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研究生:林淑貴
研究生(外文):Shu-Kuei Lin
論文名稱:不連續股價下變異數交換之定價與避險
論文名稱(外文):The Valuation and Hedging of Variance Swaps with Jumps in Returns and Volatility
指導教授:張傳章張傳章引用關係
指導教授(外文):Chuang-Chang Chang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:財務金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
畢業學年度:93
語文別:英文
論文頁數:36
中文關鍵詞:不連續混和過程NGARCH(11)跳躍模型定價避險
外文關鍵詞:JumpPricingMixed processNGARCH(11)-Jump modelHedge
相關次數:
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在這篇論文中,我們推導一個對股價報酬的變異數交換做定價公式,
並且與Carr and Wu(2004)此篇論文中的定價公式在相同的架構之下做比較。
此外,我們也在Duan, Ritchken and Sun (2004)所提出假設股價報酬跟變異數都產生內容的
NGARCH(1,1) 不連續模型之下,推導出對變異數交換的定價公式。
我們也發現,跳躍現象的發生在變異數跟報酬均不連續的情況之下,
對變異數交換的價格有明顯的影響。
In this paper we developed a model for valuing variance swaps with jumps in the returns of underlying asset.
We compare our simulation results with those of Carr and Wu (2004) model under the same framework.
We find that our model value of variance swap contracts are very close to those of Carr and Wu model.
We then applied Duan, Ritchken and Sun (2004) GARCH jump framework which analyzes which jumps could happen in both asset return and volatility
to develop a more general model for valuing variance swaps.
From the simulation results, we find that both jumps in return and volatility will significantly affect the values of variance swaps.
Contents
1 Introduction 1
2 Variance swaps 3
2.1 How to price variance when the underlying asset price is continuous . 3
2.2 Hedging for Variance Swaps . . . . . . . . . . . . . . . . . . . . . . . 6
3 Pricing variance swaps when underlying stock return processes are
discontinued 6
3.1 The mixed processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 Hedging for Variance Swaps under Mixed-Jump Process . . . . . . . . 10
3.5 The Comparison of our Model and Carr-Wu (2004) model . . . . . . 10
4 Pricing Variance Swaps When the Underlying Stocks Return Processes
Follow GARCH Jump Model 12
4.1 A NGARCH(1,1) Jump Model . . . . . . . . . . . . . . . . . . . . . . 12
4.2 Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3 Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4 Hedging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5 Conclusion 18
References 20
A The proof of equations (26)-(27) 22
B The proof of equation (40) 23
C The proof of equation (41)-(42) 24
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of Political Economy 81, pp.637-654.
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Brenner, M., and D. Galai, 1989,”New financial instruments for hedging changes
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Carr, P., and Wu, Liuren, 2004, ”Variance Risk Premia”.
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Carr, P.,and D. Madan, 1998, ”Towards a theory of volatility trading”, Volatility, Risk
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Merton, R. 1976, ”Option pricing when underlying returns are discontinues”, Journal
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in Finance (S.T. Rachev, ed.),Elesevier/North-Holland.
Sulima, C., 2001, ”Volatility and variance swaps”, Capital Market News, Federal Reserve
Bank of Chicago.
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