The Symmetric Relationships Between Put And Call Barrier Options

In recent years, barrier options are used widely in the foreign currency markets. In this paper, we study the symmetric relationships between put and call barrier options so that the hedgers and investors can choose the type of barrier options more flexible and use the barrier options to hedge and invest in the foreign currency markets. The results of this paper can simplify the process of barrier options pricing.Firstly, we give a brief review of the basic concepts in option pricing and stochastic calculus that will be used in this study.Secondly, we obtain the following symmetric relationships between put and call Eu-ropean barrier options with different strick prices, different underlying asset prices and different barrier levels, by using simple analytic pricing formulae under the different con-ditions:Thirdly, we use the decomposition technique to verify the following symmetric re-lationships about the values and the optimal exercise prices between American put and call out-barrier options: Lastly, the following symmetric relationships between American put and call in-barrier options are obtained, with the help of the integral expresstions of these options:...