隨機波動度下選擇權訂價模型之探討- 以股權及匯率結構型商品為例

使用Heston模型對結構型商品訂價前，有兩個重要的前置作業：參數校準及模擬。首先是參數校準，本文利用最小平方法，進而探討在對損失函數加入不同的權重(1、vega及1/vega)、不同類型商品(匯率及股權)及市場環境(空頭及多頭)之下，何種校準效果最好。最後得到空頭市場優於多頭市場、匯率型商品優於股權型商品及權重為1優於另外兩種的結果。此外，本文亦觀察在連續天數之下，校準出來的參數是否穩定，其結果是會受到每天市場訊息的影響，故不穩定；另外是模擬的部分，本文使用Euler法展開標的資產的路徑，在劃分不同的模擬期數之下，探討蒙地卡羅模擬法在Heston與BS模型中的差異。最後可以得到不論劃分期數為何，兩種模型模擬之結果差異不大。

關鍵字

Heston模型； Black-Scholes模型；參數校準；模擬

並列摘要

Before we use Heston model to price structured products, there are two important things we need to do first. One is calibration , and the other is simulation. In the thesis, we use the least square method to adjust the parameters. We find that the bear market is better than the bull market, while the FX linked note are better than equity linked note in parameters calibration. Besides, we also find that our result is not stable. It will be affected by daily market information. In order to differentiate Heston model from BS model in Monte Carlo, we use Euler method to simulate those. We find that there is no difference between the two models.

並列關鍵字

Heston model ； Black-Scholes model ； Calibration ； Simulation

參考文獻

Hurn A.S., Lindsay K.A. and McClelland A. J. (2012), “Estimating the Parameters of Stochastic Volatility Models using Option Price Data“,working paper, School of Economics and Finance, Queensland University of Technology

Heston S. L. (1993), “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”,The Review of Financial Studies,6,327-343.

Melino A. and Turnbull S.M. (1990),“ Pricing Foreign Currency Options With Stochastic Volatility”, Journal of Econometrics, 45,239-265.

Rouah F. D. (2013),“The Heston Model and its Extensions in Matlab and C#”, John Wiley & Sons Inc. ,New York.

Wilmott P. (2013) ,“The Best of Wilmott 1: Incorporating the Quantitative Finance Review”, John Wiley & Sons Inc. ,New York.

國際替代計量

隨機波動度下選擇權訂價模型之探討- 以股權及匯率結構型商品為例

未授權

主題瀏覽