界內、界外及界上—區間計息債券定價之探討

In, Out, or On the Boundary — Exploration of Range Accrual Note Pricing

本研究以風險中立評價法推導多期付息區間計息債券之一般化評價模型。區間計息債券的利息支付是由標的資產落入設定區間的天數比例乘上契約設定的利率來決定。透過台灣證券商實際發行之結構型商品與市場資料，本研究詳細分析其中標的資產價格、標的波動率、計息區間大小及契約設定利率等參數，對於內嵌選擇權價值之影響，並對Delta、Gamma及Vega等攸關避險操作的參數進行敏感度分析及深入探討。研究結果顯示，標的波動率與區間計息債券價值的關係並不一致，而是隨著標的資產價格位於區間內、外及上、下邊界時，具有不同的價格與風險特性。此外，當標的資產價格接近區間上、下邊界時，會有Delta跳躍的現象發生，此時標的資產價格的微幅改變將導致應避險部位的劇烈變動。

This research derives a pricing model for range accrual notes through the derivation of the embedded range option value. The interest payment of the range accrual note is defined as the proportion of how many days the reference underlying asset price lies within a specified range times an interest rate specified at initiation of the note. Using parameters obtained from Taiwan market data, we conduct detailed analysis on how the underlying price, the underlying return volatility, the size of range, and the specified interest rate, affect the option value. The sensitivity analysis of Delta, Gamma, and Vega that are essential for hedging practice are also provided. The results show that the relationship between the volatility and note value is not monotonic, depending on whether the underlying price is in, out, or on the range boundary. Also, one needs to pay attention to the delta jump when the underlying asset price moves near the upper and lower boundaries, since the jump can make the hedging position dramatically changed due to a small change in the underlying asset price.