臺灣博碩士論文加值系統

隨著科技的進步，金融創新的腳步愈走愈快，金融市場亦日趨競爭，風險管理於是日益重要。風險管理中金融機構對於未預期損失部分所提列的資本保護，吾人稱之為風險資本；而現行的風險值便是衡量此風險資本的一種方法。本論文延續 Merton and Perold (1993) 之「金融機構風險資本理論」－ 以選擇權評價方式衡量風險資本的架構下,對現行的風險值方法提出比較。再者，以選擇權評價方式衡量風險資本的架構下，因應較長的到期日（通常為一年），應考慮隨機利率的效果；本論文採用 Duan and Simonato (2002) 的存款保險評價模型，導出隨機利率經濟環境中風險資本評價的封閉解，並以 Don Mcleish (2005) 的高效率蒙地卡羅模擬法來加以支持。最後，以台灣銀行為例子並將以 Duan and Simonato (2002) 的兩階段最大概似估計法所估出的參數代入封閉解來進行實證分析並獲得結果。

Improved computer and telecommunicatoins technology, advances in the theory of finance, and new financial product designs have led to highly competitive financial market, and risk management has become more and more important. In risk management, the term "risk capital" is to provide protection against unexpected losses; and value at risk is the prevailing method that provides a useful
proxy for risk capital. In this thesis, starting from a proposal by Merton and Perold (1993), "Theory of Risk Capital in Financial Firms" - an option-based approach, we make a comparison with the prevailing value at risk method. Furthermore, for pricing a long-term maturity option, the consideration of a stochastic interest rate effect should be taken. Similar to Duan and Simonato (2002) depository insurance pricing model, in this thesis, we have derived the closed-form solution for risk capital valuation supported by Don Mcleish (2005) high efficiency Monte-Carlo simulation. Via the Duan and Simonato (2002) maximum-likelihood estimation methodology, this closed-form solution is performed on the Taiwan banks empirical study in the last part of this thesis.

Acknowledgement . . . . . . . . . . . . . . . . . . . . i
Chinese Abstract . . . . . . . . . . . . . . . . . . . .ii
English Abstract . . . . . . . . . . . . . . . . . . . iii
Notations . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction . . . . . . . . . . . . . . . . . . . . . 1
2 Literature Review - The Theory of Risk Capital . . . . 5
3 The Constant Interest Rate Model . . . . . . . . . . . 8
3.1 Value at Risk Methodology . . . . . . . . . . . . . .8
3.2 Merton and Perold''s Framework . . . . . . . . . . . 11
4 The Stochastic Interest Rate Model . . . . . . . . . 22
4.1 Closed-Form Solution . . . . . . . . . . . . . . . 23
4.1.1 Closed-form for default-free zero-coupon bond . . 23
4.1.2 Closed-form for risk capital as a put option . . 29
4.2 Monte-Carlo Simulation . . . . . . . . . . . . . . 38
4.3 Risk Capital Estimation with MLE . . . . . . . . . 44
4.3.1 Unobservable parameters estimation . . . . . . . 44
4.3.2 Duan and Simonato (2002) MLE two-step procedure . 45
5 Empirical Study . . . . . . . . . . . . . . . . . . . 48
5.1 Data and Assumptions . . . . . . . . . . . . . . . 48
5.1.1 Interest rate . . . . . . . . . . . . . . . . . . 48
5.1.2 Sample banks . . . . . . . . . . . . . . . . . . 50
5.1.3 Assumptions . . . . . . . . . . . . . . . . . . . 50
5.2 Empirical Results . . . . . . . . . . . . . . . . . 51
6 Conclusion . . . . . . .. . . . . . . . . . . . . . . 60
References . . . . . . . . . . . . . . . . . . . . . . 62
Appendix A . . . . . . . . . . . . . . . . . . . . . . 64
Appendix B . . . . . . . . .. . . . . . . . . . . . . . 65
Appendix C . . . . . . . . . . . . . . . . . . . . . . 66

[1] Black, F., and Scholes, M. The pricing of options and corporate liabilities. Journal of Political Economy 81 (1973), 637–659.
[2] Brigo, D., and Mercurio, F. Interst rate models : theory and practice. Springer, 2001.
[3] Cairns, A. J. G. Interest rate model : an introduction. Princeton University Press, 2004.
[4] Culp, C. L. The art of risk management : alternative risk transfer, capital structure, and the convergence of insurance and capital markets. Wiley-Finance, 2002.
[5] Duan, J. C., and Simonato, J. G. Maximum likelihood estimation of deposit insurance value with interest rate risk. Journal of Empirical Finance 9, 1 (2002), 109–132.
[6] Hull, J. C. Options, futures, and other derivatives, 5 ed. Prentice-Hall, 2003.
[7] Jorion, P. Value at risk. McGraw-Hill, 2000.
[8] Lin, Y. C. Deposit insurance premium under stochastic interest rate : An empirical study of Taiwan’s banks. Master’s thesis, Yuan-Ze University, 2003.
[9] Mcleish, D. L. Monte carlo simulation and finance. Wiley-Finance, 2005.
[10] Merton, R. C. A functional perspective on financial intermediation. Financial Management 24 (1973), 23–41.
[11] Merton, R. C. On the pricing of corporate debt : The risky structure of interest rate. Journal of Finance 29 (1974), 449–470.
[12] Merton, R. C., and Perold, A. F. The theory of risk capital in financial firms. Journal of Applied Corporate Finance 5 (1993), 16–32.
[13] Perold, A. F. Capital allocation in financial firms. Journal of Applied Corporate Finance 17, 3 (2005), 110–118.
[14] Rabinovitch, R. Pricing stock and bond options when the default-free rate is stochastic. Journal of Financial and Quantitative 24 (1989), 447–457.
[15] Ronn, E. I., and Verma, A. K. Pricing risk-adjusted deposit insurance : An option-bases model. Journal of Finance 41 (1986), 871–895.
[16] Vasicek, O. An equilibrium characterization of term structure. Journal of Financial Economics 5 (1977), 177–188.