Does volatility pay?

An investor with quadratic utility invests amounts changing with his perceptions of risk and expected return in a market with changing risk. Optimal investment policies are derived under several hypotheses for expected returns. These policies are combined in a Bayesian framework to yield a policy that performs better than the ‘buy and hold’ policy in our tests, except in the case of the FTSE index

GARCH Options in Incomplete Markets

We propose a new method to compute option prices based on GARCH models. In an incomplete market framework, we allow for the volatility of asset return to differ from the volatility of the pricing process and obtain adequate pricing results. We investigate the pricing performance of this approach over short and long time horizons by calibrating theoretical option prices under the Asymmetric GARCH model on S&P 500 market option prices. A new simplified scheme for delta hedging is proposed.

The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

In this paper we deal with some problems concerning minimal hypersurfaces in Carnot-Caratheodory (CC) structures. More precisely we will introduce a general calibration method in this setting and we will study the Bernstein problem for entire regular intrinsic minimal graphs in a meaningful and simpler class of CC spaces, i.e. the Heisenberg group H^n. In particular we will positively answer to the Bernstein problem in the case n=1 and we will provide counterexamples when n>=5

Conditioning the information in asset pricing

This thesis analyzes different theoretical and empirical aspects related to the use of the information in asset pricing. As a main innovation I extend the asset pricing literature proposing a new highly flexible technique for the estimation of the markets subjective distribution of future returns. Applying this technique to different problems I answer to some long-lasting puzzles present in literature. The contribution of this project to the literature is two-fold: first, in line with the new findings of Ross (2015) but from a fully different prospective I propose a new technique to estimate the market's subjective distribution of future returns using, jointly, stock and options data. Second, after studying the theoretical reason behind the superiority of the proposed technique, I use it for different empirical applications

Average conditional correlation and tree structures for multivariate GARCH models

We propose a simple class of multivariate GARCH models, allowing for time-varying conditional correlations. Estimates for time-varying conditional correlations are constructed by means of a convex combination of averaged correlations (across all series) and dynamic realized (historical) correlations. Our model is very parsimonious. Estimation is computationally feasible in very large dimensions without resorting to any variance reduction technique. We back-test the models on a six-dimensional exchange-rate time series using different goodness-of-fit criteria and statistical tests. We collect empirical evidence of their strong predictive power, also in comparison to alternative benchmark procedures

Essays on credit risk

The work investigates two major topics: the presence of a systematic and an idiosyncratic component in CDS spreads and the credit spread puzzle. We verify that a systematic factor is priced in the cross-section of CDS returns. We also notice that the systematic component of risk increases after the financial crisis. We finally verify that the fraction of systematic risk is not the same in different industrial sectors. In particular, more cyclical and systemic sectors show a much larger impact of the systematic factor. Regarding the second topic, we extend the literature proposing a bivariate state space model and verify that it actually improves the performances of standard inversion techniques in explaining the observed credit spreads. The improvement is particularly significant during the crisis period, characterized by a larger noise contaminating the observed equity price and equity volatility. This supports the ability of the state space model to remove the noise component and to produce better estimates of the asset value of the company and, consequently, more accurate predictions of spreads. In the last chapter we identify some explicit drivers for the noise postulated in the second paper. In particular, we verify that the errors produced by structural credit risk models significantly depend on liquidity indicators and that their explained variability is not negligible. We finally verify that the errors left by both structural variables and liquidity indicators are strongly correlated with market-wide measures of limits of arbitrage and/or deleveraging pressures

A multivariate FGD technique to improve VaR computation in equity markets

We present a multivariate, non-parametric technique for constructing reliable daily VaR predictions for individual assets belonging to a common equity market segment, which takes also into account the possible dependence structure between the assets and is still computationally feasible in large dimensions. The procedure is based on functional gradient descent (FGD) estimation for the volatility matrix (see Audrino and Bühlmann, 2002) in connection with asset historical simulation and can also be seen as a multivariate extension of the filtered historical simulation method proposed by Barone-Adesi et al. (1998). Our FGD algorithm is very general and can be further adapted to other multivariate problems dealing with (volatility) function estimation. We concentrate our empirical investigations on the Swiss pharmaceutical and the US biotechnological equity market and we collect, using statistical and economical backtests, strong empirical evidence of the better predictive potential of our multivariate strategy over other univariate techniques, with a resulting significant improvement in the measurement of risk