首中时在新型期权定价中的运用

Applications of the first hitting time to price exotic options

当市场是完备时,任意衍生证券的现值等于该证券未来收益折现值在等价鞅测度下的数学期望.利用L ap lace逆变换求得障碍是常数以及障碍随时间变化这两种情况下的股票价格首中时的密度函数,再根据首中时的性质、等价鞅测度变换,通过求期望,给出了固定执行价格的欧式回望期权和变界障碍时刻的欧式上升敲出看涨期权这两类新型期权的定价公式.其中,变界障碍时刻的欧式上升敲出看涨期权的定价公式具有较好的实用性.这种期权定价方法简单且直接,提供了定价新型期权的另一种途径.

When the market is complete, the present value of any derivative security is equivalent to mathematical expectation of its underlying profit discount value under equivalent martingale measurement. By Laplace adverse transform and characters of the first hitting time, density function of the first hitting time is obtained when the barrier is a constant and when it varies with time. Furthermore, the pricing formulas of two exotic options are deduced by the way of expectation. One is an European lookback call option with the fixed executive price, and the other is an European up-and-out call option with varied barriers. The pricing formula of European up-and-out call option with varied barriers is practicable. This way of option pricing is simple and direct. It provides another way to price exotic options.