利用重點抽樣的有效率選擇權訂價

Efficient option pricing with importance sampling

陳醇潔(Chun-chieh Chen)

指導教授 ： 鄧惠文

國立中央大學/理學院/統計研究所/碩士(2012年)

摘要

隨著金融商品迅速發展，在學術界和業界中，如何正確且有效率的對選擇權做定價依然是一個重要的問題。奇異選擇權或複雜的選擇權通常沒有封閉解，就算在布萊克-肖爾斯假設下也是如此，因此需要使用數值方法。蒙地卡羅近似是一個簡單且合適的方法，但蒙地卡羅估計量通常會有較大的變異數。為了解決這個問題，我們提出了一個重點抽樣的方法，可以找到一個指數平移測度來極小化蒙地卡羅估計量的變異數。我們應用此方法在幾個選擇權上做定價和計算希臘字母。

關鍵字

彩虹選擇權 ； 選擇權定價 ； 蒙地卡羅 ； 重點抽樣 ； 變異數縮減

並列摘要

Along with the rapid development of financial instruments, pricing options correctly and efficiently remains a critical issue both in industry and in academy. However, closedform
formulas for exotic or complicated options price rarely exist even under the standard Black-Scholes assumptions, and consequently additional numerical techniques are required. Among them, Monte Carlo approaches are invaluable tools and are easy to implement, but Monte Carlo estimators usually suffer from large variances. To tackle this problem, we propose an importance sampling procedure with an exponentially tilted measure to minimize the variance of Monte Carlo estimators. We apply our method to calculate both the price and the Greek letters for several popular options, such as spread and maximum options.

並列關鍵字

rainbow option ； variance reduction ； importance sampling ； Monte Carlo ； option pricing

參考文獻

Boyle, P., M. Broadie, and P. Glasserman (1997). Monte carlo methods for security

Boyle, P. P. (1977). Options: A monte carlo approach. Journal of Financial Economics 4,

Dupuis, P. and H. Wang (2004). Importance sampling, large deviations, and differential

games. Stochastics and Stochastics Reports 76 (6), 481–508.

Dupuis, P. and H. Wang (2005). Dynamic importance sampling for uniformly recurrent