次分数Vasicek利率模型下可分离交易可转债的定价  

Pricing for Warrant Bonds under Sub-fractional Vasicek Interest Rate Model

作　　者：程潘红 许志宏 CHENG Pan-hong;XU Zhi-hong(Business School, University of Shanghai for Science & Technology, Shanghai 200093, China;School of Mathematics and Finance, University of Chuzhou, Anhui Chuzhou 239000, China;Public Teaching Department, Rizhao Polytechnic College, Shandong Rizhao 276826, China)

机构地区：[1]上海理工大学管理学院,上海200093 [2]滁州学院数学与金融学院,安徽滁州239000 [3]日照职业技术学院公共教学部,山东日照276826

出　　处：《重庆工商大学学报（自然科学版）》2021年第4期84-92,共9页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：安徽省高校自然科学重点研究项目(KJ2018A0429).

摘　　要：金融产品的合理定价是其交易的前提;考虑到利率的随机性、金融资产的长记忆性及利率同金融资产价格的相关性,因此,在假定无风险利率满足次分数Vasicek模型、股票支付连续红利且股票价格遵循几何次分数布朗运动的条件下,提出可分离交易可转债定价模型;运用次分数布朗运动的It公式、随机分析理论与风险中性定价理论,推导得到次分数Vasicek利率模型下可分离交易可转债定价公式;依据定价模型进行数值模拟,研究结果表明:利率的随机性影响可分离交易可转债的价值,且利率的波动越剧烈,可分离交易可转债的价值变化越显著,说明构建模型时考虑利率变化是非常有必要的;股票价格、执行价格、股票价格波动率、股票价格长程相关性和利率长程相关性等因素对可分离交易可转债定价有着重要的影响。The reasonable pricing of financial products is the premise of their transaction.Considering the randomness of interest rates,the long memory of financial assets and the correlation between interest rate and financial asset price,the pricing model of warrant bonds is proposed under the assumption that the risk-free interest rate satisfies the sub-fractional Vasicek model,the stock pays continuous dividends and the stock price follows the geometric sub-fractional Brownian motion.By applying the Itformula of sub-fractional Brownian motion,stochastic analysis theory and risk neutral pricing theory,the pricing formula of warrant bonds is obtained.According to the pricing model,the numerical simulation results show that the randomness of interest rates affects the value of warrant bonds,and the more intense the fluctuation of interest rates,the more significant the value changes of warrant bonds.This shows that it is necessary to consider the change of interest rates when constructing the model.Stock price,exercise price,volatility of stock price,long-range correlation of stock price and long-range correlation of interest rates have important influence on the pricing of warrant bonds.

关 键 词：次分数布朗运动 VASICEK利率模型 可分离交易可转债 随机分析理论 风险中心定价原理 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]