Time Dependent Barrier Option Values

Time dependent barrier options have barrier periods covering a portion of option life. This feature makes them hybrids of barrier options and ordinary European options. There are two types of time dependent barrier options: 1. front end barrier options; 2. rear end barrier options. The options are more flexible than regular barrier options for investors who hold particular views on values of foreign exchanges, equities or commodities in certain periods of time. They can be used for hedging and investment in financial market. Analytical solutions of the option values are derived in a conventional Black-Scholes option-pricing environment. Their delta, gamma and vega risks are discussed and compared with the risk factors of the ordinary options