Tolga Umut Kuzubas

A Comparative Goodness-of-Fit Analysis of Distributions of Some Lévy Processes and Heston Model to Stock Index Returns

In this paper, we investigate the goodness-of-fit of three Levy processes, namely Variance-Gamma (VG), Normal-Inverse Gaussian (NIG) and Generalized Hyperbolic (GH) distributions, and probability distribution of the Heston model to index returns of twenty developed and emerging stock markets. Furthermore, we extend our analysis by applying a Markov regime switching model to identify normal and turbulent periods. Our findings indicate that the probability distribution of the Heston model performs well for emerging markets under full sample estimation and retains goodness of fit for high volatility periods, as it explicitly accounts for the volatility process. On the other hand, the distributions of the Levy processes, especially the VG and NIG distributions, generally improves upon the fit of the Heston model, particularly for developed markets and low volatility periods. Furthermore, some distributions yield to significantly large test statistics for some countries, even though they fit well to other markets, which suggest that properties of the stock markets are crucial in identifying the best distribution representing empirical returns.

Second Price Auctions with Resale Under State Uncertainty

We study the equilibrium of second-price auctions with resale when the value of the asset is subject to future state uncertainty. We assume bidders differ in their sensitivities toward each state, resulting in alternating orderings of use values. In both complete and incomplete information settings, equilibrium bids are higher than expected use values, equilibrium bidding functions are non-monotone and convex, with a minimum at the median of type distribution. Under incomplete information, the winner of the auction is unable to infer the type of losing bidder with certainty, which can result in scenarios where she cannot capture all surplus.