探討B-S模型分段模擬匯率波動性及適用性-以新台幣兌美元為例

Employing Piecewise Simulation to investigate on the Volatility and Applicability of the B-S Model for Exchange Rate-Example of NT dollar to US dollar

呂孟柔(Meng-Jou Lu)

指導教授 ： 謝浩明

國立中央大學/管理學院/企業管理學系/碩士(2007年)

摘要

現在大部分的投資者偏向使用Black-Scholes模型來定價金融資產的價格。原因在於我們將基本的資產價格、執行價格、無風險利率、到期日及波動性的參數帶入B-S模型而可以發現封閉解。B-S模型的研究學者通常認為波動性常數是固定的。然而在此篇研究論文裡，經由分段模擬我們證明了B-S模型可以接近新台幣兌美元匯率途徑的實際值。根據每一組 及 ，我們可以預測下一個10天、20天、30天的新台幣兌美元的匯率，且發現在B-S模型下所預期匯率的可適用性。
此篇論文的研究包含了Metlab程式所進行的蒙地卡羅模擬，有三種方法來決定模擬的期間，當求出每一組 及 時，經由天真的方法我們預測到下一期新台幣兌美元匯率的實際值。
經由模擬過去歷史的匯率，此篇研究結果顯示固定時間區間法(Fixed Time Interval method)是優越於其他的方法，事件驅動法(Event- Drive method)是其次, 而逐月推移估計法(Month Downward method)是最後。經由固定時間區間法求得的每一組 及 值去預測下一個10天的結果是優越於其他的方法。而事件驅動法的結果是劣於固定時間區間法卻優於逐月推移估計法。在預測下一個20天的結果中，固定時間區間法是優越於其他的方法，而逐月推移估計法的結果是劣於固定時間區間法卻優於事件驅動法。
在結論上，此篇的研究是可以用來解釋 、 及跳躍之間動態關係的重要性，也證明出一個最好的方法來預測匯率。

關鍵字

蒙地卡羅模擬 ； B-S 模型 ； 波動性

並列摘要

Now a day, most investors like to use the Black-Scholes model to
price the financial asset value. Because we substitute the underlying asset
price, exercise price, the risk-free interest rate, time to maturity and
volatility to the B-S model, we can find the closed-form solution.
Researchers of Black-Scholes model often reject the constant-volatility.
However, in this article we proof that the B-S model can be close to the
path of the exchange rate’s actual value for NTD/USD by individual
simulation. By each bank of μ and σ, we can predict the next 10 days,
20 days, and 30days of NTD/USD, and find the applicability of
predicting under the B-S model.
This research involves the Monte Carlo simulation by the Metlab
program. There are three kind of method for deciding the duration for
simulation. When drawing on each bank of μ and σ, we predict the
next period’s actual value of NTD/USD by Naïve method.
Results of this study show the Fixed Time Interval method is
superior to the others by simulating the historic exchange rate. The Event-
Drive method is second, and the Month Downward method is last. For
predicting the next 10 days, it is drawn out μ and σ by the Fixed Time
Interval method that is superior to the others. The Event-Drive method is
inferior to Fixed Time Interval method but superior to Month Downward
method. For predicting the next 20 days, the built-in duration method is
superior to the others. The Month Downward method is subordinate to
the Fixed Time Interval method but better than the Event-Drive method.
To conclude, this study may be of importance in explaining the
dynamic relationship between μ , σ and jumps, as well as providing the
best method to anticipate the exchange rate.

並列關鍵字

volatility ； Monte Carlo Simulation ； B-S model

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