题目：Mean-variance indifference pricing
报告人：Yang Shen （York University）
时间：4月24日（周一）10：00-11：00
地点：统计楼103
摘要：
In this paper, we propose a new theory of derivatives pricing, namely, mean-variance indifference pricing, which synthesizes the idea of utility indifference pricing and Markowitz's mean-variance analysis. We develop the theory under continuous-time Markovian regime-switching models, with a focus on unhedgable risk due to market incompleteness and regime switches. The pricing framework is not limited to the chosen underlying models, but works for and is worth being extended to other models.
As the dynamic mean-variance optimization is essentially a time-inconsistent optimal control problem, Bellman's dynamic programming principle is not applicable. We resort to the notion of equilibrium in game theory and solve the problem via an extended regime-switching HJB equation.
We find that the buyer's and seller's indifference prices are both given by nonlinear pricing operators, which are not only mathematically neat, but also have profound financial implications. In fact, the buyer's (resp. seller's) indifference price equal a linear price minus (resp. plus) correction terms accounting for the volatility of the derivative in the linear pricing framework and quantifying instantaneous fluctuations from the financial market and structural changes of macro-economic conditions. Indeed, the linear price of the derivative reduces to the risk-neutral price under certain conditions.
As application, we compute mean-variance indifference prices of European call and put options. We also give a new version of put-call parity in our framework. Our ultimate goal is to apply the buyer's and the seller's indifference pricing formulas to calibrate model parameters from the bid-ask spread observed in the real market. In particular, the estimated risk aversion parameters of the representative buyer and seller can serve as good indicators for market sentiment.