SIAM Journal on Financial Mathematics, Volume 12, Issue 2, Page 823-866, January 2021.
It is well-known that using delta hedging to hedge financial options is not feasible in practice. Traders often rely on discrete-time hedging strategies based on fixed trading times or fixed trading prices (i.e., trades occur only if the underlying asset's price reaches some predetermined values). Motivated by this insight and with the aim of obtaining explicit solutions, we consider the seller of a perpetual American put option who can hedge her portfolio once until the underlying stock price leaves a certain range of values $(a,b)$. We determine optimal trading boundaries as functions of the initial stock holding, and an optimal hedging strategy for a bond/stock portfolio. Optimality here refers to the variance of the hedging error at the (random) time when the stock leaves the interval $(a,b)$. Our study leads to analytical expressions for both the optimal boundaries and the optimal stock holding, which can be evaluated numerically with no effort.

中文翻译：

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单笔交易的永久美式看跌期权的最优对冲

SIAM 金融数学杂志，第 12 卷，第 2 期，第 823-866 页，2021 年 1 月。
众所周知，使用delta对冲对金融期权进行套期保值在实践中是不可行的。交易者通常依赖基于固定交易时间或固定交易价格的离散时间对冲策略（即，交易仅在标的资产价格达到某个预定值时发生）。受此见解的启发并为了获得明确的解决方案，我们考虑永久美式看跌期权的卖方，该卖方可以对冲其投资组合一次，直到标的股票价格离开特定范围的价值 $(a,b)$。我们确定最佳交易边界作为初始股票持有量的函数，以及债券/股票投资组合的最佳对冲策略。这里的最优性是指当股票离开区间 $(a,b)$ 时（随机）时间的套期保值误差的方差。