随机波动率模型下场外期权的定价和对冲策略研究

After the subprime mortgage crisis in 2007, researchers and market practitioners have paid much more attention on counterparty credit risk. In a financial contract, one has to suffer from financial losses once the other defaults. Hence it is necessary to take counterparty credit risk into account when pricing credit-sensitive OTC contracts. This project is to investigate the pricing issue of OTC options with stochastic correlation. On the other hand, we consider hedging strategies for OTC options under different market assumptions. Firstly, we investigate the case when only the underlying asset is available to hedge. Then the results are extended to the case when there are CDS on the firm who issues the options in the markets. The effects of CDS on option prices are illustrated based on the derived hedging strategies.

金融危机过后，对手信用风险受到了金融业界和学者的广泛关注。一旦合约一方发生违约行为，合约的另一方必然会遭到损失。因此，在金融产品的定价中需要体现对手违约风险溢价。本项目旨在在随机波动率的框架下研究对手信用风险的定价问题。另一方面，场外期权的风险管理需要相对应的对冲策略，我们计划研究不同市场环境下场外期权的对冲策略问题。首先考虑只采用标的资产来管理场外期权。之后考虑市场上有以期权发行方为标的的信用违约掉期交易，在此假设下求解相对应的对冲策略，并分析信用违约掉期在场外期权对冲策略的作用。

项目首先考虑了随机波动率模型下场外期权的定价问题。受资本资产定价模型(CAPM)启发，项目通过市场组合（指数）联系各项资产，建立和实际更加贴近的理论模型。在此基础上，我们研究了场外普通欧式期权、场外亚式期权、场外多资产期权以及场外巨灾期权的定价问题。另外，我们讨论了具有相关离职影响的高管股票期权定价问题，该问题的研究非常类似于场外期权的定价。最后，我们探讨了巨灾风险管理相关金融合约的设计与定价，以及这些合约在风险管理的表现。