考慮模型錯置下的不完備市場資產訂價 : 以 Robust Good-Deal Bounds 為例

Asset Pricing with Model Misspecification in Incomplete Markets : Robust Good-deal Bounds

賴昭安(CHAO-AN LAI)

指導教授 ： 黃裕烈

國立清華大學/科技管理學院/計量財務金融系/碩士(2014年)

摘要

本文將特定的模型錯置形式加入 Cochrane and Saa-Requejo’s (2000) 中，推導出不完備市場中具有穩健性質的訂價區間。在資產價格服從幾何布朗運動之下，本文模型不僅對於考量不確定性的投資人的決策有意義，且對於歐式買權具有方便分析的封閉解。此外，以一個標的物資產無法在市場被交易的指數選擇權為例，利用我們的模型訂價具有許多值得探討的性質，相較於 Cochrane and Saa-Requejo’s (2000) 的訂價區間，我們發現在特定的模型錯置形式下，會有足夠多的實際價格落入我們推導出的訂價區間。

關鍵字

不完備市場 ； 資產訂價 ； 不確定性

並列摘要

In this paper, we extend the analysis of Cochrane and Saa-Requejo (2000) to deriving good-deal bounds on asset prices when investors worry about model uncertainty and seek robust pricing decisions in incomplete markets. Under the assumption that asset prices are driven by geometric Brownian motion processes, we propose a framework that is meaningful and very natural for investors' decision problems involving uncertainty about the pricing models, and derive closed-form solutions for the pricing bounds of the European option. We investigate properties of the proposed pricing bounds and apply these bounds to value a European option whose underlying asset is a non-traded stock index. We find that, under certain circumstances of model uncertainty, the proposed pricing bounds can contain sufficient amounts of the actual option prices, which is in contrast with the empirical finding of the good-deal bounds proposed by Cochrane and Saa-Requejo (2000).

並列關鍵字

Incomplete markets ； Asset pricing ； Uncertainty ； Good-deal bound ； Robust control

參考文獻

Anderson, E. W., Hansen, L. P., and Sargent, T. J. (2003). A quartet of semigroups for model specification, robustness, prices of risk, and model detection. Journal of the European Economic Association 1, 68-123.

Arrow, K. J. (1953). Le rôle des valeurs boursières pour la répartition la meilleure des risques. Colloques Internationaux du Centre National de la Recherche Scientifique 11, 41-47.

Ben-Tal, A., and Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations research letters 25, 1-13.

Bernardo, A. E., and Ledoit, O. (2000). Gain, loss, and asset pricing. Journal of Political Economy 108, 144-172.

Bondarenko, O., and Longarela, I. R. (2009). A general framework for the derivation of asset price bounds: an application to stochastic volatility option models. Review of Derivatives Research 12, 81-107.