OPTIMAL CONTINUOUS‐TIME HEDGING WITH LEPTOKURTIC RETURNS
研究了股票价格服从离散采样指数Lévy过程时，最优均值方差对冲策略在高频再平衡下的行为，发现所有对冲属性随再平衡间隔趋零而逐点收敛，并给出快速傅里叶变换计算公式。
We examine the behavior of optimal mean–variance hedging strategies at high rebalancing frequencies in a model where stock prices follow a discretely sampled exponential Lévy process and one hedges a European call option to maturity. Using elementary methods we show that all the attributes of a discretely rebalanced optimal hedge, i.e., the mean value, the hedge ratio, and the expected squared hedging error, converge pointwise in the state space as the rebalancing interval goes to zero. The limiting formulae represent 1‐D and 2‐D generalized Fourier transforms, which can be evaluated much faster than backward recursion schemes, with the same degree of accuracy. In the special case of a compound Poisson process we demonstrate that the convergence results hold true if instead of using an infinitely divisible distribution from the outset one models log returns by multinomial approximations thereof. This result represents an important extension of Cox, Ross, and Rubinstein to markets with leptokurtic returns.