Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy
用马尔可夫机制转换模型刻画不同经济状态，研究标的资产与交易对手资产价值服从相关跳扩散过程时脆弱欧式期权的定价，通过二维拉普拉斯变换得到解析定价公式。
In this paper, we use a Markov-modulated regime switching approach to model various states of the economy, and study the pricing of vulnerable European options when the dynamics of the underlying asset value and the asset value of the counterparty follow two correlated jump-diffusion processes under regime switching. The correlation is modelled by both the diffusion parts and the pure jump parts which describe the uncertainty of the value of the risky assets. We develop a method to determine an equivalent martingale measure and a parsimonious representation of the risk-neutral density is provided. Based on this, we derive an analytical pricing formula for vulnerable options via two-dimensional Laplace transforms, and implement the formula through numerical Laplace inversion.