Mathematical Finance and Applied Probability Seminar Tensor PCA for Implied Volatility Surfaces Andrew Papanicolaou (NYU)
Wednesday, September 18th, 20194:00 PM - 5:00 PMStorrs CampusMONT 313
Principal component analysis (PCA) is a useful tool when trying to uncover factor models from historical asset returns. For the implied volatilities of U.S. equities, there is a PCA-based model with a so-called principal eigenportfolio whose returns time series lies close to that of an overarching market factor. Specifically, this market factor is a new volatility index that we have constructed to be a weighted average of implied-volatility returns with weights based on the options' vega and open interest (OI). This OI-weighted index is one among several possible new indices that can be constructed by collecting implied volatilities from options on many individual equities. We analyze the singular values from the tensor structure of implied volatilities from the S&P500 constituents, and find evidence indicating there to be at least two significant factors in this market, with the first component have similarities with the OI-weighted index.
Mathematical finance and applied probability seminar On pricing rules and optimal strategies in general Kyle-Back models Albina Danilova (London School of Economics)
Wednesday, October 30th, 20194:00 PM - 5:00 PMStorrs CampusMONT 313
The folk result in Kyle-Back models states that the value function of the insider remains unchanged when her admissible strategies are restricted to absolutely continuous ones. In this talk I will show that, for a large class of pricing rules used in current literature, the value function of the insider can be finite when her strategies are restricted to be absolutely continuous and infinite when this restriction is not imposed. This implies that the folk result doesn't hold for those pricing rules and that they are not consistent with equilibrium. I will derive the necessary conditions for a pricing rule to be consistent with equilibrium and prove that, when a pricing rule satisfies these necessary conditions, the insider's optimal strategy is absolutely continuous, thus obtaining the classical result in a more general setting.
This, furthermore, allows to justify the standard assumption of absolute continuity of insider's strategies since one can construct a pricing rule satisfying the derived necessary conditions that yield the same price process as the pricing rules employed in the modern literature when insider's strategies are absolutely continuous.