一类累计期权的定价

The Pricing of Class-One Accumulator

累计期权是一种以合约形式买卖资产的金融衍生工具,其实质是投资者和发行商之间的一个金融合约。通过假设累计期权为合约一方没有收益上限要求和有收益上限要求两种情况以及股票价格服从几何布朗运动,然后,利用B-S模型对这两种情况下的累计期权定价,分别解出解析解和数值解,得出当合约一方有收益上限要求时,其需要支付的期权金会随着股票波动率和无风险利率的增大而减少,随着敲定价的增大,其期权金的最大值会受到收益上限的约束等结果,从而研究累计期权的风险价值。对于包含多个实施时间的累计期权定价问题,可采用蒙特卡罗方法模拟期权价格的思路。

Accumulator is a financial derivative tool, buying and selling assets in the form of contract, the essence of which is the financial corm＇acts between investors and vendors. In order to study the value-at-risk of accumulators, supposing that there are two circumstances of accumulators, one with income ceiling requirements, the other not, and that share prices comply with geometric Brewnian motion and then, making use of Black-Scholes model to pricing the accumulators under these two circumstances, we＇ll work out respectively the analytical solution and the numerical solution and learn that when one party has income ceiling requirements, the needed premium will reduce along with the stock volatility and the increase of risk-free rate and that with the increasing of strike price, the maximum of premium will be restrained by income ceiling. With regard to the pricing of accumulators which include multiple implementary times, Monte Carlo method might be adopted to imitate the pricing process of share options.