2006 Fiscal Year Final Research Report Summary
Studies on the accuracy of numerical algorithms used in financial engineering
| Project/Area Number |
16510110
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | National Graduate Institute for Policy Studies |
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Principal Investigator |
MOROHOSI Hozumi National Graduate Institute for Policy Studies, Graduate School of Policy Studies, Associate Professor, 政策研究科, 准教授 (10272387)
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| Co-Investigator(Kenkyū-buntansha) |
FUSHIMI Masanori Nanzan University, Department of Mathematical Informatics, Professor, 数理情報学部, 教授 (70008639)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Financial Engineering / Monte Carlo Method / Simulation / Numerical Algorithm |
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| Research Abstract |
We investigated the difference between computed option prices of discrete and continuous time models. Not a few algorithms for computing option price are proposed in the decade. It is in their nature to be in the form of discrete time setting, as is rarely recognized in many financial engineers. First we checked the difference between the analytic solution of continuous time barrier options price and their discrete time version price that are computed by Monte Carlo simulation. The computational comparison showed the difference is significant and cannot be removed by increasing the time steps. This result also indicate that the approximation by continuous time model to discrete time model in option pricing problem may have a serious defect in its accuracy. Then we experimented Kou's continuous correction method for barrier options. It showed great improvement of analytic solution for continuous time models for the approximation of discrete time models, and in some cases lost its superiority.
Second we investigated the exercise boundary of American options. Several asymptotic expansion approximations and a numerical approximation method are compared. It was proved that asymptotic expansion approximations do not give good approximation for the exercise boundary in whole option alive time, although they have high accuracy in very short time near to the expiry. Comparison of discrete time model and continuous time model offers the observation that discrete boundary is shifted into continuation region of the American option from continuous boundary. This result is in consistent with barrier options study in discrete and continuous time setting.
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