Pricing Of The Extendible Option

This dissertation mainly study the option pricing problem of the extendible option.This dissertation contains four chapters. Chapter one is foreword,give the background of the Extendible option and the results of precursor's. Chapter two introduce Brown motion ,Ito integral and Poisson process. Last section is the theory of changing numeraire.Chapter three mainly study the extendible option under the diffusion process of the stochastic interest rate. The first section is the knowledge preparation and give two propositions about Brown motion(See theorem 3.1.5,theorem 3.1.6).the second and third section are option pricing.The pricing formulas of the Holder extendible and Writer extendible are deduced by means of choosing different numeriare and changing the probability measure (See theorem 3.2.1,theorem3.3.1).Such work done by Longstaff is extended directly.Chapter four mainly study the extendible option under the jump diffusion process of the stochastic interest rate. The first section is also the knowledge preparation and give a proposition of the Brown motion under more general condition (See corollary 4.1.7 ).the second and third section are option pricing.The pricing formulas of the Holder extendible and Writer extendible are deduced by means of choosing different numeriare and changing the probability measure (See theorem 4.2.1,theorem 4.3.1).Such work done by C .R .Gukhal and Qian are extended directly.