A Market Model for Stochastic Implied Volatility and Volatility swap

A Market Model for Stochastic Implied Volatility and Volatility swap

張書瑋(shu-way chang)

指導教授 ： 鄭光甫

國立中央大學/理學院/統計研究所/碩士(2006年)

摘要

過往研究波動率大都是拿部分的市場資料，帶入特定的模型內求出其隱含波動率；在近幾年對於波動率的研究中，有了新的方法(model-free implied volatility)來求其隱含波動率，此方法是利用市場上選擇權所有的市場資料，帶入簡單的運算來算出其隱含波動率．在這篇論文中，用此新方法從台指選擇權的算出其隱含波動率，再找出符合其隱含波動率走勢的模型，進而應用在波動率交換契約上的訂價和避險．

關鍵字

none

並列摘要

In this paper a class of stochastic volatility models was presented that is based on model-free implied volatilities that are observed in the price of TX options, and identify the process that describes well the evolution of model-free implied volatility in continuous time. We have compared various diffusion and jump diffusion processes. We price the volatility swap contract with MRSRPJ model in risk neutral world and calculate the price of the volatility swap.

並列關鍵字

stochastic volatiliy ； model-free implied volatility ； volatility swap ； vix

參考文獻

Ait-Sahalia, Y. (2004). “Disentangling Diffusion from Jumps”, Journal of Financial

Impact on Call Option Pricing”, Journal of Finance, 40, 155-173.

Bakshi, G., and Cao, C. (2004). “Risk-Neutral Kurtosis, Jumps, and Option Pricing:

Bollerslev (1986). “Generalized autoregressive conditional heteroskedasticity”, Journal

of Econometrics, 31, 307-327.