基于Hull-White利率下O-U过程的复合期权定价
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摘要
采用Hull-White模型和指数O-U过程来刻画利率和股票价格的变化规律,考虑到标的资产价格和利率的随机性与均值回复性,利用鞅理论和Girsanov定理,研究了股票价格在随机利率下遵循指数O-U过程的复合期权定价问题,得到了复合期权的定价公式.
The changing rules of interest rate and stock price are described by applying Hull-white model and exponential Ornstein-Uhlenbeck process.The randomness and mean-recoversion of interest rate and underlying asset are considered.The pricing problem of compound option under Ornstein-Unlenbeck process and stochastic rate are studied by using the martingale theory and the Girsanov theorem.Finally,the pricing formulas of compound options are obtained.
The changing rules of interest rate and stock price are described by applying Hull-white model and exponential Ornstein-Uhlenbeck process.The randomness and mean-recoversion of interest rate and underlying asset are considered.The pricing problem of compound option under Ornstein-Unlenbeck process and stochastic rate are studied by using the martingale theory and the Girsanov theorem.Finally,the pricing formulas of compound options are obtained.
引文
[1]李翠香.基于随机利率下跳-扩散过程的复合期权的定价[J].黑龙江大学自然科学学报,2012,29(4):431-436.LI C X.Pricing compound options under jump-diffusion processes with stochastic interest rates[J].Journal of Natural Science Of Heilongjiang University,2012,29(4):431-436.(Ch).
[2]杨淑彩.股票价格遵循Ornstein-Uhlenbeck过程的复合期权定价[J].西安工程大学学报,2014,28(30):376-380.YANG S C.Compound option pricing under Ornstein-Uhlenbeck process[J].Journal of Xi'an Polytechnic University,2014,28(28):376-380.(Ch).
[3]徐聪聪.股票价格服从指数O-U过程的复合期权定价方法探析[J].湖南师范大学自然科学学报,2015,38(3):74-79.XU C C.Analysis on pricing methods of compound option when stock price obeys exponential O-U process[J].Journal of Natural Science of Hunan Normal University,2015,38(30):74-79.(Ch).
[4] HULL J,WHITE A.Valuing derivative securities using the explicit finite difference method[J].Journal of Financial and Quantitative Analysis,1990,25(1):87-100.
[5]闫海峰,刘三阳.股票价格遵循指数O-U过程的最大值期权定价[J].工程数学学报,2004(3):397-402.YAN H F,LIU S Y.Pricing options on the Maximum of stocks driven by Ornsten-Uhlenback process[J].Chinese Journal of Engineering Mathematics,2004(3):397-402.(Ch).
[6]魏广华,袁明霞.随机利率下数字幂型期权的定价[J].西南师范大学学报,2013,38(12):55-60.WEI G H,YUAN M X.Pricing of digital Power-Option under stochastic interest rate[J].Journal of Southwest China Normal University,2013,38(12):55-60.(Ch).
[7]刘敬伟.Vasicek随机利率模型下指数O-U过程的幂型期权鞅定价[J].数学的实践与认识,2009,39(1):31-39.LIU J W.Pricing European Power-function option under exponential Ornstein-Uhlenbeck process and vasicek interest rate with martingale method[J].Mathematics in Practice and Theory,2009,39(1):31-39.(Ch).
[8] HARRISON J M,KREPS D M.Martingales and arbitrage in mulitiperiod securities market[J].Journal of Economic Theory,1979,20:381-408.
[9] GERMAN H,KAROUI N E,ROCHET J C.Changes of numeaire,changes of probability measure and option pricing[J].Journal of Applied Probability,1995,32:443-458.
[10]周海林,吴鑫育.随机利率条件下的欧式期权定价[J].系统工程理论与实践,2011,31(4):729-734.ZHOU H L,WU X Y.Pricing European options under stochasticinterestrate[J]. SystemsEngineeringTheory&Practice,2011,31(4):729-734.(Ch).
[11]邓国和.随机波动率跳跃扩散模型下复合期权定价[J].数理统计与管理,2015,34(5):910-922.DENG G H.Pricing compound option in a stochastic volatility jump-diffusion model[J].Journal of Applied Statistics and Management,2015,34(5):910-922.(Ch).
[2]杨淑彩.股票价格遵循Ornstein-Uhlenbeck过程的复合期权定价[J].西安工程大学学报,2014,28(30):376-380.YANG S C.Compound option pricing under Ornstein-Uhlenbeck process[J].Journal of Xi'an Polytechnic University,2014,28(28):376-380.(Ch).
[3]徐聪聪.股票价格服从指数O-U过程的复合期权定价方法探析[J].湖南师范大学自然科学学报,2015,38(3):74-79.XU C C.Analysis on pricing methods of compound option when stock price obeys exponential O-U process[J].Journal of Natural Science of Hunan Normal University,2015,38(30):74-79.(Ch).
[4] HULL J,WHITE A.Valuing derivative securities using the explicit finite difference method[J].Journal of Financial and Quantitative Analysis,1990,25(1):87-100.
[5]闫海峰,刘三阳.股票价格遵循指数O-U过程的最大值期权定价[J].工程数学学报,2004(3):397-402.YAN H F,LIU S Y.Pricing options on the Maximum of stocks driven by Ornsten-Uhlenback process[J].Chinese Journal of Engineering Mathematics,2004(3):397-402.(Ch).
[6]魏广华,袁明霞.随机利率下数字幂型期权的定价[J].西南师范大学学报,2013,38(12):55-60.WEI G H,YUAN M X.Pricing of digital Power-Option under stochastic interest rate[J].Journal of Southwest China Normal University,2013,38(12):55-60.(Ch).
[7]刘敬伟.Vasicek随机利率模型下指数O-U过程的幂型期权鞅定价[J].数学的实践与认识,2009,39(1):31-39.LIU J W.Pricing European Power-function option under exponential Ornstein-Uhlenbeck process and vasicek interest rate with martingale method[J].Mathematics in Practice and Theory,2009,39(1):31-39.(Ch).
[8] HARRISON J M,KREPS D M.Martingales and arbitrage in mulitiperiod securities market[J].Journal of Economic Theory,1979,20:381-408.
[9] GERMAN H,KAROUI N E,ROCHET J C.Changes of numeaire,changes of probability measure and option pricing[J].Journal of Applied Probability,1995,32:443-458.
[10]周海林,吴鑫育.随机利率条件下的欧式期权定价[J].系统工程理论与实践,2011,31(4):729-734.ZHOU H L,WU X Y.Pricing European options under stochasticinterestrate[J]. SystemsEngineeringTheory&Practice,2011,31(4):729-734.(Ch).
[11]邓国和.随机波动率跳跃扩散模型下复合期权定价[J].数理统计与管理,2015,34(5):910-922.DENG G H.Pricing compound option in a stochastic volatility jump-diffusion model[J].Journal of Applied Statistics and Management,2015,34(5):910-922.(Ch).