A Market Model for Stochastic Implied Volatility and Volatility swap

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：116

、訪客IP：3.16.137.38

姓名

張書瑋(shu-way chang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(A Market Model for Stochastic Implied Volatility and Volatility swap)

相關論文

★ 群集二元資料下的同質性檢定	★ 回溯性抽樣下羅吉斯迴歸模型的適合度檢定
★ 利用EM演算法分析公元2000年總統大選民調資料	★ 用統計方法看兩千年總統大選選舉策略的效應
★ Case-Control 資料下羅吉斯迴歸模型的統計推論	★ 最佳投資組合研究-以台股為例
★ 病例－對照研究之貝氏分析	★ 美式選擇權定價調整法-利用拔靴法
★ 利用高斯數值方法估計美式賣權價格	★ 最佳投資組合研究-以台灣50指數為例
★ 傳遞-不平衡相關檢定在錯誤基因型資料之表現	★ 隱含波動率之模型及預測：以台灣市場為例
★ 病例－對照分析之基因研究	★ KMV and Maximum Likelihood Methods for Structural Credit Risk Models: Evidence from Taiwan Market
★ 多重基因－疾病關聯性檢定之研究

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

過往研究波動率大都是拿部分的市場資料，帶入特定的模型內求出其隱含波動率；在近幾年對於波動率的研究中，有了新的方法(model-free implied volatility)來求其隱含波動率，此方法是利用市場上選擇權所有的市場資料，帶入簡單的運算來算出其隱含波動率．在這篇論文中，用此新方法從台指選擇權的算出其隱含波動率，再找出符合其隱含波動率走勢的模型，進而應用在波動率交換契約上的訂價和避險．

摘要(英)

In this paper a class of stochastic volatility models was presented that is based on model-free implied volatilities that are observed in the price of TX options, and identify the process that describes well the evolution of model-free implied volatility in continuous time. We have compared various diffusion and jump diffusion processes. We price the volatility swap contract with MRSRPJ model in risk neutral world and calculate the price of the volatility swap.

關鍵字(中)

關鍵字(英)

★ stochastic volatiliy
★ model-free implied volatility
★ volatility swap
★ vix

論文目次

1. Introduction 1
2. Volatility 4
2.1 Variance Swap………………....................................4
2.2 Volatility Index……………………...………………7
2.3 Model-free Implied Volatility……………………...........8
2.4 Stochastic Volatility Processes…………………….........10
3. Data Description 12
4. The Method Of Estimate 15
4.1 The Estimation of Diffusion Processes……………...........16
4.2 The Estimation of Jump-Diffusion Processes…………........17
5. Results and discussion 19
5.1 MLE results............................................................19
5.2 volatility swap with the best model…………...................23
6. Conclusions 26
References 27
Appendix 30

