金融衍生品是指其价值取决于一种或多种标的资产价值的金融工具，并且其定价往往涉及复杂的数学模型。衍生品市场发展迅速，目前权益市场的全球价值为70万亿美元， 而衍生品市场的全球价值已超过500万亿美元。衍生品的定价理论一直是学术界和工业界研究的热点之一。 衍生品定价理论有着悠久的历史。在1973年之前，衍生品的定价通常是基于供求关系。在1973年，著名的BS模型问世，并在短时间内在学术界以及业界都得到了广泛应用。此后，学者们研究了基于不同假设下的多种衍生品定价模型。等风险定价模型的框架于2017年首次提出。该模型是一个相对新颖的模型，不依赖于完备市场的假设，假设条件较为宽松，应用较为广阔。 本文主要研究等风险定价模型，并将其应用于实际领域。首先，本文对选题背景进行了介绍，并对相关文献进行了总结归纳，在此基础上提出了论文的框架。其次，本文对等风险定价的理论框架进行介绍，并且给出对于欧式期权的显式公式，同时介绍了一种严谨的数值计算方法，进行了敏感性分析。此外，本文还进行了实证研究，并在中国内地、香港和印度指数期权市场对模型进行了检验，并且与作为基准的BS模型进行比较。本文最后介绍了基于等风险定价模型的障碍期权的定价方法，展示了其更多的应用可能。 本文的创新点和主要成果包括：本文引入较为新颖的衍生品定价框架，并且给出相应方法完成数值计算过程；除此之外，本文在数值过程中新引入Heston模型，来模拟标的资产的价格过程，并与离散BS模型进行性质上的比较，同时进行对应的敏感性分析；并且，本文首次对等风险定价模型进行了实证研究，在不同市场的情况下得出了等风险定价与作为基准的BS模型的表现相似的结论，而且在某些情况下，等风险定价具有更好的表现；最终，本文对一种奇异期权，即障碍期权，引入等风险定价模型。
Financial derivatives are financial instruments whose values are dependent on the value of one or more underlying assets. The derivatives market expends rapidly and is now worth more than $500 trillion globally, compared to the equity market worth $70 trillion. The pricing theory of derivatives has always been one of the hottest topics both in the academic world and the industrial world. The pricing theory of derivatives has a long history. Before 1973, derivatives were typically priced based on supply and demand. In 1973, the famous BS model came into the public and were widely used in a short time. Since then, different derivatives pricing models based on different assumptions have been studied by scholars. Equal Risk Pricing, whose framework was first introduced in 2017, is a novel derivative pricing model based on the assumption of an incomplete market. This paper mainly focuses on the Equal Risk Pricing Model and utilizes it into the practical field. First, the background of the topic and relevant literatures are summarized, and the framework of the paper is put forward. Then, the theoretical framework of Equal Risk Pricing is summarized, the explicit formula and numerical procedure is presented. Certain sensitivity analyses are also conducted. Moreover, empirical studies are presented, and the model is tested and compared in different markets, including Chinese, Hong Kong and Indian index option markets. Finally, a method to price barrier options is introduced. The innovation points and main results of this paper include: this paper introduces a novel derivative pricing framework and complete the numerical procedure; Moreover, this paper introduces the Heston Model in the numerical procedure to simulate the price process of the underlying asset and compare the result with the Discrete BS Model; Furthermore, this paper conducts empirical studies on Equal Risk Pricing in different markets for the first time and conclude that the performance of Equal Risk Pricing is similar to that of normal BS Model, and under certain situations, Equal Risk Pricing has better performance. Finally, this paper applies Equal Risk Pricing to a certain exotic product: the barrier option.
