隨機波動性下障礙選擇權之評價分析

Pricing Barrier Options Under Stochastic Volatility

10.6545/JoFS.2000.8(3).2

張傳章(Chuang-Chang Chang)；張森林(San-Lin Chung)；許博翔(Bor-Shayang Hsu)

障礙選擇權 ； 隨機波動性 ； 常數彈性變異數 ； Barrier Options ； Stochastic Vohitility ； Constant Elasticity Variance

中國財務學刊

8卷3期（2000 / 12 / 31）

41 - 77

繁體中文

文獻上有關障礙選擇權訂價方法之探討者眾，其中Boyle-Tian（1999）利用變數轉換技巧，成功地建構一個可以計算常數彈性變異數（Constant Elasticity Variance）之障礙選擇權訂價模型，本文之貢獻在於將Hilliard- Schwartz（1996）之隨機波動性簡單型選擇權訂價模型，加以擴展至障礙選擇權的訂價之上，此外，我們亦驗證了Hillard-Schwartz和Boyle-Tian的模型，在特定參數設定下為本文模型的一個特例，再則，由模擬結果得知，隨機波動性對障礙選擇權價格的影響程度，遠較對簡單型選擇權價格的影響程度來得大。

There are tremendous papers to construct models for valuing barrier options. Recently, Boyle and Tian (1999) used change variable technique to succeed in building a model, which is able to value barrier options under constant elasticity variance process. The contribution of this paper is to extend the Hilliard and Schwartz's (1995) plain vanilla option pricing model with stochastic volatility to the case of barrier options. We also show that both the Hilliard and Schwartz's model and Boyle and Tian's model are special cases of our model under some specifications of pararreters. From the simulation results. we find that the stochastic volatility effects for barrier options are much larger than those of plain vanilla options

1. Bakshi, G.,Cao, C.,Chen, Z.(1997).Empirical Performance of Alternative Option Pricing Models.Journal of Financial Economics,52,2003-2049.
2. Black, F.,M. Scholes.(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy,3,637-654.
3. Boyle, P. P. March(1988).A Lattice Framework for Options with Two State Variables.Journal of Financial and Quantitative Analysis,23,1-12.
4. Boyle, P. P.,S. H. Lau.(1994).Bumping Up against the Barrier with the Binomial Method.Journal of Derivatives,2,6-14.
5. Boyle, P. P.,Y. S. Tian(1999).Pricing Lookback and Barrier Option under the CEV Process.Journal of Financial and Quantitative Analysis,34,241-264.
6. Cheuk, T. H. F.,T. C. F. Vorst(1994).Real-Life Barrier Option.Erasmus Univ:Rotterdam, the Netherlands.
7. Cheuk, T. H. F.,T. C. F. Vorst(1996).Complex Barrier Option.Journal of Derivatives,4,8-22.
8. Cox, J. C.(1996).special issue honoring Fischer Black, “The Constant Elasticity of Variance Option Pricing Model.Journal of Portfolio Management,22,15-17.
9. Cox, J. C.(1975).Notes on Option PricingⅠ:Constant Elasticity of Variance Diffusions.Stanford Univ.
10. Cox, J. C.,S. A. Ross,M. Rubinstein.(1979).Option Pricing: A Simplified Approach.Journal of Financial Economics,7,229-264.
11. Derman, E.,I. Kain,D. Ergener,I. Bardhan.(1995).Enhanced Numerical Methods for Options with Barriers.Financial Analysts Journal,51,65-74.
12. Duan, J.(1995).The GARCH Option Pricing Model.Mathematical Finance,5,13-32.
13. Engle, R.(1982).Autoregressive Conditional Heteroscedacity with Estimates of the Variance of UK Inflation.Econometrica,50,987-1108.
14. Hilliard J. E.,A. Schwartz.(1996).The Journal of Derivatives.
15. Hull, J.,A. White.(1988).An Analysis of the Bias in Option Pricing Caused by Stochastic Volatility.Advances in Futures and Option Research,3,27-61.
16. Hull, J.,A. White.(1987).The Pricing of Option on Assets with Stochastic Volatilities.Journal of Finance,42,287-300.
17. Kamrad, B.,P. Ritchken.(1991).Multinomial Approximating Models for Options with k-State Variables.Management Science,37,1640-1652.
18. Merton, R. C.(1973).Theory of Rational Option Pricing.Bell Journal of Economics and Management Science,4,141-183.
19. Nelson D. B.,K. Ramaswamy.(1990).Simple Binomial Processcs as Diffusion Approximations in Financial Models.Review of Financial Studies,3,393-430.
20. Ritchken, P.(1995).On Pricing Barrier Options.Journal of Derivatives,3,19-28.
21. Rubinstein, M.E.(1976).The Valuation of Uncertain Income Streams and the Pricing of Options.Bell Journal of Economics,7,407-425.
22. Scott, L.(1996).Journal of Derivatives.
23. Sharpe, W. F..Investments.
24. Valuing Derivative Securities Using the Explicit Finite Difference Method(1990).Journal of Financial and Quantitative Analysis.25,87-100.

1. Shih-Kuei Lin(林士貴);Kendro Vincent(羅秉政);Chung-Jen Lin(林崇仁);Zong-Wei Yeh(葉宗瑋)(2024)。Delta Hedging in the USD/JPY Options Market: Insights from Implied Stochastic Volatility。管理評論。43(3)。1-17。