準蒙地卡羅方法在資產風險值模擬下效率之探討

Quasi-Monte Carlo Efficiency in Portfolio Value-at-Risk Simulation

林敬舜(Chen-Shun Lin)

指導教授 ： 林志娟

淡江大學/管理學院/統計學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00674

摘要

在金融商品的衡量中，風險值(VaR)成為了近年來大家關注的一項指標。用以了解投資風險以便做好風險的規避。在風險值模擬中，無母數方法裡的蒙地卡羅模擬法(Monte Carlo Method , MC)為電腦隨機抽取的亂數，加入到價格模擬的隨機過程裡，且無任何模型上的假設，故須承擔模型之風險，較能因應市場的變化。但由於電腦隨機抽取的亂數，容易發生亂數聚集性，而影響了估計的穩定性。為改善此問題，在亂數模擬的部份改以低差異性數列去產生亂數值，稱之為準蒙地卡羅模擬法(Quasi-Monte Carlo Method , Q-MC)，並舉出常見的兩個低差異性數列Halton數列及Sobol數列。在給定不同的衡量準則下，比較其差異。本文模擬的結果顯示，低差異性數列中之Sobol數列，其亂數本身的差異性小，在低差異數列中為較適合的估計風險值的模擬法，且與風險值真值的差距也是最接近的。有效的改進了傳統蒙地卡羅模擬法的缺點，使應用電腦模擬風險值更為穩定和精確。

關鍵字

風險值 ； 蒙地卡羅模擬法 ； 準蒙地卡羅模擬法 ； 低差異性數列

並列摘要

VaR (Value-at-Risk) has been used as an indicator to respond to the market risk and certainly caused a revolution in risk management. It has drawn a lot of attention especially after the Orange County and many others events. Therefore how to estimate the true VaR has become an important issue.
Monte Carlo method is one of the methods to estimate VaR. It is done by computer simulation. Though it is the most powerful method, Monte Carlo method is always accompanied with lengthy computation time and subject to model risk of stochastic processes assumed. Quasi-Monte Carlo Method can be another alternative method to overcome this efficiency disadvantage by incorporating the Low Discrepancy Sequences in generating random number. Two commonly used sequences, Halton and Sobol, along with naive Monte Carlo Method are used to study the VaR estimation problem in this research.
It is found that Sobol Sequences of the Low Discrepancy Sequences has smaller MSE and better effientcy among three estimation methods.

並列關鍵字

Value-at-Risk ； Monte Carlo Method ； Quasi-Monte Carlo Method ； Low Discrepancy Sequences

參考文獻

3.Dowd K. (1999), “Financial Rick Management”, Financial Analysis Journal, 55, 4, 65-70.

4.Galanti S. & A. Jung (1997), “Low-discrepancy Sequences: Monte Carlo Simulation of Option Prices”, Journal of Derivatives. 5, 63-83.

5.Glasserman, P. (2004), “Monte Carlo Methods in Financial Engineering”, New York: Springer.

6.Hendricks D. (1996), “Evaluation of Value-at-Risk Models Using Historical Data”, Economic Policy Review, Federal Reserve Bank of Philadelphia.

8.Jorion, P. (1996 a), “Risk-Measuring the Risk in Value at Risk”, Financial Analysis Journal, 52, 47-56.