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| Title: | 上限型股權連結保本票券之評價、避險和風險控管
Valuation, Hedge and Risk Management of Capped, Equity-linked and Principal-protected Notes |
| Authors: | 陳芬英
Chen, Fen-ying |
| Contributors: | 廖四郎
Liao, Szu-lang
陳芬英
Chen, Fen-ying |
| Keywords: | 上限型股權連結保本票券
Delta 跳躍
調整因子
路徑依賴
平賭過程評價法
避險策略
風險值
股價波動度之預測
風險控管
匯率風險
Capped equity-linked and principal-protected note
Delta jump
Adjustable factor
Path dependence
Martingale method
Hedging strategy
Value at risk
Forecast of volatility of stock price
Risk management
Exchange rate risk |
| Date: | 2004 |
| Issue Date: | 2009-09-18 19:21:16 (UTC+8) |
| Abstract: | 本論文含蓋三篇文章，分別從評價、避險和風險控管三方面，分析上限型股權連結保本票券。
第一篇文章為上限型股權連結保本票券之設計、評價和比較。本文考量投資人保守的投資行為與設限型股權連結票券所存在的delta跳躍(delta jump)現象，延伸Brennan and Schwartz (1976)模型，提出一個能在股價波動之際，使發行的避險部位delta呈現平滑變動且兼具保本(protected principal)功用的一般化模型(general form)。相較於一般的設限型股權連結保本模型，本模型具有以下特色。第一，加入股價成長率的調整因子(adjustable factor)，當景氣低靡，股價不停下跌時，正的調整因子可減緩股價下滑之勢，進而增加投資人在票券到期日時獲取更多資本利得(capital gain)的機會。同時，調整因子縮小了當期股價成長率與股價上限成長率(capped stock growth rate)之間的差距，繼而減緩delta 跳躍的幅度，降低發行者的避險成本。並且在HJM利率模型下，delta隨股價與股價波動度的變化更顯平滑(smooth)。第二，在保本率(protection rate)和參與率 (participation rate)不變之下，本模型的期初合理價格(fair price)較低，投資人能以較低的成本取得同等的投資保障。第三，若將本票券的名目面額(notional principal)視作共同基金(mutual fund)的淨值(net value)，而該淨值與股價連動，則本模型即成為股權連結的保本型基金(principal-protected fund)。
第二篇文章是路徑依賴之上限型股權連結保本模型之評價和風險測量。該文是擴展Brennan and Schwartz (1976)模型發展一個路徑依賴之上限型股權連結保本模型，並且提出一個比二元數模型更精確的封閉解。此外，也對七個時間序列進行股價波動度之精確檢定，得知AR-ARCH(1)模型對上限型股權連結保本票券而言，較其它時間序列模型，更能有效估計股價之波動度。
第二篇文章是外國資產的風險管理。目前在國內金融市場上，國外金融商品很多，大都以外幣計價，因此匯率風險是投資人不可忽視的因子。本文拓展Kupiec(1999)模型，將匯率風險加入模型中，使投資人更有效進行風險管理。
This thesis studies valuation, hedge and risk management of capped equity-linked and principal-protected notes by means of the following essays:
(1) Design, Valuation and Comparison of Capped Equity-linked and Principal-protected Notes
(2) Valuation and Risk Measurement of Capped Equity-linked and Principal-protected Notes with Path Dependence
(3) Risk Management of Foreign Assets
Capped equity-linked and principal-protected notes are similar with barrier options. There exists delta jump as stock price or growth rate reaches the barrier. But previous studies about equity-linked and principal-protected notes with a restricted growth rate of stock price never explicitly discussed how the delta jump could be solved. In my first essay, I present a new design for capped equity-linked and principal-protected notes and add an adjustable factor to growth rate of stock price in such a way that the adjustable factor narrows the gap between the current stock growth rate and the capped stock growth rate and thus really reduces the magnitude of the delta jump and hence lowers the hedging cost for brokers.
Recently, the focus of previous studies about principal-protected notes has been on either the restriction on the rate of stock return or the path dependence on the underlying asset, but not both in the same context. In my second essay, I develop a model on the capped, equity-linked and principal-protected notes with path dependence. There are two issues in this article. The first issue is valuation on the capped, equity-linked and principal-protected notes with path dependence. I find a closed-form approximation using the 2nd-order Taylor approximation and the method of Vorst (1992) that has higher accuracy than binomial tree model as maturity time or volatility becomes large. The second issue is risk measurement. I use VaR model to evaluate market risk of the principal-protected notes, and employ seven univariate time series models to forecast volatility and examine the accuracy.
