雪球期权的定价机制与动态解码——偏微分方程模型下雪球期权定价与动态对冲机制研究

The Pricing Kernel and Dynamic Decoding of Snowball Options—A Study of Snowball Option Pricing and Dynamic Hedging Mechanism under a PDE Model

摘要: 雪球全称为“雪球型自动敲入敲出式券商收益凭证”，是一种奇异期权类产品。很多人不希望承担过大投资风险的同时获得不俗的收益，所以雪球期权自出现就深受广大群众的追捧，由此衍生的一系列金融产品，凭借高票息在金融市场上占有一席之地。本文从雪球期权概述出发，介绍产品基本要素，并进行情景分析。接着建立雪球期权定价模型，分敲出离散情景和敲出连续情景讨论，每个情景又区分当前未敲入和当前已敲入两种情形，得到相应的定价公式。本文进行了定价参数的估计，通过GARCH (1, 1)模型确定波动率，然后确定了雪球期权的所有参数取值。使用蒙特卡洛和有限差分两种方法进行求解，将结果进行比较，发现结果基本一致，同时进行了动态对冲，最后对雪球期权的投资进行分析，得出主要结论。

Abstract: The snowball option, fully known as the “Auto-Callable Snowball Structured Note with Knock-In and Knock-Out Features”, is a type of exotic derivative. Many investors seek attractive returns without taking on excessive risk, which has made snowball options highly popular since their introduction. Consequently, a series of financial products derived from them have secured a place in the financial market due to their high coupon rates. This paper begins with an overview of snowball options, introducing their fundamental components and conducting scenario analysis. Subsequently, a pricing model for snowball options is established, examining discrete and continuous knock-out scenarios. Each scenario is further divided into two cases: when the option has not been knocked in and when it has already been knocked in, leading to the derivation of corresponding pricing formulas. The paper also involves the estimation of pricing parameters, where volatility is determined using the GARCH (1, 1) model, and all parameters for the snowball option are finalized. The pricing is solved using both the Monte Carlo method and the finite difference method, and the results are compared, showing general consistency. Additionally, dynamic hedging is performed. Finally, an investment analysis of snowball options is conducted, leading to the main conclusions.