution, while a trinomial model can match higher moments, thus reduces the distribution approximation error. Numerical results show that the high order matching trinomial model significantly outperforms low order models. The second essay develops an Adaptive Mesh Method (AMM), which is a general procedure for increasing the "fineness" of a pricing lattice in the regions that are particularly critical for valuation, while maintaining a coarse grid elsewhere. For example, using the AMM to improve the resolution of the grid near the "out" strike for a "down and out" option can easily produce values that are orders of magnitude more accurate in the same computation time as the standard binomial approach. Possible AMM applications cover a very wide range, including many exotic options but also ordinary American and European calls and puts. We also show how to extend the procedure to higher dimensions, with still greater improvements in relative performance. The AMM can produce such a large increase in efficiency that new classes of problems that were previously computationally infeasible can now be explored. The third essay considers the efficient valuation of barrier options. Closed form valuation equations exist when the critical barrier is continuously observed, but for real-world contracts, it is only examined at discrete intervals, e.g., once a day. This seemingly small difference actually has quite a large effect on option value, but interaction between the discreteness of the barrier and discreteness in the approximation lattice can create major problems for standard valuation methods. We show how to overcome these problems using a suitably modified trinomial model.
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