流動性風險下之臺股指數選擇權定價

Pricing Stock Index Options in a Liquidity Adjusted Black-Scholes Model

徐憶文(Yih-Wen Shyu) ； 沈文玲(Wen-Ling Shen)

《台灣金融財務季刊》 9卷4期 (2008/12) Pp. 23-46

https://doi.org/10.6985/TBFQ.200812.0023

摘要

本研究旨在探討考慮流動性風險後的選擇權定價，並比較修正後之價格是否優於Black-Scholes(1973)的評價結果。模型以Black-Scholes model為基礎，分別加入標的資產的流動性以及選擇權本身的流動性，而發展出流動性修正評價模型，並藉由數值分析中的有限差分法求取封閉解。經由實證結果發現，當選擇權契約分處不同價性等級下，評價結果均以流動性修正模型較佳，並隨著價外、價平、價內，評價誤差逐漸減少。另外，研究發現當選擇權契約處於近月時，對價內及價外的評價效果較佳，當處於遠月時，則以價外契約的評價效果為佳。

關鍵字

選擇權定價 ； 流動性風險 ； Black-Scholes ； 模型

並列摘要

Due to the existence of liquidity risk, we propose a generalized liquidity-adjusted Black-Scholes model. This generalized model takes into account the liquidity risk of options and underlying assets simultaneously. It offers an alternative to demonstrate the effect of liquidity, with the consideration of both underlying assets and derivatives, on the cost of hedging and, consequently, pricing of derivatives. Prices of the Taiwan Stock Index call options (TXO) which are of European style are used as the data for the empirical test. The empirical results strongly support that the liquidity-adjusted Black-Scholes model outperforms the traditional Black-Scholes model.

並列關鍵字

Option pricing ； Liquidity risk ； Black-Scholes Model

參考文獻

夏煥庭(2003)。流動性對選擇權價之影響：台灣選擇權市場之分析(碩士論文)。淡江大學財務金融所。

Amihud, Y.,H. Mendelson,H.C. Lucas (Eds.),R.A. (Eds.)(1989).The Effect of Computer Base Trading on Volatility and Liquidity.(Schwartz, Challenge of Information Technology for the Securities Markets, Liquidity, Volatility, and Global Trading).

Amihud, Y.(1986).Asset Pricing and the Bid-ask Spread.Journal of Financial Economics.17,223-249.

Black, F.,M. Scholes(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy.81,637-659.

Cetin, U.,R. Jarrow,P. Protter,M. Warachka(2003).Option Pricing with Liquidity Risk.(Working Paper, Cornell University).