利用隱含樹狀模型評價波動率及變異數交換

Abstract

波動率交換及變異數交換提供交易員一個有效率的方式擁有波動率的部位。一般用來評價波動率交換及變異數交換的方式為複製的方式，由Demeterfi, Derman, Kamal和Zou 在1999年提出。在本篇論文中，嘗試以較為直觀的方式來進行波動率交換及變異數交換的評價，我們將使用由Derman和Kani在1996年所提出的隱含三元樹狀模型，利用此模型所找出的局部的波動率及變異數評價波動率及變異數交換，接著再將其結果與一般的評價方式進行比較。我們發現利用此方式亦可有效的評價波動率交換及變異數交換。

Equity-index volatility and variance swaps offer an efficient way for traders to take synthetic positions in pure volatility. General pricing method for volatility and variance swaps uses the replication method in Demeterfi, Derman, Kamal, and Zou (1999). In this thesis, we try to use the more direct and intuitive way to price volatility and variance swaps. Specifically, we will use implied trees introduced in Derman, Kani, Chriss (1994) and Derman, Kani (1996) which can match the implied local volatilities and variances. Then we employ these local volatilities and variances to price volatility and variance swaps. After using the implied tree to price, we also compare the result of this method to the general pricing method. We find out that using this method can also get the value of volatility and variance swaps just similar to the general method.