Option pricing with a compound CARMA( p , q )-Hawkes
提出一种基于复合CARMA(p,q)-Hawkes模型的资产价格动态模型，该模型能复现金融市场的波动率微笑，并通过实证校准展示了高阶自回归和移动平均参数在期权定价中的作用。
A self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p, q)-Hawkes model, has recently been introduced. The model generalises the Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p, q) model where the associated state process is driven by the counting process itself. The proposed model preserves the same degree of tractability as the Hawkes process, but it can reproduce more complex time-dependent structures observed in several market data. The paper presents a new model of asset price dynamics based on the CARMA(p, q)-Hawkes model. It is constructed using a compound version of it with a random jump size that is independent of both the counting and the intensity processes and can be employed as the main block for pure jump and (stochastic volatility) jump-diffusion processes. The numerical results for pricing European options illustrate that the new model can replicate the volatility smile observed in financial markets. Through an empirical analysis, which is presented as a calibration exercise, we highlight the role of higher order autoregressive and moving average parameters in pricing options.