TY - JOUR AU - Wang, Jixia AU - Zhang, Dongyun PY - 2018 TI - Timer option pricing of stochastic volatility model with changing coefficients under time-varying interest rate JO - Journal of Nonlinear Sciences and Applications SP - 1294--1301 VL - 11 IS - 12 AB - Considering economic variables changing from time to time, the time-varying models can fit the financial data better. In this paper, we construct stochastic volatility models with time-varying coefficients. Furthermore, the interest rate risk is one of important factors for timer options pricing. Therefore, we study the timer options pricing for stochastic volatility models with changing coefficients under time-varying interest rate. Firstly, the partial differential equation boundary value problem is given by using \(\Delta\)-hedging approach and replicating a timer option. Secondly, we obtain the joint distribution of the variance process and the random maturity under the risk neutral probability measure. Thirdly, the explicit formula of timer option pricing is proposed which can be applied to the financial market directly. Finally, numerical analysis is conducted to show the performance of timer option pricing proposed. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.12.01 DO - 10.22436/jnsa.011.12.01 ID - Wang2018 ER - TY - JOUR TI - Pricing Timer Options AU - C. Bernard AU - Z. Cui JO - J. Comput. Finance PY - 2011 DA - 2011// VL - 15 ID - Bernard2011 ER - TY - JOUR TI - Quadratic-variation-based dynamic strategies AU - A. Bick JO - Manage. Sci. PY - 1995 DA - 1995// VL - 41 ID - Bick 1995 ER - TY - JOUR TI - Anniversary article: Option pricing: Valuation models and applications AU - M. Broadie AU - J. B. Detemple JO - Manage. Sci. PY - 2004 DA - 2004// VL - 50 ID - Broadie2004 ER - TY - JOUR TI - Pricing and Hedging Volatility Derivatives AU - M. Broadie AU - A. Jain JO - The Journal of Derivatives PY - 2008 DA - 2008// VL - 15 ID - Broadie2008 ER - TY - JOUR TI - Hedging variance options on continuous semimartingales AU - P. Carr AU - R. Lee JO - Finance Stoch. PY - 2010 DA - 2010// VL - 14 ID - Carr2010 ER - TY - JOUR TI - A Theory of the Term Structure of Interest Rates AU - J. C. Cox AU - J. Ingersoll AU - E. Jonathan AU - S. A. Ross JO - Econometrica PY - 1985 DA - 1985// VL - 53 ID - Cox1985 ER - TY - JOUR TI - Efficient Monte Carlo Simulation of Security Prices AU - D. Duffie AU - P. Glynn JO - Ann. Appl. Probab. PY - 1995 DA - 1995// VL - 5 ID - Duffie1995 ER - TY - JOUR TI - Bounds on European Option Prices under Stochastic Volatility AU - R. Frey AU - C. A. Sin JO - Math. Finance PY - 1999 DA - 1999// VL - 9 ID - Frey1999 ER - TY - JOUR TI - A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options AU - S. L. Heston JO - Rev. Financ. Stud. PY - 1993 DA - 1993// VL - 6 ID - Heston1993 ER - TY - JOUR TI - The pricing of options on Assets with Stochastic Volatilities AU - J. C. Hull AU - A. D. White JO - J. Finance PY - 1998 DA - 1998// VL - 42 ID - Hull1998 ER - TY - JOUR TI - Bessel Process, Stochastic Volatility and Timer Options AU - C. Li JO - Math. Finance PY - 2016 DA - 2016// VL - 26 ID - Li2016 ER - TY - JOUR TI - Closed Form Approximation of Timer Option Prices Under General Stochastic Volatility Models AU - M. Li AU - F. Mercurio JO - University Library of Munich PY - 2013 DA - 2013// VL - 2013 ID - Li2013 ER - TY - BOOK TI - Volatility Trading AU - A. J. Neuberger PB - Londan Business School PY - 1990 DA - 1990// CY - London ID - Neuberger1990 ER - TY - JOUR TI - Pricing Timer Options Under Fast Mean-reverting Stochastic Volatility AU - D. Saunders JO - Can. Appl. Math. Q. PY - 2009 DA - 2009// VL - 17 ID - Saunders2009 ER - TY - BOOK TI - Stochastic Calculus for Finance I: The Binomial Asset Pricing Model AU - S. E. Shreve PB - Springer-Verlag PY - 2004 DA - 2004// CY - New York ID - Shreve 2004 ER -