A direct method for calculating Greeks under some L

A direct method for calculating Greeks under some L

王聖翔(Wang Sheng-Xiang)

指導教授 ： 鄧惠文

國立中央大學/理學院/統計研究所/碩士(2014年)

摘要

根據經驗的證據顯示，一些Levy過程提供了比Black-Scholes models更好的期權價格市場模型。Greeks是金融衍生性商品的價格敏感度和避險指標與風險管理的指標。要計算Levy過程下的Greeks是一個極具挑戰性的任務。為了克服這個困難，本文提出了一種直接計算的方法來計算Greeks。簡要地說，我們的方法是在指定的條件下來交換微分和積分的順序，並使用Dirac delta函數來表示指標函數的微分。並給出了在Merton's model和variance-gamma process下計算歐式和亞式選擇權deltas、vegas、gammas的例子。數值結果證實了該方法在不偏性、效率和時間上優於現有的方法。

關鍵字

Greeks ； 價格敏感度 ； 新興選擇權 ； L ； pathwise method ； 蒙地卡羅模擬

並列摘要

Empirical evidence has shown that some Levy processes provide a better model t for market option prices compared with the Black-Scholes models. Greeks are price sensitivities of financial derivatives and are essential for hedging and risk management. To calculate the Greeks under Levy process is a challenging task. To overcome this difficulty, this paper proposes a direct method for calculating the Greeks. Briefly speaking, our method identifies conditions to switch the order of integration and differentiation, and use the differentiation of an indicator function via the Dirac delta function. Explicit examples for calculating deltas, vegas, and gammas of European and Asian options under Merton's model and the variance-gamma process are given. Numerical results conrm that the proposed method outperforms existing methods in terms of unbiasedness, efficiency, and time.

並列關鍵字

Greeks ； price sensitivities ； exotic options ； L ； pathwise method ； Monte Carlo simulation

參考文獻

Ahn, C. M. and H. E. Thompson (1988). Jump-diffusion processes and the term structure of interest rates. Journal of Finance 43(1), 155-174.

Bates, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies 9(1), 69-107.

Broadie, M. and P. Glasserman (1996). Estimating security price derivatives using simulation. Management Science 42(2), 269-285.

Chan, J. and M. Joshi (2013). Fast Monte-Carlo Greeks for nancial products with discontinuous payoffs. Mathematical Finance 23(3), 459-495.

Chen, Z. and P. Glasserman (2008). Sensitivity estimates for portfolio credit derivatives using monte carlo. Finance and Stochastics 12, 507-540.