L 2 -discrete hedging in a continuous-time model
L 2 -discrete hedging in a continuous-time model
复制标题
L 2 - 连续时间模型中的离散对冲
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Trad
中科院分区：
文献类型：
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作者：
F. Trabelsi;A. Trad
在Black-Scholes期权定价市场模型中，欧式期权的卖方必须在时间上连续交易。当然，这从实际角度来看是不现实的。然后他必须遵循离散的交易策略。然而，无论现货价格的变动如何，在确定性时间进行对冲似乎并不自然。在本文中，它是假设套期保值交易在一个固定的数量N的再平衡（停止）时间。考虑了最优套期保值次数和比率的选择问题（PN），使复制误差的方差最小。对于给定的N再平衡，离散的最优套期保值策略确定此标准。问题（PN），然后转化为一个多维的最优停止问题的边界约束。当比率由Black-Scholes给出时，还考虑了对于相同准则选择最优再平衡的限制性问题（PN BS）。利用向量值最优停止理论，证明了问题（PN）和（PN BS）中每一个的最优再平衡序列的存在性。它还表明BS，它们是渐近等价的，当再平衡的数量变得很大，并为问题（PN）的最优性准则。当对套期保值时间施加更现实的限制时，也进行了同样的研究。在两次再平衡的特殊情况下，求解了问题（P2BS），并将问题（P2BS）和（P2）转化为两个最优停止问题。这种变换对于数值计算很有用。
In the setting of the Black-Scholes option pricing market model, the seller of a European option must trade continuously in time. This is, of course, unrealistic from the practical viewpoint. He must then follow a discrete trading strategy. However, it does not seem natural to hedge at deterministic times regardless of moves of the spot price. In this paper, it is supposed that the hedger trades at a fixed number N of rebalancing (stopping) times. The problem (PN) of selecting the optimal hedging times and ratios which allow one to minimize the variance of replication error is considered. For given N rebalancing, the discrete optimal hedging strategy is identified for this criterion. The problem (PN) is then transformed into a multidimensional optimal stopping problem with boundary constraints. The restrictive problem (PN BS) of selecting the optimal rebalancing for the same criterion is also considered when the ratios are given by Black-Scholes. Using the vector-valued optimal stopping theory, the existence is shown of an optimal sequence of rebalancing for each one of the problems (PN) and (PN BS). It also shown BS that they are asymptotically equivalent when the number of rebalances becomes large and an optimality criterion is stated for the problem (PN). The same study is made when more realistic restrictions are imposed on the hedging times. In the special case of two rebalances, the problem (P2 BS) is solved and the problems (P2 BS) and (P2) are transformed into two optimal stopping problems. This transformation is useful for numerical purposes.