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．

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.

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