博碩士論文 103428030 詳細資訊




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姓名 謝明翰(Ming-Han Heish)  查詢紙本館藏   畢業系所 財務金融學系
論文名稱
(PRICING DYNAMIC GUARANTEED FUND WITH JUMP RISK AND INTEREST RATE RISK)
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摘要(中) 摘要
本文主要在討論基金價格的利率風險以及跳躍風險,文章中假設標的基金價格服從雙重指數跳躍擴散過程,另外假設利率過程服從Vasicek model。文章中推導出動態保本型基金的價格公式,並利用Laplace轉換求出價格封閉解,最後利用Gaver-Stehfest演算法進行拉普拉斯逆轉換,有效求出動態保本型基金價格。
最後文章中給出了敏感性分析,分析了在不同參數之下利率以及跳躍過程對基金價格的影響。而我們發現無論是利率風險或是跳躍性擴散風險均會對基金價格造成相當程度的影響。
摘要(英) In this thesis we discuss how the interest rate risk and jump diffusion risk effect the value of dynamic guaranteed fund. We assume the dynamic underlying of the guaranteed fund follows a double exponential jump process and stochastic interest rate process follows Vasicek model. We then derive the dynamic guaranteed fund’s pricing formula, and use Laplace transform to obtain closed-form solution. Finally, in order to calculate more efficiently, we apply Gaver-Stehfest algorithm to Laplace inverse to obtain dynamic guaranteed fund values. We also provide numerical results. We analyze the different results with different jump-related parameters and interest rate-related parameters. We find that both of the interest rate risk and jump risk can significantly affect the value of dynamic guaranteed funds.
Key Words: Dynamic Guaranteed Fund, Vasicek Model, Double Exponential Jump, Laplace Transform, Gaver-Stehfest Algorithm
關鍵字(中) ★ 動態型保本基金
★ 隨機利率
★ 跳躍過散
★ 拉普拉斯轉換
關鍵字(英)
論文目次 Contents
1. Introduction p.1
2. The Double Exponential Jump Diffusion Model p.3
3. The Valuation of Dynamic Guaranteed Funds p.8
4. Numerical Result p.15
5. Conclusion p.24
6. Reference p.25
7. Appendix p.27

參考文獻 [1] Abudy, M. and Y, Izhakian (2011), “Pricing Stock Options with Stochastic Interest Rate,” NYU Working Paper No. 2451/30272.
[2] Carr, P., and D. B. Madan (1999), “Option Valuation using the Fast Fourier Transform,” Journal of Computational Finance, 2, pp.61-73
[3] Chang, C.C., Lian, Y.H., Tsay, M.H. (2012), “Pricing Dynamic Guaranteed Funds under a Double Exponential Jump Diffusion Model,” Academia Economic Thesiss, 40, pp.269-306.
[4] Dong, Y (2013), “Pricing Dynamic Guaranteed Funds with Stochastic Barrier under Vasicek Interest Rate Model”, Chinese Journal of Applied Probability and Statistics, 29(3), pp237-245.
[5] Gerber H. U., and G. Pafumi (2000), “Pricing dynamic investment fund protection”, North American Actuarial Journal, 4(2), pp. 28–36.
[6] Gerber, H. U. and E. S. Shiu (1998), “Pricing Perpetual Options for Jump Process,” North American Actuarial Journal, 4(2), 101–112.
[7] Gerber, H. U. and E. S. Shiu (1999), “From Ruin Theory to Pricing Reset Guarantees and Perpetual Put Options,” Insurance: Mathematics and Economics, 24, 3-14.
[8] Kou, S. G. (2002), “A jump diffusion model for option pricing”, Management Science, 48, pp. 1086–1101.
[9] Kou, S. G. (2008), “Jump-Diffusion Model for Option Pricing,” Management Science, 48, 1086-1101.
[10] Kou, S. G., and H. Wang (2003), “First passage times for a jump diffusion process”, Advances in Applied Probability, 35, pp. 504–531.
[11] Kou, S. G., and H. Wang (2004), “Option Pricing Under a Double Exponential Jump Diffusion Model,” Management Science, 50, 1178-1192.
[12] Merton, R. (1976), “Option Pricing When the Underlying Stock Returns Are Discontinuous,” Journal of Financial Economics, 3, 125-144.
[13] Rabinovitch R. (1989), “Pricing Stock and Bond Options when the Default-Free Rate is Stochastic,” The Journal of Financial and Quantitative Analysis, 4, 447-457.
[12] Vasicel Oldrich (1997). An equilibrium characterization of term structure. Journal of Financial Economics, 5, pp.177 – 188.
指導教授 張傳章 審核日期 2016-7-6
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