在首次通透模型下評價可違約障礙選擇權

Abstract

在首次通過模型(First Passage Model, FPM)下評價可違約選擇權十分困難——尤其在公司違約門檻和選擇權價值相關時，評價公式無法推導，且數值模型也會因線性誤差而不可靠。本論文提出一個立體樹可同時模擬標的物價格和公司資產，而且可透過和違約門檻及障礙重合的方式縮減非線性誤差，本論文所提出的樹狀結構如不考慮FPM，可收斂至Klein (1996)與Klein and Inglis (2001)的模型。評價可違約障礙選擇權可收斂至潘政宏(2010)的結果。

Pricing vulnerable options under first passage model can be very difficult – especially when the default boundary depends on the option value. Analytical formula can’t be derived and numerical approaches become unstable due to nonlinearity error. This thesis provides a three dimension tree that can simultaneously simulates the evolution of the underlying asset’s value and firm’s value. The nonlinearity error problem can be alleviated by making the tree align with the default boundary and the barrier. Our tree model can evaluate the both model of Klein (1996) and Klein and Inglis (2001) and the pricing results converge to the closed form of Klein (1996.) The pricing results of vulnerable barrier option under the Merton’s model converge to the closed form of Pan (2010), too.