半马氏市道轮换利率期限结构模型——基于最小Tsallis熵鞅测度

Semi-Markov regime switching interest rate term structure models——Based on minimal Tsallis entropy martingale measure

基于Ho-Lee模型,讨论零息债券价格的演变,应用无套利原理和鞅测度的方法,建立了一个离散时间半马氏过程控制的市道轮换下的二叉树期限结构模型.运用最小Tsallis熵鞅测度(the minimal Tsallis entropy martingale measure,MTEMM)处理上述模型,并在马氏和半马氏市道下给出在欧式债券期权定价方面的应用.研究发现模型结果与最小熵鞅测度下的结果具有一致性.

Based on Ho-Lee model, we discussed the evolution of the prices of zero-coupon. A discrete time regime switching binomial model of the term structure where the regime switches are governed by a discrete time semi-Markov process is introduced by applying the arbitrage free principle and martingale measure method. This paper use minimal Tsallis entropy martingale measure （MTEMM） to deal with the above model, and give an application to the pricing of a European bond option in Markov and semi-Markov regime switching framework. The study found the model result is consistent with the result under minimal entropy martingale measure.