We introduced a new method to compute the European Call (and Put) Option price under the assumption of multifractional Brownian motion (mBm). The reason why we need a procedure for estimating the Option price is due to the absence of a closed formula for this process. To compute the Option price, we first simulated the logarithmic price under mBm and, by using a discount factor, we computed the option’s pay-off. Then, we fitted the best probability distribution associated to the discounted pay-off, computing the European Call Option price as its average.

中文翻译：

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多重过程和长期依赖下的期权定价

我们介绍了一种在多分数布朗运动 (mBm) 假设下计算欧式看涨（和看跌）期权价格的新方法。我们需要一个估计期权价格的程序的原因是因为这个过程没有一个封闭的公式。为了计算期权价格，我们首先模拟了 mBm 下的对数价格，并通过使用折扣因子计算了期权的收益。然后，我们拟合与贴现收益相关的最佳概率分布，将欧式看涨期权价格计算为其平均值。