Valuation Analysis for Interest Rate Caps with Various Term Structure Models
Date Issued
2007
Date
2007
Author(s)
Lin, Shin-Hung
DOI
en-US
Abstract
This study evaluates the interest rate caps with various term structure models, including HJM, BGM, and GK models. We systematically analyze and compare cap values with different cap rates, maturities, and volatility structures. Applying HJM model with time-dependent volatility functions, we derive cap prices with short rates and LIBOR rates as underlyings, respectively. Under BGM and GK models, we review the derivations for the pricing formulas of interest rate caps. Next, we provide two one-factor HJM models, namely volatility model I and II, and prove the uniqueness of the forward rate under these specific models. Furthermore, this study provides some numerical examples and simulation results for the practice to issuing exotic interest rate options and choosing an adequate pricing term structure model.
Firstly, this study analyzes the cap values with time-dependent volatility functions under HJM and BGM models. The result presents that the standard interest rate cap becomes more valuable as the reset dates of interest rates increase, but less valuable as the cap rate increases. For convenience, the cap values in various types relative to the flat one are called “value ratios” throughout this study. Next, as the cap rate increases, value ratios for the increase and hump types increase, but decrease for the decrease and exponential decrease types. Additionally, as the time to maturity increases, value ratios for the increase and hump types increase, but decrease for the decrease and exponential decrease types. Moreover, as time to maturity increases, short-term caplets become more valuable, but long-term caplet values decrease.
Secondly, this study investigates the cap values under volatility models I and II. Using a numerical simulation, we examine the cap value differences between various volatility structures, cap rates, and maturities. Moreover, sensitivity analysis for model coefficients on cap values is also investigated. Next, this study investigates the jump effects of interest rates on cap values under BGM and GK models. The decreasing speeds of cap values would decrease as the cap rate increases. Additionally, the increasing speeds of cap values increase as time to maturity increases. Furthermore, we observe that the cap values priced by GK model are more valuable than those priced by BGM model. Finally, the volatility structure effects on cap values are also examined.
Subjects
利率上限契約
利率選擇權
利率買權
利率期間結構
利率波動結構
Interest Rate Cap
Interest Rate Option
Interest Rate Call
Term Structure
Volatility Structure
Type
thesis
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