Abstract
摘要:在各種選擇權評價模式中,以連續時間架構為分析基礎的模型,因為其在理論推導上的方便性,已被廣泛地探討。在這一類的選擇權評價模式的發展過程中,資產價格與波動率的隨機項是有相關的隨機波動率及存在於價格和/或報酬率的跳躍因子已被發現是對於改善描述選擇權隱含波動率函數的重要因素。本研究目的在於達成以下幾項對相關文獻的貢獻:衡量各模型在選擇權定價、機率分配預測及避險上的表現,除此之外,也將探討隨著選擇權市場越來越成熟,選擇權隱含的訊息是否對未來的資產價格更具訊息性或預測性。以Duffie等人(2000)所提出的仿射跳躍擴散選擇權定價模型為架構,本研究將探討的模型包括隨機波動率模型(SV)、價格跳躍隨機波動率模型(SVI-Y)及價格與波動率跳躍隨機波動率模型(SVJJ)。
本研究將藉由最小化選擇權市價與理論價格差異或百分比差異總合的方式來估計模型參數,對於各模型在機率分配預測上的表現則用Berkowitz(2001)的檢定方法來衡量隱含在選擇權價格中的風險中立密度函數及真實世界機率密度函數。對於各模型在避險上的表現則先用Scott(1987)的策略形成理論上無風險的投資組合,然後再比較這些投資組合實現值的變異程度。除此之外,本研究也將藉由比較最小定價誤差模型在不同樣本期間的機率分配預測及避險的效果來探討選擇權價格的資訊性的變化。所有實証研究將針對FTSE 100指數及幾個交易量較大的個股選擇權進行分析。
總之,本研究將針對如何有效地運用衍生性金融商品市場所隱含的資訊提供一個完整的了解,因此研究結果將有助於風險管理、衍生性金融品商品定價及政策之制定。
Abstract: Of various options pricing models, those based on the continuous-time framework have been intensively explored because of their theoretical convenience. In the development of this type of option pricing models, stochastic volatility whose innovation is correlated with that of returns and jumps in returns or/and volatility are found important for the improvement in fitting the observed implied volatility function. In this study, we aim to contribute to literature by evaluating the performance of alternative option pricing models in option pricing, density prediction and option hedging. In addition, we will investigate whether the options implied information has become more informative to the dynamics of future asset prices as the option markets have become more matured. Nested in the affine jump-diffusion option pricing model of Duffie et al. (2000), the stochastic volatility (SV) model, the stochastic volatility model with jumps in price only (SVJ-Y) and the stochastic volatility model with simultaneous jumps in price and volatility (SVJJ) will be explored in this study.
We will estimate the parameters in the models by minimizing the sum of squared (percentage) differences between actual and theoretical option prices. The performance of the models in density prediction will be evaluated with the tests proposed by Berkowitz (2001) for both risk-neutral densities (RNDs) and real-world densities. To investigate the performance of the models in option hedging, we first use the strategy of Scott (1987) to construct a theoretically risk-free portfolio for each model and then compare the realized variances of these portfolios. In addition, we will explore the dynamics of informativeness of options implied information by comparing the performance of the model with the least pricing errors in density prediction and option hedging across time. All of the empirical implementations will be conducted with the prices of options on FTSE 100 index and some heavily traded individual stocks.
This study aims to provide a compete understanding as to how to effectively utilize derivatives implied information. The results will be useful for risk management, derivative pricing and policy making.
Keyword(s)
選擇權評價
隨機波動率
跳躍
機率分配預測
避險
Option pricing
Stochastic Volatility
Jumps
Density Prediction
Hedging