衍生性金融商品訂價之研究

Abstract

本論文包含四篇衍生性金融商品訂價之論文。論文第一部份「波動模型設定：以波動指數衍生性金融商品訂價為證」利用波動指數衍生性金融商品的市場價格探討多種隨機波動模型的實證表現。本文識別加入跳躍因子與加入多重因子對於建構波動模型的各別價值，並提出有效率且易執行的數值方法解決波動指數衍生性金融商品在訂價上的困難。論文第二部份「由各股選擇權價格萃取違約資訊：一般均衡模型」提出一個新的選擇權訂價模型，從股票的市場價格萃取前瞻性的違約資訊，並推導出一般均衡架構下的違約風險溢酬。論文第三部份「評價保險公司的或有資本：考量交易對手風險與價格內生性」建構一個結構式模型評價保險公司在考量交易對手風險下的或有資本，並解決訂價上所產生的內生性問題。本文亦探討巨災權益賣權如何影響買方的違約機率，發現巨災權益賣權能降低高風險保險公司的違約機率，但對於低風險保險公司則不必然。本論文最後一部份「亞式選擇權的動差配適近似公式」提出一般化的架構訂價所有型式的亞式選擇權，利用動差配適方法推導選擇權價格的可析近似公式，並提出有效的遞迴方法計算動差值。

This dissertation contains four essays on derivatives pricing. Specifically, the first part of dissertation “Volatility Model Specification: Evidence from the Pricing of VIX Derivatives” examines the empirical performance of various stochastic volatility models by investigating the pricing of VIX derivatives. This study identifies the respective values of adding a jump component and specifying an additional factor for volatility modeling and proposes an efficient and easily implemented numerical approximation for the pricing of VIX derivatives. The second part of dissertation “Extracting Default Information from Equity Option Prices: A General Equilibrium Approach” proposes a new option pricing model to extract the forward-looking default information from the market prices of stock options. This study also derives the theoretical default risk premium under a general equilibrium framework. The third part of dissertation “Valuation of Insurers’ Contingent Capital with Counterparty Risk and Price Endogeneity” develops a structural framework to value insurers’ contingent capital with counterparty risk and overcomes the problem of price endogeneity in the valuation model. This study also examines how catastrophe equity put options affect the buyer’s probability of default and concludes that buying a catastrophe equity put option lowers the probability of default for high-risk insurers, but not necessarily so for low-risk insurers. The last part of dissertation “On Moment-Matching Approximations for Asian Options” provides a generalized framework under which all types of Asian options can be priced. This study utilizes the moment-matching approach, deriving analytic approximations for option prices and providing a tractable iterative method to calculate the moments.