券商和投資大眾越來越了解價格風險管理的重要性，但是對於波動度風險管理工具及其重要性的認知卻較為貧乏。論文探討的即是美歐新興的波動度管理工具：波動度交換契約(volatility swaps)和變異數交換契約(variance swaps)。藉著波動度交換契約，交易者就可以將所暴露的不確定風險轉換為固定的風險。

論文的焦點在於變異數交換契約(variance swaps)公平履約價的訂定。文章中所使用的評價方法是複製法(replictions strategy)，在唯一的假設條件下：股價的變動是連續的，用已知的金融商品複製成新的商品，而複製成本也就是變異數交換契約的公平價格。

在完美的市場中，我們用履約價從零到無限大的選擇權複製變異數交換契約，但是現實的情況下並不允許如此，改用有限範圍的選擇權複製其損益。故再加以討論當假設不成立：股價跳空時，以及用有限範圍履約價對複製策略的影響。

而波動度交換契約(volaility swaps)不管在理論上或是實務上的評價、避險的難度都遠高於變異數交換契約，在第七章節中，引用泰勒展開式和Heston的波動度模型，求得波動度交換契約公平履約價Kvol的評價公式。

一、中文部分：

1.、 寶來金融創新雙月刊 p31-p38 ‘波動性風險可以規避嗎？’ 陳凌鶴、林瑞瑤

2 、國際金融市場泛論與分析 陳松男著

3 、選擇權與期貨：衍生性商品 陳松男著

4 、期貨市場分析 朱浩民著

二、英文部分：

1. Black F, and M Scholes, 1973 ‘The pricing of options and Corporate liabilities” Journal of Political Economy 81, pages 637-659.

2. Carr P ,and D Madan, 1999 “Introducing the covariance swaps” Risk February, pages 47-51

3. Chriss N ,and W Morokoff, 1999 “Market risk for variance swaps” Risk October, pages 55-59

4. Derman E, 1999 “Regimes of volatility” Risk April, pages 55-59

5. Demeterfi K, E Derman, M Kamal and J Zou, 1999 “A guide to variance swaps”Risk June, pages 54-49

6. Dupire B, 1993 ” Model art risk” Risk September, pages 118-120

7. Andreas Grynbichler, Francis A, Longstaff, 1995, “Valuing futures and options on volatility”. Journal of Banking & Finance 20.

8. Carr, P., and D. Madan. “Towards a Theory of Volatility Trading.” In R. Jarrow, ed. Volatility: New Estimation Techniques for Pricing Derivatives. London: Risk Books, 1998, pp. 417-427.

9. Brenner, M., and D. Galai 1989, “New Financial Instruments for Hedging changes in Volatility”, Financial Analysis’s Journal , July-August, pp.61-65.

10 Demeterfi K., E. Derman, M. Kamal and J. Z. Zou, 1999”A guide to Volatility and Variance Swaps.” Journal of Derivatives, summer pp.9-32.

11. Derman, E. and I. Kani. “Riding on a Smile.” Risk. 7, No. 2 (1994), pp.32-39.

─. “Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility.” International Journal of Theoretical and Applied Finance, Vol. 1, No. 1 (1998), pp. 61-110.

12 Neuberger, A. “The Log Contract: A New Instrument to Hedge Volatility.” Journal of Porfolio Management, Winter 1994, pages 74-80.

13 Neuberger, A. 1996. “The Log Contract and Other power Contracts “The Handbook of Exotic Options. Chicago: Irwin Professional Publishing, pages 220-212.

14 Oilver Brockaus and Douplas Long 2000 ‘Volatility Swaps Made Simple' Risk , January, pages 118-120

15 Jim Gatheral “Case studies in Financial course Notes” Spring 2000,Merrill Lynch

16 Bemd Rolfes and Eric Henn ,1999 “A vega nation.” Risk December, pages 26-28

17 Whaley R, 1993 “Derivatives on market volatility :hedging tools long overdue.” Journal of Derivatives, fall, pages 71-84

18 Cheryl L.Sulima , 2001 “Volatility and Variance Swaps” Capital Markets .News, Federal Reserve Bank of Chicago,March ,pages 1-4

19 Nina Mehta “Equity Vol Swaps Grow UP.”, Derivatives Strategy Magazine , July 1999

20 Dean Curnutt “The Art of the Variance swaps ” Derivatives Strategy Magazine , February 2000