Pricing path-dependent derivatives

碩士 === 國立臺灣大學 === 資訊工程學研究所 === 87 === A financial derivative is a financial instrument whose payoff is based on other elementary financial instruments, such as bonds or stocks. With the rapid growth and deregulation of many economies, more derivatives are being designed by the financial...

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Main Authors: Dai, Tian-Shyr, 戴天時
Other Authors: Lyuu, Yuh-Dauh
Format: Others
Language:zh-TW
Published: 1999
Online Access:http://ndltd.ncl.edu.tw/handle/20971664531418736276
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spelling ndltd-TW-087NTU003920222016-02-01T04:12:40Z http://ndltd.ncl.edu.tw/handle/20971664531418736276 Pricing path-dependent derivatives 一般性複雜衍生性金融商品定價研究 Dai, Tian-Shyr 戴天時 碩士 國立臺灣大學 資訊工程學研究所 87 A financial derivative is a financial instrument whose payoff is based on other elementary financial instruments, such as bonds or stocks. With the rapid growth and deregulation of many economies, more derivatives are being designed by the financial institutions to satisfy the needs of their clients. This also gives rise to new problems in pricing and hedging. It has been proved that pricing arbitrary European options is a #P-hard problem. Even now, there are some notorious derivatives, such as Asian options, that can not be efficiently priced. These sophisticated derivatives are playing important roles in financial markets. Pricing path-dependent derivatives with tree models combined with state variables is a standard numerical approach, especially when we can not get proper closed form. Monte Carlo simulation is also a good alternative, but it is less efficient than the tree methods in general. A systematic approach to constructing data structures and algorithms for pricing is the first goal of this thesis. I will first introduce how the idea works by illustrating the underlying ideas. Then I will apply the ideas to European-style path-dependent options, such as barrier options, geometric average-rate option and Asian-like interest rate options. For American-style options, the early exercise property of these options is critical, and the numerical data from Asian-like derivatives also suggests that it is a monotone curve rather than an oscillated one. The second goal of this thesis is therefore about demonstrating these properties of the pricing data. Pricing the arithmetic average rate options is a hard problem. This is because we can''t derive a proper formula for describing the distribution of the sums of log-normal random variables. A new lattice model is designed for pricing the arithmetic average-rate options. This efficient approach can give a more reliable answer than other approaches. Lyuu, Yuh-Dauh 呂育道 1999 學位論文 ; thesis 51 zh-TW
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description 碩士 === 國立臺灣大學 === 資訊工程學研究所 === 87 === A financial derivative is a financial instrument whose payoff is based on other elementary financial instruments, such as bonds or stocks. With the rapid growth and deregulation of many economies, more derivatives are being designed by the financial institutions to satisfy the needs of their clients. This also gives rise to new problems in pricing and hedging. It has been proved that pricing arbitrary European options is a #P-hard problem. Even now, there are some notorious derivatives, such as Asian options, that can not be efficiently priced. These sophisticated derivatives are playing important roles in financial markets. Pricing path-dependent derivatives with tree models combined with state variables is a standard numerical approach, especially when we can not get proper closed form. Monte Carlo simulation is also a good alternative, but it is less efficient than the tree methods in general. A systematic approach to constructing data structures and algorithms for pricing is the first goal of this thesis. I will first introduce how the idea works by illustrating the underlying ideas. Then I will apply the ideas to European-style path-dependent options, such as barrier options, geometric average-rate option and Asian-like interest rate options. For American-style options, the early exercise property of these options is critical, and the numerical data from Asian-like derivatives also suggests that it is a monotone curve rather than an oscillated one. The second goal of this thesis is therefore about demonstrating these properties of the pricing data. Pricing the arithmetic average rate options is a hard problem. This is because we can''t derive a proper formula for describing the distribution of the sums of log-normal random variables. A new lattice model is designed for pricing the arithmetic average-rate options. This efficient approach can give a more reliable answer than other approaches.
author2 Lyuu, Yuh-Dauh
author_facet Lyuu, Yuh-Dauh
Dai, Tian-Shyr
戴天時
author Dai, Tian-Shyr
戴天時
spellingShingle Dai, Tian-Shyr
戴天時
Pricing path-dependent derivatives
author_sort Dai, Tian-Shyr
title Pricing path-dependent derivatives
title_short Pricing path-dependent derivatives
title_full Pricing path-dependent derivatives
title_fullStr Pricing path-dependent derivatives
title_full_unstemmed Pricing path-dependent derivatives
title_sort pricing path-dependent derivatives
publishDate 1999
url http://ndltd.ncl.edu.tw/handle/20971664531418736276
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