使用Hull-White短利模型與求面積法評價雪球型債券

Pricing Snowball Notes with Hull-White Model and Quadrature Method

本文討論以Hull-White短利模型評價雪球型利率連動商品，此商品為一複雜的反浮動債券，每期支付的票面利率具有路徑相關之特性，同時票面利率不可小於零，再加上可提早贖回債券之條款，因此定價複雜無封閉公式解，也不易建構數值模型評價。本文發現在Hull-White三元利率樹下，票面利率及債券價格計算問題可大幅化簡，結合求面積法（quadrature method）後進一步減少利率樹的分配誤差，建構出有效率並精確的評價方法。本文最後以市場資料與已經發行之雪球型債券實際進行演算，提供業者參考。

This paper investigates the pricing of the snowball note based on Hull-White term structure model and Quadrature method. Snowball notes can be considered as sophisticated inversing floating rate bonds with path-dependent coupons and redemption right. Because of these complications, there are no accurate closed form solutions for snowball notes. It is also difficult to develop an efficient numerical pricing method. This study shows that the calculation of coupons for snowball notes can be drastically simplified under Hull-White interest rate tree model. To further reduce the distribution error, we combine Hull-White model with Quadrature method, and then construct an efficient and accurate pricing method. Numerical simulations using market data are provided as examples of applications for practitioners in the industry.