隱含波動與股票風險值

Implied Volatility and Value at Risk of Stock

劉曉燕(Shiao-yen Liu)

指導教授 ： 吳博欽

中原大學/商學院/國際貿易研究所/碩士(2009年)

https://doi.org/10.6840/cycu200900469

摘要

隨著金融市場的開放與自由化，金融商品間的關聯性日益密切，使得在金融市場中如何建立一個完善的風險管理評價機制，成為目前相當重要的課題。一般財務理論以變異數表達市場風險，投資人所關心的是在機率分配中不常發生的金融市場崩盤時的影響，故本論文將風險值的觀念應用於選擇權市場中，利用不同波動率模型行進行風險評估，期能找出最適的衡量數值，提供投資大眾或企業者在數量化風險管理的依據。

首先以Black-Scholes選擇權評價模型為出發點，分別求算出選擇權之隱含波動率及歷史波動率，再利用歷史模擬法及蒙地卡羅模擬法預估2007年9至12月樣本外之各波動率，並估算不同波動率下之最小風險值。為了求取隱含波動，必須使用買權市場價格、標的資產之收盤價、履約價格、一銀三個月定存利率及選擇權之存續期間等資料。

實證上以台灣期貨交易所掛牌之10家公司的股票選擇權為對象，實證期間介於2006年1月至2007年12月共計24筆月資料。由樣本外預測能力比較得知，以Monte Carlo模擬法之向前一期滾動預測法所預測的個股隱含波動及歷史波動結果較歷史模擬法所預估之風險值保守，至於資產組合風險值亦與個股風險值衡量結果相同。

關鍵字

Monte Carlo模擬法 ； Black-Scholes選擇權評價模型 ； 歷史模擬法 ； 風險值

並列摘要

With the liberalization and openness of financial markets, the relationships among financial commodities become much closer and the risk of investor’s asset holding becomes more complicated. Therefore, how to establish a perfect measure method to evaluate the risk in the financial market has become an important topic. This thesis applies the concept of value of risk to assess the risk in stock price by using different volatility and VaR estimation methods. Through the estimated results we try to provide useful information for investor or management to manage investment risk.

By utilizing Black-Scholes Model we can first find out the historical volatility and implied volatility of the underlying stock price, then through history simulation and Monte Carlo simulation to fit the path of the underlying stock price and further to estimate the value of risk of the underlying stock price for one-step-ahead forecasts from the 2007, Sep. to 2007, Dec. Finally we can decide the best evaluation method of VaR. To estimate implied volatility of stock, we must make use of the variables of price of the call option, price of the underlying stock, option exercise, risk-free interest rate and current time until expiration.

In empirical study, this research selects 10 companies listed in Taiwan Future Exchange Market. Sample period spans from the 2006, Jan. to 2007, Dec. The empirical result shows that for single stock or stock portfolio implied volatility is a best method to measure the variability of underlying stock price and the Monte Carlo Simulation is the best instrument method to evaluate its VaR.

並列關鍵字

Historical Simulation. ； Monte Carlo Simulation ； Black-Scholes Model ； Value at Risk

參考文獻

聶建中、陳芾文與王友珊 (2003)，金融機構承做選擇權的模型風險與市場風險，風險管理學報，第5卷第3期，295-317頁。

沈大白、柯瓊鳳與鄒武哲 (1998)，風險值衡量模式之探討-以台灣上市公司權益證券為例，東吳經濟商學學報，第22期，57-76頁。

Black, F. and M. Sholes (1973), “The Pricing of Option and Corporate Liabilities,” Journal of Political Economy, 81, 637-654.

Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroscedasticity,” Journal of Econometrics, 31, 307-327.

Bollerslev, T., R. F. Engle, and J. M. Wooldridge (1988), “A Capital Asset Pricing Model with Time-Varying Covariance,” Journal of Ploitical Economy, 96, 116-131.