Michal Czerwonko

Tick Size, Microstructure Noise, Informed Trading and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price, as well as on the statistical technique used to estimate these metrics. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics, all statistical techniques used for their estimation, and all inversion methods. In addition, we document systematic differences in option market information shares between equities and exchange traded funds both before and after the tick size change, and we present strong event-type empirical evidence of informed trading in the equity option market after the tick size change, with extreme values of the IS and CS metrics in that market producing similar abnormal underlying asset returns.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics I: A Numerical Solution

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete-time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous-time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics II: Economic Implications

We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs; we allow cash dividends on the risky asset. The allocation shifts toward the riskless asset relative to diffusion in varying degrees depending on parameter values. It is sensitive to the proportion of the jump component to total volatility, but also to the expected amplitude for a given proportion. The shift becomes small when the relative risk aversion increases, but it becomes major when the solvency constraint is active in the presence of jumps. We derive utility losses and risk premia due to jumps under realistic parameter values, and show that even when the no transaction region is very similar between pure diffusion and the mixed process the latter corresponds to lower utility because of higher portfolio restructuring costs.

Mispriced Index Option Portfolios

The optimal portfolio of a utility-maximizing investor trading in the S&P 500 index and cash, subject to proportional transaction costs, becomes stochastically dominated when overlaid with a zero-net-cost portfolio of S&P 500 options bought at their ask and written at their bid price in most months over 1990-2013. Dominance is prevalent when the ATM-IV is high, right skew is low, and option maturity is short. The portfolios include mostly calls and positions are overwhelmingly short. Similar results obtain with options on the CAC and DAX indices. The results are explained neither by priced factors nor a non-monotonic stochastic discount factor.

Tick Size Reduction and Price Discovery in Option Markets: An Empirical Investigation

We examine the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. We first document a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the inversion method of the option value to find the implied stock price. We then introduce a more accurate inversion method that results in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. In all cases, however, we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Tick Size, Microstructure Noise and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

One Security, Four Markets: Canada-US Cross-Listed Options and Underlying Equities

In this paper we examine the relative contributions of US and Canadian markets to price discovery for Canadian cross-listed options and their cross-listed underlying stocks. We use two different econometric approaches in assessing the contributions of each market to price discovery, the information shares approach and the common factor approach. Our empirical results are consistent in both approaches. We show that on average price discovery for cross-listed Canadian stocks and options takes place overwhelmingly in the underlying asset markets, where Canadian equity markets dominate the discovery process. The results show that option markets information shares remain comparable, although slightly higher in the US, which contrasts with the fact that its relative volume is almost ten times greater than that of Canadian options markets. The results also indicate a high degree of integration between Canadian and US markets for the underlying stocks of cross-listed options and show that the foreign exchange market does not contribute to the co integration between these markets to any significant extent. An analysis of the determinants of the relative information shares between firms with all markets analyzed simultaneously shows that the most important factor explaining the information shares is the volatility of underlying returns.

Portfolio Selection with Transaction Costs and Jump-Diffusion Asset Dynamics

We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion process in the presence of proportional transaction costs. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in earlier work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.