參考文獻

Ait-Sahalia, Y. (2004). “Disentangling Diffusion from Jumps”, Journal of Financial
Economics, 74, 487-528.
Ball, A. C., and Torous W. N. (1985). “On Jumps in Common Stock Prices and Their
Impact on Call Option Pricing”, Journal of Finance, 40, 155-173.
Bakshi, G., and Cao, C. (2004). “Risk-Neutral Kurtosis, Jumps, and Option Pricing:
Evidence from Most Actively Traded Firms on the CBOE”, Working Paper, University of Maryland.
Black, F. (1976). “Studies of Stock Price Volatility Changes”, in Proceeding of the 1976 Meetings of the Business and Economic Statistics Section, American Statistical Association, 177-181.
Bollerslev (1986). “Generalized autoregressive conditional heteroskedasticity”, Journal
of Econometrics, 31, 307-327.
Broadie, M., Chernov, M., and Johannes, M. (2004). “Model Specification and Risk
Premiums: The Evidence from the Futures Options”, Working Paper, Columbia Business School.
Britten-Jones, M., and A. Neuberger, 2000, "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, 55, 839–866
Brockhaus, O. and Long, D. (2000): "Volatility swaps made simple", RISK, January, 92-96.
Campbell, John Y., Andrew W. Lo and A. Craig McKinley (1997), “The Econometrics of Financial Markets”, Princeton University Press.
Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1985). “A Theory of the Term Structure of Interest Rates”, Econometrica, 53, 385-408.
Das, S. R. (2002). “The Surprise Element: Jumps in Interest Rates”, Journal of
Econometrics, 106, 27-65.
Dotsis, George, Psychoyios, Dimitris and Skiadopoulos, George S., "Implied Volatility Processes: Evidence from the Volatility Derivatives Markets" (August 2006)”. Available at SSRN: http://ssrn.com/abstract=796192
Duffie, D., Pan, J., and Singleton, K. (2000). “Transform Analysis and Asset Pricing for Affine Jump-Diffusions”, Econometrica, 68, 1343-1376.
Eraker, B., Johannes M., and Polson N. (2003). “The Impact of Jumps in Volatility and Returns”, Journal of Finance, 53, 1269-1300.
Elerian, O., Chib, S., and Shephard, N. (1999), “Likelihood Analysis of Discretely Observed Diffusions,” working paper, Nuffield College, Oxford University.
Engle R.F. (1982). "Autoregressive conditional heteroscedasticity with estimates of the
variance of United Kingdom ination" Econometrica 50,987-1007.
G. Sandmann, SJ. Koopman (1998), “Estimation of Stochastic Volatility models through Monte Carlo Maximum Likelihood”, Journal of Econometrics.
Gallant and Tanchen (1996), "Testing continuous-time models of the spot interest rate[J]". Review of financial. studies, 1996, 3:197-215
George J. Jiang and YS Tian (2005). "The Model-Free Implied Volatility and Its Information Content". The Review of Financial Studies, vol. 18 #4, Winter 2005, pages 1305-1342.
H. Windcliff, K. Vetzal (2002). “Pricing methods and hedging strategies for volatility”, derivatives Journal of Banking and Finance 30 (2006) 409-431.
Hansen, L.P. (1982): "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, 50(4), 1029-1053.
Harvey, A.C. ., Ruiz, E., and Shephard, N. (1994) "Multivariate stochastic variance models", Review of Economic Studies 61, 247-264.
Hull, J. C., and White, A. (1987). “The Pricing of Options with Stochastic Volatility”,
Journal of Finance, 42, 281-300.
Howison, Sam, Avraam Rafailidis, and Henrik Rasmussen, 2004, On the pricing and
hedging of volatility derivatives, Applied Mathematical Finance, 11, 317-346 (2004).
Javaheri, A., Wilmott, P. and Haug, E. (2002): GARCH and volatility
swaps, Wilmott Technical Article, January, 17p.
Johnson, H., and Shanno, D. (1987). “Option Pricing When the Variance is Changing”, Journal of Financial and Quantitative Analysis, 22, 143–151.
Kou, S., G. (2002). “A Jump-Diffusion Model for Option Pricing”, Management Science, 48 1086–1101.
Kim, Shephard and Chib (1998), "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models", Review of Economic Studies 65, 361-393.
Merton, R. C. (1976). “Option Pricing when Underlying Stock Returns are
Discontinuous”, Journal of Financial Economics, 3, 125-144.
Melino, A. and and Turnbull S.M. (1990) “Pricing foreign currency options with stochastic volatility”, Econometrics 45, 239-265.
Nelson, D.B. (1990),” ARCH models as diffusion approximations”, Journal of Econometrics 45, 7-38.
P. Carr and K. Lewis. (2002), "Corridor variance swaps", Working Paper, 2002.
Polson and Rossi (1994). "Bayesian Analysis of Stochastic Volatility Models", Journal of Business & Economic Statistics, October 1994, Vol. 12, No. 4.
Peter Carr and Dilip Madan (2002). “Towards a Theory of Volatility Trading”, Volatility edited by Robert A. Jarrow, Risk Books.
Pedersen A.R. (1995), “A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations”. Scand. J. Statistics 22, 55-71.
Swishchuk, A. (2004), “Modeling of Variance and Volatility Swaps for Financial Markets with Stochastic Volatilities”, 19 p. (accepted for publication by "WILMOTT Serving the Quantitative Finance Community", www.wilmott.com)
W. Härdle; P. Schmidt (2000). “Common Factors Governing VDAX Movements and the Maximum Loss”, Quantification and Simulation of Economic Processes 97
(SFB 373 Papers)
Windcliff and Vetzal (2002), ”Pricing Methods and Hedging Strategies for Volatility Derivatives”
Yu, J. (2004). “Empirical Characteristic Function Estimation and Its Applications”,
Econometric Reviews, 23, 93-123.
Yacine Aït-Sahalia (1996), “Nonparametric pricing of interest rate derivative securities”, Econometrica, Vol. 64, No. 3, 527-560
Yacine Aït-Sahalia (2004). "Disentangling diffusion from jumps", Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528.
謝志輝 (2005). “指數變動及星期效應對隱含波動度變化之影響- 以台指選擇權為例”, 中央大學企業管理學研究所

指導教授

鄭光甫(K.F. Cheng)

審核日期

2006-6-26

推文