Pricing Lookback Options and Dynamic Guarantees
Pricing Lookback Options and Dynamic Guarantees
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DOI：
10.1080/10920277.2003.10596076
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Hans U. Gerber A.S.A.;E. S. S. A.S.A.-E.-S.-S.-A.S.A.-2082624298
中科院分区：
文献类型：
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作者：
Hans U. Gerber A.S.A.;E. S. S. A.S.A.-E.-S.-S.-A.S.A.-2082624298
股票指数年金中的奇异期权或担保的定价可能是有问题的。作者提出了封闭形式的公式定价回望期权和动态保证，方便对冲和保留这些产品。所使用的主要工具是B（u，T）的封闭形式表达式，即在长度为T的有限时间间隔内，维纳过程的运行最大值在正常数u之上的预期超额的拉普拉斯-斯蒂尔捷斯变换。如果一家公司的总净收益用维纳过程建模，那么超过u的运行最大值的部分可以解释为总股息支付，数量B（u，T）是到时间T的股息支付贴现值的期望。B（u，T）的公式用于欧式回望期权（看涨期权和看跌期权，固定和浮动执行价）的定价。它也被用来定价动态基金保护，这是对投资基金的保证：投资基金的单位数量随着时间的推移而增加。
Abstract Pricing exotic options or guarantees in equity-indexed annuities can be problematic. The authors present closed-form formulas for pricing lookback options and dynamic guarantees that facilitate the hedging and reserving for such products. The principal tool used is a closed-form expression for B(u, T), the Laplace-Stieltjes transform of the expected excess of the running maximum of a Wiener process above a positive constant u in a finite time interval of length T. If the aggregate net income of a company is modeled with a Wiener process, then the excess of the running maximum above u can be interpreted as aggregate dividend payments, and the quantity B(u, T) is the expectation of the discounted value of the dividend payments up to time T. The formula for B(u, T) is used to price European lookback options (call and put, fixed and floating strike). It is also used to price dynamic fund protection, which is a guarantee on an investment fund: The number of units of the investment fund is increased wh...