เปรียบเทียบวิธี

	แบบจำลอง Hull-White	Local Volatility (Dupire)	แบบจำลอง SABR
สาขาวิชา	การเงินเชิงปริมาณ	การเงินเชิงปริมาณ	การเงินเชิงปริมาณ
ตระกูล	Regression model	Regression model	Regression model
ปีกำเนิด	1990	1994	2002
ผู้ริเริ่ม	John C. Hull and Alan White	Bruno Dupire	Patrick S. Hagan
ประเภท	Interest Rate Model	Equity/FX Model	Interest Rate Model
แหล่งต้นตำรับ	Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3(4), 573-592.	Dupire, B. (1994). Pricing with a smile. Risk Magazine, 7(1), 18-20.	Hagan, P. S., Kumar, D., Lesniewski, A. S., & Woodward, D. E. (2002). Managing smile risk. Wilmott Magazine, 1, 84-108.
ชื่อเรียกอื่น	Extended Vasicek, Generalized Vasicek	Deterministic Volatility Function, DVF	Stochastic Volatility Model
ที่เกี่ยวข้อง	4	4	4
สรุป	The Hull-White model (1990) is a one-factor short-rate model with time-dependent mean reversion and volatility, designed to fit the initial yield curve exactly. It generalizes the Vasicek model to allow better calibration to observed bond and derivative prices, and is widely used for pricing interest rate exotics and managing interest rate risk.	Dupire's local volatility model (1994) is a deterministic framework that extracts a term and strike-dependent volatility function from market option prices. Unlike constant volatility, local volatility perfectly fits the observed implied volatility smile and is implemented via finite difference methods for European and American option pricing.	The SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions and has become industry standard for swaption and caplet pricing.