Actuarial Science and Financial Mathematics seminar series
Yang Lu
Concordia University
Room: M3 3127
Identification of Covariance Matrix Distributions Under Partial Observability: From Implied Covolatility Imputation to Multi-peril Insurance Pricing
(Random) covariance matrix plays an essential role in many financial applications. This talk focuses on the (possibility of) estimating parametric models on such symmetric positive definite matrices, when we only have partial observability. A motivating example is the pricing of options written on several stocks. Whereas data on implied volatilities are available for a large number of stocks, this is less frequently the case of implied covolatilities between pairs of stocks. In other words, very often, we observe only the diagonal (volatility) terms of a covariance matrix, but not the off-diagonal covolatility terms. In this case, can we identify the joint distribution of the entire matrix, given the observation of the diagonal terms only? We introduce a new approach based on static or dynamic Wishart models to solve this problem of missing data. We show that the parameter of the Wishart models are identified, possibly up to some signs. Then we derive the filtering approach for implied covolatilities and apply it to different financial applications. We end this talk with a discussion of the implication of the identification results on i) the pricing of multi-peril insurance policies ii) the modelling of realized covariance matrices, when this latter is fully observable.