用微笑曲线对比特币期权进行Delta对冲 摘要 我们使用一组隐含微笑曲线和其他微笑调整的Delta来分析比特币期权的稳健动态Delta对冲。这些Delta要么是无模型的，从某种意义上说，它们对于每个尺度不变的随机和/或局部波动率模型都是相同的，要么是基于简单的制度依赖参数化的局部波动率。

Thoughts on High-Frequency Trading Strategies (5) In the previous article, various methods for calculating mid-price were introduced, and a revised mid

Thoughts on High-Frequency Trading Strategies (4) The previous article demonstrated the need for dynamically adjusting parameters and how to evaluate t

上篇文章初步介绍了各种中间价的计算方法，并给出了一种中间价的修订，本文继续深入这个话题。 所需数据 订单流数据和十档的深度数据，来自于实盘收集，更新频率都是100ms。实盘的只包含买一卖一盘口数据是实时更新的，为了简洁，暂时不用。考虑到数据太大，只保留了10万行深度数据，并且把逐档行情也独立为单独的

上篇文章通过研究订单到达间隔，展示了为什么要动态调整对参数以及如何评价估计的好坏。本篇文章将聚焦深度数据，研究中间价mid-price(或者叫fair-price,micro-price等等）。 深度数据 币安提供了最优报价的历史数据下载，包含best_bid_price:最优买价，即最大的买价，be

Thoughts on High-Frequency Trading Strategies (3) In the previous article, I introduced how to model cumulative trading volume and analyzed the phenomen

上篇文章，我介绍了如何建模累计成交量，以及简单对价格冲击现象进行了分析。本篇文章还将围绕着trades订单数据继续分析。这两天YGG上线币安U本位合约，价格波动很大，甚至成交量一度超过了BTC，今天就那它进行分析。 订单时间间隔 一般情况下都假设订单到达的时间符合泊松过程，这里有一篇文章介绍了[泊松过程

Thoughts on High-Frequency Trading Strategies (2) Accumulated Trading Amount Modeling In the previous article, we derived an expression for the pr

文章主要探讨高频交易策略，重点研究累计成交量建模和价格冲击。文章通过分析单笔成交、固定间隔的价格冲击以及成交量对价格的影响，提出了一个初步的最优挂单位置模型。此模型基于对成交量和价格冲击的理解，试图找到最优的交易位置。对模型的假设进行了深入讨论，并通过比较实际与模型预测的期望收益，对最优挂单位置进行了初步评估。 #

Thoughts on High-Frequency Trading Strategies (1) I have written two articles on high-frequency trading of digital currencies, namely “[Digital Currency

文章探讨了数字货币高频交易策略，包括利润来源（主要来自市场剧烈波动和交易所手续费返佣），挂单位置和仓位控制的问题，以及用帕累托分布对成交量进行建模的方法。此外，还引用了币安提供的逐笔成交和最优挂单数据进行回测，并计划在后续文章中深入讨论高频交易策略的其他问题。 以前我曾经写过两篇关于数字货币高频交易的两篇文

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