published_or_final_version / Economics and Finance / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

巨災權益賣權(CatEPut option) 是種常見的與風險掛鉤的證券(risk-linked security) ，它經常被用來對沖巨災風險，在這篇文章中，我們在隨機利息率和隨機波動率的條件下對巨災權益實權進行定價。我們使用了高維傅利葉變換的方法來進行定價，并得到了巨災權益賈權價格的顯式表達，數據實驗的結果顯示，我們的定價公式和方法是高效和精確的。此外，我們還發現隨機利息率和隨機波動率對巨災權益賣權的價格有很大影響。 / The catastrophic equity put (CatEPut) options which serve as a kind of risklinked securities are quite popular in hedging catastrophic risk. In this thesis, the CatEPut options are priced with the stochastic interest rate and stochastic volatility (SISV). We use a two-dimensional Fourier transform over the log price and the catastrophic loss to derive the closed-form CatEPut option price. The numerical examples show that our pricing formula and method are efficient and accurate. We also find that the price of the CatEPut options are greatly in uenced by the stochastic volatility and stochastic interest rate. / Detailed summary in vernacular field only. / Li, Yiran. / "September 2012." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 54-55). / Abstracts also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgements --- p.iii / Contents --- p.v / List of Tables --- p.vii / List of Figures --- p.viii / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- The model --- p.5 / Chapter 2.1. --- The model of CatEPut options under risk-neutral measure --- p.5 / Chapter 2.2. --- Change to the forward measure --- p.7 / Chapter 3. --- Pricing CatEPut using “conditioning on the catastrophic lossmethod --- p.10 / Chapter 4. --- Pricing CatEPut using Fourier transform --- p.15 / Chapter 5. --- Numerical experiments --- p.26 / Chapter 5.1 --- The FFT algorithm --- p.26 / Chapter 5.2 --- The impact of the stochastic interest rate and the stochastic volatility --- p.27 / Chapter 5.3 --- The advantage of the Fourier transform method --- p.36 / Chapter 6. --- Conclusions --- p.41 / Chapter A. --- Measure change to risk neutral measure Q --- p.43 / Chapter B. --- Proof of integrability --- p.48 / Bibliography --- p.53