財務金融研究

Essays in Finance

張龍福(Lung-fu Chang)

指導教授 ： 洪茂蔚

國立臺灣大學/管理學院/國際企業學研究所/博士(2007年)

https://doi.org/10.6342/NTU.2007.10303

摘要

本篇論文主要探討關於選擇權的訂價與避險的議題。本篇論文包含二大主題:第一部份是考慮交易對手風險(Counterparty Risk)，以及選擇權標的物價格與選擇權發行者之資產價格具有關聯性之下，有關美式選擇權的評價模型之推導。本文在第一部份延續Klein(1996)文章中所提之架構，由具有交易對手風險的歐式選擇權(Vulnerable European Options)的評價模式推廣至考量交易對手風險的美式選擇權(Vulnerable American Options)之評價，以彌補Klein(1996)之訂價模型只能侷限在歐式契約下使用。並且利用本文之評價公式進一步探討具有交易對手風險的美式選擇權之敏感度分析，以及交易對手風險對於美式選擇權價格之影響；本文在第二部份假設選擇權標的物價格之價格波動乃是由漂移項(Drift Term)、布朗運動(Brownian Motion)、跳耀過程(Jump Process)之線性組合(Lévy process)的隨機過程，並納入利率風險，考慮在HJM(1992)之隨機利率(Stochastic Interest Rate)模型之架構下，推導出巨災選擇權的的封閉公式解(Closed-Form Solution)，同時利用公式解進一步來對巨災選擇權進行的價格評估與敏感度分析。

關鍵字

美式選擇權 ； 信用風險 ； 隨機利率 ； 巨災選擇權 ； 選擇權定價 ； 平賭過程

並列摘要

This thesis has contained two main parts. In the first section, this thesis follows the framework of Klein’s (1996) model to derive the analytical pricing formula for vulnerable American options based on the two-point Geske and Johnson method. The motivation for our extension of Klein’s (1996) model is that a number of financial derivatives in the over-the-counter market have American-style properties. We also perform the sensitivity analyses for vulnerable American options and demonstrate how the values of vulnerable American options vary with the correlation between the underlying asset of the option and the option writer’s asset. The second part of this thesis is to analyze values of catastrophe put options subject to interest rate risk when the underlying asset price is modeled through a Lévy process with finite activity. This thesis derives the explicit closed-form formulas for evaluating the value of a catastrophe put option and hedge parameters. The numerical examples exhibit how the financial risks and catastrophic risks affect the prices of catastrophe put options.

並列關鍵字

American options ； Derivatives ； Default ； Credit risk ； Multi-exercisable ； Martingale ； Catastrophe derivatives ； L&eacute ； vy process ； Stochastic interest rate ； Reinsurance ； Option pricing ； Time-changed L&eacute ； vy process

參考文獻

Bakshi, G., and D. B. Madan, 2000, “Spanning and derivative-security valuation.” Journal of Financial Economics, 55, 205-238.

Ballotta, L., 2005, “A Lévy process-based framework for fair valuation of participating life insurance contracts.” Insurance: Mathematics and Economics, 37, 173-196.

Barndorff-Nielsen, O. E., 1998, “Processes of normal inverse Gaussian type.” Finance and Stochastics, 2, 41-68.

Black, F. and M. Scholes, 1973, ‘‘The pricing of options and corporate liabilities.’’ Journal of Political Economy 81 , 637-654.

Bunch, D.S. and H. Johnson, 1992, ‘‘A simple and numerically efficient valuation method for American puts using a Geske-Johnson approach.’’ Journal of Finance 47, 809-816.