Essays on optimal hedging and investment strategies and on derivative pricing

This dissertation encompasses four essays on various topics within the field of finance. Chapter 1 presents an overview of the contributions of each essay. Chapter 2, titled Risk Aversion, Price Uncertainty, and Irreversible Investments, extends the theory of irreversible investment under uncertainty by allowing for risk averse instead of risk neutral investors in an incomplete markets setting. Chapter 3, titled Economic Hedging Portfolios, studies portfolios that investors hold to hedge economic risks. Using a model of state-dependent utility, it provides a generalization of the traditional mean-variance model. In Chapter 4, titled Multivariate Option Pricing Using Dynamic Copula Models, the price behavior of derivatives written on multiple underlying assets is examined. The association between the underlying assets is modeled using parametric families of copulas which offer various alternatives to the commonly assumed normal dependence structure. Chapter 5, titled An Anatomy of Futures Returns: Risk Premiums and Trading Strategies, provides an empirical analysis of trading strategies which capture the various risk premiums that have been distinguished in futures markets. Sorting strategies designed to exploit the information in the term structure of futures yields and past hedging pressure are found to yield expected returns that cannot be explained by equity, bond, and currency benchmarks.

Multivariate Option Pricing Using Dynamic Copula Models

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets.Parametric families of copulas offering various alternatives to the normal dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets.These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the S&P500 and Nasdaq indexes.Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels.Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.option pricing;dynamic models;options

Risk Aversion, Price Uncertainty and Irreversible Investments

This paper generalizes the theory of irreversible investment under uncertainty by allowing for risk averse investors in the absence of com-plete markets.Until now this theory has only been developed in the cases of risk neutrality, or risk aversion in combination with complete markets.Within a general setting, we prove the existence of a unique critical output price that distinguishes price regions in which it is optimal for a risk averse investor to invest and price regions in which one should refrain from investing.We use a class of utility functions that exhibit non-increasing absolute risk aversion to examine the e ects of risk aversion, price uncertainty, and other parameters on the optimal investment decision.We nd that risk aversion reduces investment, particularly if the investment size is large.Moreover, we nd that a rise in price uncertainty increases the value of deferring irreversible investments.This e ect is stronger for high levels of risk aversion.In addition, we provide, for the rst time, closed-form comparative statics formulas for the risk neutral investor.risk;prices;uncertainty;investment;options;incomplete markets

Economic Hedging Portfolios

In this paper we study portfolios that investors hold to hedge economic risks.Using a model of state-dependent utility, we show that agents economic hedging portfolios can be obtained by an intuitively appealing, risk aversion-weighted approximate replication of the economic risk variables using the investment opportunity set, as opposed to the unweighted hedging demand obtained in the traditional mean-variance framework.We find that agents across a broad range of levels of risk aversion are willing to pay significant compensations for hedges against inflation risk, real interest-rate risk, and dividend-yield risk.Furthermore, our results show that all economic risk variables we consider require significant, often risk aversion-dependent hedging adjustments with respect to one or more securities.Moreover, we analyze investors speculative positions and find that hedges against economic risks may potentially explain the anomalies found in stock markets as well as the term and default premiums in bond markets.hedging;risk;investment

Risk Aversion, Price Uncertainty and Irreversible Investments

This paper generalizes the theory of irreversible investment under uncertainty by allowing for risk averse investors in the absence of com-plete markets.Until now this theory has only been developed in the cases of risk neutrality, or risk aversion in combination with complete markets.Within a general setting, we prove the existence of a unique critical output price that distinguishes price regions in which it is optimal for a risk averse investor to invest and price regions in which one should refrain from investing.We use a class of utility functions that exhibit non-increasing absolute risk aversion to examine the e ects of risk aversion, price uncertainty, and other parameters on the optimal investment decision.We nd that risk aversion reduces investment, particularly if the investment size is large.Moreover, we nd that a rise in price uncertainty increases the value of deferring irreversible investments.This e ect is stronger for high levels of risk aversion.In addition, we provide, for the rst time, closed-form comparative statics formulas for the risk neutral investor.

Multivariate Option Pricing Using Dynamic Copula Models

This paper examines the behavior of multivariate option prices in the presence of association between the underlying assets.Parametric families of copulas offering various alternatives to the normal dependence structure are used to model this association, which is explicitly assumed to vary over time as a function of the volatilities of the assets.These dynamic copula models are applied to better-of-two-markets and worse-of-two-markets options on the S&P500 and Nasdaq indexes.Results show that option prices implied by dynamic copula models differ substantially from prices implied by models that fix the dependence between the underlyings, particularly in times of high volatilities. Furthermore, the normal copula produces option prices that differ significantly from non-normal copula prices, irrespective of initial volatility levels.Within the class of non-normal copula families considered, option prices are robust with respect to the copula choice.

Economic Hedging Portfolios

In this paper we study portfolios that investors hold to hedge economic risks.Using a model of state-dependent utility, we show that agents economic hedging portfolios can be obtained by an intuitively appealing, risk aversion-weighted approximate replication of the economic risk variables using the investment opportunity set, as opposed to the unweighted hedging demand obtained in the traditional mean-variance framework.We find that agents across a broad range of levels of risk aversion are willing to pay significant compensations for hedges against inflation risk, real interest-rate risk, and dividend-yield risk.Furthermore, our results show that all economic risk variables we consider require significant, often risk aversion-dependent hedging adjustments with respect to one or more securities.Moreover, we analyze investors speculative positions and find that hedges against economic risks may potentially explain the anomalies found in stock markets as well as the term and default premiums in bond markets.

The harm of class imbalance corrections for risk prediction models: illustration and simulation using logistic regression

OBJECTIVE: Methods to correct class imbalance (imbalance between the frequency of outcome events and nonevents) are receiving increasing interest for developing prediction models. We examined the effect of imbalance correction on the performance of logistic regression models. MATERIAL AND METHODS: Prediction models were developed using standard and penalized (ridge) logistic regression under 4 methods to address class imbalance: no correction, random undersampling, random oversampling, and SMOTE. Model performance was evaluated in terms of discrimination, calibration, and classification. Using Monte Carlo simulations, we studied the impact of training set size, number of predictors, and the outcome event fraction. A case study on prediction modeling for ovarian cancer diagnosis is presented. RESULTS: The use of random undersampling, random oversampling, or SMOTE yielded poorly calibrated models: the probability to belong to the minority class was strongly overestimated. These methods did not result in higher areas under the ROC curve when compared with models developed without correction for class imbalance. Although imbalance correction improved the balance between sensitivity and specificity, similar results were obtained by shifting the probability threshold instead. DISCUSSION: Imbalance correction led to models with strong miscalibration without better ability to distinguish between patients with and without the outcome event. The inaccurate probability estimates reduce the clinical utility of the model, because decisions about treatment are ill-informed. CONCLUSION: Outcome imbalance is not a problem in itself, imbalance correction may even worsen model performance