Pricing Barrier Options With Copulas

Barrier options are contingent claims in which the exercise is conditional on the event that the value of the underlying asset has been above or below a given value over a given reference period. They are one of the most widely traded derivatives in the financial markets. One reason that an investor prefers a barrier option to an ordinary vanilla option is that barrier options are generally cheaper than standard options. The other reason is that barrier options may match risk hedging needs more closely. But, the pricing process of barrier option will be affected by the barrier level and more complicated than other options. Therefore, the simple and accurate pricing of barrier option has a strong practical significance.We referred to copulas as functions that join multivariate distribution func-tions to their one-dimensional marginal distribution functions. The paper mainly use copula function to pricing barrier options. First of all, introduces the defi-nition and classification of barrier option and some commonly used copulas and its theory of knowledge. Secondly, giving the pricing formulas based on the cop-ulas, main task is to choose the correct copula function by the market data. In addition, we made empirical analysis on the barrier option pricing model with applying domestic stock data and give the price of digital barrier option based on BS model?Gumbel Copula?Clayton Copula respectively. According to the analysis of results, the pricing model based on copula is more simple and easy to calculate.