Additionally, investors may well encounter potential loss as the prices of financial products are reduced in the secondary market. The VaR is mainly concerned with the downside risk and becomes a standard measure of financial market risk that is increasingly used by investors. But if we want to apply 〝textbook〞formulation to risk management of foreign assets, there leaves exchange rate risk out of consideration. Therefore, I extend the work by Kupiec (1999) to present VaR formula with exchange rate risk for foreign assets and then to manage market risk usefully. |
| Reference: | 1. Baillie RT, and T. Bollerslev, 1992. Prediction in Dynamic Models with Time-dependent Conditional Variances. Journal of Econometrics 52, p91-114.
2. Brennan, M.J. and E.S. Schwartz, 1976. The Pricing of Equity-Linked Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics 3, p195-213.
3. Brooks, C., 1998. Predicting Stock Index Volatility: Can Market Volume Help? Journal of Forecasting 17, p59-80.
4. Burth, S., T. Kraus and H. Wohlwend, 2001. The Pricing of Structured Products in the Swiss Market, Journal of Derivatives 4 (Winter), p30-40.
5. Chance, D.M., and J.B. Broughton, 1988. Market-Index Depository Liabilities: Analysis, Interpretation, and Performance. Journal of Financial Service Research, p335-352.
6. Chen, A.H. and J.W. Keinsinger, 1990. An Analysis of Market-Index Certificates of Deposit. Journal of Financial Service Research 4, No.2, p93-110.
7. Chen, A.H., J.A. Bennett and P. Mcguinness, 1996. An Analysis of Capital Guaranteed Funds, International Review of Economics and Finance 5, No.3, p259-268.
8. Chen, K. and R.S. Sears, 1990. Pricing the SPIN, Financial Management 19, No.2, p36-47.
9. Diebold, F.X. and R.S. Mariano, 1995. Comparing Predictive Accuracy. Journal of Business and Economic Statistics 13, p253-263.
10. Gerber, H.U. and G. Pafumi, 2000. Pricing Dynamic Investment Fund Protection. North American Actuarial Journal 4, No. 2, pp28-41.
11. Heath, D., R.A. Jarrow and A. Morton, 1992. Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation, Econometrica 60, p77-105.
12. Imai, J. and P.P. Boyle, 2001. Dynamic Fund Protection. North American Actuarial Journal 5, No. 3, p31-51.
13. Jorion, Philippe, 2000. The New Benchmark for Managing Financial Risk in Value at Risk. American, McGraw-Hill, Second edition
14. Kupiec, Paul, 1995. Techniques for Verifying the Accuracy of Risk Measurement Models. Journal of Derivatives 4 (Winter), p73-84.
15. Kupiec, Paul, 1999. Risk Capital and VaR. Journal of Derivatives 4 (Winter), p41-52.
16. Liao, S.L., R.B. Kon and G.C. Chang, 2003. Pricing and Hedging of Principal-protected Notes, Security and Futures Management 7, p1-10. (in Chinese )
17. Pandey, M.D., 1998. An effective Approximation to Evaluate Multinormal Integrals. Structural Safety 20, p51-67.
18. Taylor, J., 1999. Evaluating Volatility and Interval Forecasts. Journal of Forecasting 18, p111-128.
19. Vorst, T., 1992. Prices and Hedge Ratios of Average Exchange Rate Option. International Review of Financial Analysis 1, No. 3, p179-194.
20. West, KD. and D. Cho, 1995. The Predictive Ability of Several Models of Exchange Rate Volatility. Journal of Econometrics 69, p367-391.
21. Wilkens, S., C. Erner and K. Roder, 2003. The Pricing of Structured Products in Germany, Journal of Derivatives 3 (Fall), p55-69.
22. Zimmermann, H., 1996. Constant Return Participating (CRP) Portfolio Insurance Strategies. Journal of Derivatives 4 (Winter), p80-88. |
| Description: | 博士
國立政治大學
金融研究所
89352502
93 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0893525022 |
| Data Type: | thesis |
| Appears in Collections: | [金融學系] 學位論文
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