%0 Journal Article %T Timer option pricing of stochastic volatility model with changing coefficients under time-varying interest rate %A Wang, Jixia %A Zhang, Dongyun %J Journal of Nonlinear Sciences and Applications %D 2018 %V 11 %N 12 %@ ISSN 2008-1901 %F Wang2018 %X 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. %9 journal article %R 10.22436/jnsa.011.12.01 %U http://dx.doi.org/10.22436/jnsa.011.12.01 %P 1294--1301 %0 Journal Article %T Pricing Timer Options %A C. Bernard %A Z. Cui %J J. Comput. Finance %D 2011 %V 15 %F Bernard2011 %0 Journal Article %T Quadratic-variation-based dynamic strategies %A A. Bick %J Manage. Sci. %D 1995 %V 41 %F Bick 1995 %0 Journal Article %T Anniversary article: Option pricing: Valuation models and applications %A M. Broadie %A J. B. Detemple %J Manage. Sci. %D 2004 %V 50 %F Broadie2004 %0 Journal Article %T Pricing and Hedging Volatility Derivatives %A M. Broadie %A A. Jain %J The Journal of Derivatives %D 2008 %V 15 %F Broadie2008 %0 Journal Article %T Hedging variance options on continuous semimartingales %A P. Carr %A R. Lee %J Finance Stoch. %D 2010 %V 14 %F Carr2010 %0 Journal Article %T A Theory of the Term Structure of Interest Rates %A J. C. Cox %A J. Ingersoll %A E. Jonathan %A S. A. Ross %J Econometrica %D 1985 %V 53 %F Cox1985 %0 Journal Article %T Efficient Monte Carlo Simulation of Security Prices %A D. Duffie %A P. Glynn %J Ann. Appl. Probab. %D 1995 %V 5 %F Duffie1995 %0 Journal Article %T Bounds on European Option Prices under Stochastic Volatility %A R. Frey %A C. A. Sin %J Math. Finance %D 1999 %V 9 %F Frey1999 %0 Journal Article %T A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options %A S. L. Heston %J Rev. Financ. Stud. %D 1993 %V 6 %F Heston1993 %0 Journal Article %T The pricing of options on Assets with Stochastic Volatilities %A J. C. Hull %A A. D. White %J J. Finance %D 1998 %V 42 %F Hull1998 %0 Journal Article %T Bessel Process, Stochastic Volatility and Timer Options %A C. Li %J Math. Finance %D 2016 %V 26 %F Li2016 %0 Journal Article %T Closed Form Approximation of Timer Option Prices Under General Stochastic Volatility Models %A M. Li %A F. Mercurio %J University Library of Munich %D 2013 %V 2013 %F Li2013 %0 Book %T Volatility Trading %A A. J. Neuberger %D 1990 %I Londan Business School %C London %F Neuberger1990 %0 Journal Article %T Pricing Timer Options Under Fast Mean-reverting Stochastic Volatility %A D. Saunders %J Can. Appl. Math. Q. %D 2009 %V 17 %F Saunders2009 %0 Book %T Stochastic Calculus for Finance I: The Binomial Asset Pricing Model %A S. E. Shreve %D 2004 %I Springer-Verlag %C New York %F Shreve 2004