Analysis of Pricing and Hedging Performance of TXO with Two Volatility State Variables

[[abstract]]在傳統選擇權的評價模型中，往往將波動度視為一固定常數，然而波動度應為一隨機過程。本研究以狀態區分波動度，將波動度簡易區分為高、低兩個狀態，藉由狀態轉換的馬可夫過程來改善傳統的評價模型將波動度視為一固定常數的缺失；並以台指選擇權為例，以雙波動度狀態對台指選擇權做評價價績效分析，檢驗將波動度區分為雙波動度狀態是否對選擇權評價模型的評價績效有所改善，結果顯示，無論對於何種價位區段(深度價內、價內、價平、價外、深度價外)以及存續期間區段(遠月份、近月份)，評價能力都有改善。 雙波動度狀態評價模型如同二項式評價模型一般，具有隨著運算期數的增加，選擇權價值會逐漸收斂且穩定的特型，在同樣的條件下，雙波動度狀態評價模型會較快收斂且穩定，這與雙波動度狀態評價模型的子結點數較多有關，且雙波動度狀態評價模型雖然重組效率較不好，但是可藉由較低的運算期數達到收斂與穩定的效果。 在變數改變對選擇權價格的影響方面，雙波動度評價模型中因素改變對於選擇權價格的影響與一般所認知中因素改變對選擇權價格的影響無異，此乃為評價模型的正確性做另一佐證。 在台指選擇權的評價與避險績效方面，雙波動度狀態評價模型提供了較低的評價誤差與較好的避險績效，因此將波動度劃分為高低狀態有助於選擇權的評價，且雙波動度狀態評價模型在評價能力上較傳統評價模型有進步。[[abstract]]In the traditional option pricing model, volatility was often regarded as a constant, but that should be a stochastic process. This research classes volatility with state variable, high volatility state and low volatility state. To improve the fault that volatility was often regarded as a constant, by using Markov process of regime switch. This research used TXO to test two volatility state pricing model. The result show that no matter what kind of prices sector (deep-in-the-money , in-the-money , at-the-money , out-off-the-money , and deep-out-off-the-money) and time periods (forward and recent), the pricing ability was ameliorated. As the CRR model, the two volatility state pricing model had the characteristic that the option price was converge and stable gradually to follow the increasing of the number of period on the lattice. With the same condition of parameters, two volatility state pricing model converged faster than the CRR model. This have relations to that two volatility state pricing model had more nodes at the same level. Even through that had the badly recombine efficiency, but it could gain the effect of convergence and stable by lower periods. In pricing and hedging performance with TXO, two volatility state pricing model offered lower pricing error and better hedging performance, so to class volatility with two state is helpful to option pricing, even the two volatility state pricing models is better than the traditional option pricing model