论文标题
跳跃的几何步骤选项。平价关系，脚步和半分析定价
Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing
论文作者
论文摘要
本文研究指数lévy市场的几何步骤选项。我们的贡献是多种多样的，并扩展了几何步骤选项定价文献的几个方面。首先，我们提供对称性和平价关系，并为欧洲型和美国型几何双屏障步骤选项提供各种特征。特别是，我们能够获得美国型几何学双屏障步骤合同的早期溢价及其成熟度的同等效果，并表征对这些早期运动溢价的扩散和跳跃贡献，并通过部分跨性别的额外方程式和普通的静态等式分别贡献。作为我们特征的应用，我们为（常规）欧洲型和美国型的几何形状下降步骤呼叫选项提供了半分析定价结果。最后，我们使用后者的结果来讨论一旦添加跳跃后的几何步骤选项的早期锻炼结构，并随后对（欧洲型和美国型）几何步骤合同的价格和对冲参数进行分析。
The present article studies geometric step options in exponential Lévy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and derive various characterizations for both European-type and American-type geometric double barrier step options. In particular, we are able to obtain a jump-diffusion disentanglement for the early exercise premium of American-type geometric double barrier step contracts and its maturity-randomized equivalent as well as to characterize the diffusion and jump contributions to these early exercise premiums separately by means of partial integro-differential equations and ordinary integro-differential equations. As an application of our characterizations, we derive semi-analytical pricing results for (regular) European-type and American-type geometric down-and-out step call options under hyper-exponential jump-diffusion models. Lastly, we use the latter results to discuss the early exercise structure of geometric step options once jumps are added and to subsequently provide an analysis of the impact of jumps on the price and hedging parameters of (European-type and American-type) geometric step contracts.
