Title page for 90428014


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Student Number 90428014
Author Kun-Yi Ko(柯坤義)
Author's Email Address kunyi@ms30.url.com.tw
Statistics This thesis had been viewed 3073 times. Download 2326 times.
Department Finance
Year 2002
Semester 2
Degree Master
Type of Document Master's Thesis
Language English
Title Fast Accurate Option Valuation Using
Gaussian Quadrature
Date of Defense 2003-06-03
Page Count 55
Keyword
  • exotic option
  • GARCH model
  • numerical quadrature
  • option pricing
  • Abstract This paper develops an efficient and accurate method for numerical evaluation of the
    integral equations in option pricing problems. We suggest using the Gaussian
    quadratures, the highest order method in numerical integration, to approximate the
    option values. The idea of Gaussian quadratures is to give ourselves the freedom to
    choose not only the weight coefficients, but also the location of the abscissas at
    which the function is evaluated. It turns out that we can achieve Gaussian quadrature
    formulas whose convergence order is, essentially, twice that of Newton-Cotes
    formula (such as the Simpson's rule) with the same number of points. The numerical
    results are extremely well for a broa d range of options and underlying asset price
    processes. With this powerful tool, it would be possible to extract information such
    as implied volatility from the market prices of American options and other exotic
    options.
    Table of Content II
    Abstract ...........................................................................................................................I
    List of Tables................................................................................................................III
    List of Graph ................................................................................................................III
    1. Introduction:................................................................................................................I
    2. Literature Review:...................................................................................................... 4
    3.Gauss-Legendre formula :....................................................................................... 9
    4. Compare of Gaussian quadrature Method and AWDN’s Simpson Method............. 11
    4.1 Illustration of Gaussian quadratue Method .................................................... 11
    4.2 Single observation :European call case......................................................12
    4.3 Multiply observations: ................................................................................16
    4.3.1 Bermudan put case : ........................................................................17
    4.3.2 Other exotic options in AWDN’s paper ..............................................19
    Case 1: Discrete barrier option.............................................................20
    Case 2: Moving barrier option .............................................................21
    Case 3: Compound call option .............................................................22
    Case 4: American call option with changing strike price ....................23
    Case 5: American option with dividends .............................................25
    5.1 Reset option....................................................................................................35
    5.2 knock-in option ..............................................................................................41
    5.3 Pricing option with two underlying assets:....................................................42
    5.4 GARCH Model: .............................................................................................44
    References ....................................................................................................................54
    Reference [1] Abramowitz, M., and I.A. Stegun (ed.), 1964 Handbook of Mathematical
    Functions, National Bureau of Standa rds Applied Mathematics Series 53, USGPO,
    Washington, D.C.
    [2] Andricopoulos Ari D., Widdicks Martin, Duck Peter W., Newton David P.,
    Universal Option Valuation Using Quadrature Methods.
    [3] Black, F., and M. Scholes, 1973, The Pricing of Options and Cor porate Liabilities,
    Journal of Political Economy, 81, 637-654.
    [4] Broadie Mark, Detemple Jerome, 1996, American Option Valuation: New Bounds,
    Approximations, and a Comparison of Existing Methods, Review of Financial Studies,
    Vol.9, No.4, pp.1211-1250.
    [5] Duan Jin-Chuan, Simonato Jean-Guy, 2001, American option pricing under
    GARCH by a Markov chain approximation, Journal of Economic Dynamics &
    Control 25, 1689-1718.
    [6] Figlewski Stephen, Gao Bin, 1999, The adaptive mesh model: a new approach to
    efficient option pricing, Journal of Financial Economics 53, 313-351.
    [7] Heston Steve, Zhou Guofu, 2000, On The Rate Of Convergence Of Discrete-Time
    Contingent Claims, Mathematical Finance, Vol. 10, No. 1, 53-75.
    [8] Hull, J., 2000, Options, futures, and other derivatives, fourth edition, Prentice Hall.
    [9] Longstaff Francis A., Schwartz Eduardo S., 2001,Valuing American Options by
    Simulations: A Simple Least-Squares Approach, Review of Financial Studies Vol.14,
    No. 1,113-147.
    [10] Press,W., S.Teukolsky, W.Vetterling, and B. Flannery, 1992, Numerical Recipes
    in C 2nd Editon, Cambridge University Press, New York.
    [11] Sullivan Michael A., Pricing Discretely Monitored Barrier Options.
    [12] Sullivan Michael A., 2000, Valuing American Put Options Using Gaussian
    Quadrature,, Review of Financial Studies Vol. 13, No.1, 75-94.
    [13] Pearson Neil D., 1995, An Efficient Approach For Pricing Spread Options, The
    Journal Of Derivatives, 76-91.
    Advisor
  • Chuang-Chang Chang(張傳章)
  • San-Lin Chang(張森林)
  • Files
  • 90428014.pdf
  • approve immediately
    Date of Submission 2003-06-19

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