## Essays in asset pricing

### Orlowski, Piotr ; Trojani, Fabio (Dir.)

### Thèse de doctorat : Università della Svizzera italiana, 2017 ; 2017ECO002.

My dissertation consists of three chapters, each of which focuses on a different area of research in asset pricing. The first chapter's focal point is the measurement of the premium for jump risks in index option markets. The second chapter is devoted to non- parametric measurement of pricing kernel dispersion. The third chapter contributes to the literature on latent state variable recovery in... Plus

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- My dissertation consists of three chapters, each of which focuses on a different area of research in asset pricing. The first chapter's focal point is the measurement of the premium for jump risks in index option markets. The second chapter is devoted to non- parametric measurement of pricing kernel dispersion. The third chapter contributes to the literature on latent state variable recovery in option pricing models. In the first chapter, "Big risk", I show how to replicate a large family of high-frequency measures of realised return variation using dynamically rebalanced option portfolios. With this technology investors can generate optimal hedging payoffs for realised variance and several measures of realised jump variation in incomplete option markets. These trading strategies induce excess payoffs that are direct compensation for second- and higher order risk exposure in the market for (index) options. Sample averages of these excess payoffs are natural estimates of risk premia associated with second- and higher order risk exposures. In an application to the market for short-maturity European options on the S&P500 index, I obtain new important evidence about the pricing of variance and jump risk. I find that the variance risk premium is positive during daytime, when the hedging frequency is high enough, and negative during night-time. Similarly, for an investor taking long variance positions, daytime profits are grater in absolute value than night-time losses. Compensation for big risk is mostly available overnight. The premium for jump skewness risk is positive, while the premium for jump quarticity is negative (contrary to variance, also during the trading day). The risk premium for big risk is concentrated in states with large recent big risk realisations. In the second chapter, "Arbitrage free dispersion", co-authored with Andras Sali and Fabio Trojani, we develop a theory of arbitrage-free dispersion (AFD) which allows for direct insights into the dependence structure of the pricing kernel and stock returns, and which characterizes the testable restrictions of asset pricing models. Arbitrage-free dispersion arises as a consequence of Jensen's inequality and the convexity of the cumulant generating function of the pricing kernel and returns. It implies a wide family of model-free dispersion constraints, which extend the existing literature on dispersion and co-dispersion bounds. The new techniques are applicable within a unifying approach in multivariate and multiperiod settings. In an empirical application, we find that the dispersion of stationary and martingale pricing kernel components in a benchmark long-run risk model yields a counterfactual dependence of short- vs. long- maturity bond returns and is insufficient for pricing optimal portfolios of market equity and short-term bonds. In the third chapter, "State recovery from option data through variation swap rates in the presence of unspanned skewness", I show that a certain class of variance and skew swaps can be thought of as sufficient statistics of the implied volatility surface in the context of uncovering the conditional dynamics of second and third moments of index returns. I interpret the slope of the Cumulant Generating Function of index returns in the context of tradable swap contracts, which nest the standard variance swap, and share its fundamental linear pricing property in the class of Affine Jump Diffusion models. Equipped with variance- and skew-pricing contracts, I investigate the performance of a range of state variable filtering setups in the context of the stylized facts uncovered by the recent empirical option pricing literature, which underlines the importance of decoupling the drivers of stochastic volatility from those of stochastic (jump) skewness. The linear pricing structure of the contracts allows for an exact evaluation of the impact of state variables on the observed prices. This simple pricing structure allows me to design improved low-dimensional state-space filtering setups for estimating AJD models. In a simulated setting, I show that in the presence of unspanned skewness, a simple filtering setup which includes only prices of skew and variance swaps offers significant improvements over a high-dimensional filter which treats all observed option prices as observable inputs.