This thesis uses synthetically created variance swaps on VIX futures to quantify the variance risk premium in VIX options. The results of this methodology suggest that the average premium is -3.26%, meaning that the realized variance on VIX futures is on average less than the variance implied by the swap rate. This premium does not vary with time or the level of the swap rate as much as premiums in other asset classes. A negative risk premium should mean that VIX option strategies that are net credit should be profitable. This thesis tests two simple net credit strategies with puts and calls, and finds that the call strategy is profitable while the put strategy is not.

This thesis makes a number of contributions in the derivative pricing and risk management literature and to the growing literature that exploits information embedded in option prices. First, it develops an effective numerical scheme for importance sampling scheme of Fouque and Tullie (2002) based on a 2-dimensional lookup table of stock price and time to maturity that dramatically improves the speed of this importance sampling scheme. Second, the thesis presents an application of this importance sampling scheme in a Multi-Level Monte Carlo simulation. Such combination yields greater variance reduction compared to Multi-Level Monte Carlo or importance sampling alone. Third, it demonstrates how the Greeks can be computed using the Likelihood Ratio Method based on characteristic function, and how combining it with importance sampling leads to a significant variance reduction for the Greeks. Finally, it documents the positive relationship between the risk-neutral skewness (RNS) and future realized stock returns that is driven by the underperformance of highly negative RNS portfolio. The results provide strong evidence that the underperformance of stocks with the lowest RNS is driven by those stocks that are associated with a higher hedging demand, relative overvaluation and are also too costly or too risky to sell short. Moreover, by decomposing RNS into its systematic and idiosyncratic components, this thesis shows that the latter drives the positive relationship with future realized stock returns.

The aim of this thesis is to improve risk measurement estimation by incorporating extra information in the form of constraint into completely non-parametric smoothing techniques. A similar approach has been applied in empirical likelihood analysis. The method of constraints incorporates bootstrap resampling techniques, in particular, biased bootstrap. This thesis brings together formal estimation methods, empirical information use, and computationally intensive methods. In this thesis, the constraint approach is applied to non-parametric smoothing estimators to improve the estimation or modelling of risk measures. We consider estimation of Value-at-Risk, of intraday volatility for market risk, and of recovery rate densities for credit risk management. Firstly, we study Value-at-Risk (VaR) and Expected Shortfall (ES) estimation. VaR and ES estimation are strongly related to quantile estimation. Hence, tail estimation is of interest in its own right. We employ constrained and unconstrained kernel density estimators to estimate tail distributions, and we estimate quantiles from the fitted tail distribution. The constrained kernel density estimator is an application of the biased bootstrap technique proposed by Hall & Presnell (1998). The estimator that we use for the constrained kernel estimator is the Harrell-Davis (H-D) quantile estimator. We calibrate the performance of the constrained and unconstrained kernel density estimators by estimating tail densities based on samples from Normal and Student-t distributions. We find a significant improvement in fitting heavy tail distributions using the constrained kernel estimator, when used in conjunction with the H-D quantile estimator. We also present an empirical study demonstrating VaR and ES calculation. A credit event in financial markets is defined as the event that a party fails to pay an obligation to another, and credit risk is defined as the measure of uncertainty of such events. Recovery rate, in the credit risk context, is the rate of recuperation when a credit event occurs. It is defined as Recovery rate = 1 - LGD, where LGD is the rate of loss given default. From this point of view, the recovery rate is a key element both for credit risk management and for pricing credit derivatives. Only the credit risk management is considered in this thesis. To avoid strong assumptions about the form of the recovery rate density in current approaches, we propose a non-parametric technique incorporating a mode constraint, with the adjusted Beta kernel employed to estimate the recovery density function. An encouraging result for the constrained Beta kernel estimator is illustrated by a large number of simulations, as genuine data are very confidential and difficult to obtain. Modelling high frequency data is a popular topic in contemporary finance. The intraday volatility patterns of standard indices and market-traded assets have been well documented in the literature. They show that the volatility patterns reflect the different characteristics of different stock markets, such as double U-shaped volatility pattern reported in the Hang Seng Index (HSI). We aim to capture this intraday volatility pattern using a non-parametric regression model. In particular, we propose a constrained function approximation technique to formally test the structure of the pattern and to approximate the location of the anti-mode of the U-shape. We illustrate this methodology on the HSI as an empirical example.

I propose a global risk factor – Currency Traded Risk (CTR). This risk factor is the first to identify the directional link between currencies and equities. CTR captures the genesis of financial globalization, and contains the greatest predictive ability to date for monthly returns on a global stock portfolio. Theoretically, return expectation is intimately linked to time-varying risk premia. Due to the intrinsic scope of currency values in integrating the world’s financial markets, information on time-varying risk premia prices into currencies at greater speed, scale, and global consensus, relative other asset classes. High interest rate currencies proxy as a risk-on asset class. Low interest rate currencies proxy as a risk-off asset class. Innovations in these currencies’ values summarize global risk premia and forecast equity market returns. CTR measures two sources of global risk premia; the difference between averaged spot returns of high interest rate currencies and low interest rate currencies, and the difference between implied and realized volatility of high interest rate currencies. Using recursive regressions, CTR predicts monthly MSCI World Index© returns out of sample, with R2’s consistent at 10% from 2008 to 2017. Currencies track global risk premia, whereas equities respond to it.

In this dissertation, I explore the impact of idiosyncratic risk on asset returns. The first essay examines how idiosyncratic risk affects the cross-section of stock returns. I use an exponential GARCH model to forecast expected idiosyncratic volatility and employ a combination of the size effect, value premium, return momentum and short-term reversal to measure relative mispricing. I find that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks. This phenomenon is robust to various subsamples and industries, and cannot be explained by risk factors or firm characteristics. Further, transaction costs, short-sale constraints and information uncertainty cannot account for the role of idiosyncratic risk. Overall, these findings are consistent with the limits of arbitrage arguments and demonstrate the importance of idiosyncratic risk as an arbitrage cost. The second essay studies the cross-sectional determinants of delta-hedged stock option returns with an emphasis on the pricing of volatility risk. We find that the average delta-hedged option returns are significantly negative for most stocks, and they decrease monotonically with both total and idiosyncratic volatility of the underlying stock. Our results are robust and cannot be explained by the Fama-French factors, market volatility risk, jump risk, or the effect of past stock return and volatility-related option mispricing. Our results strongly support a negative market price of volatility risk specification that is proportional to the volatility level. Reflecting this volatility risk premium, writing covered calls on high volatility stocks on average earns about 2% more per month than selling covered calls on low volatility stocks. This spread is higher when it is more difficult to arbitrage between stock and option. / text

In this companion paper to Broll and Mukherjee (2017), we empirically analyse how exchange rate volatilities affect firms optimal production and exporting decisions. The firms elasticity of risk aversion determines the direction of the impact of exchange rate risk on exports. Based on a flexible utility function that incorporates all possible risk preferences, a unique structurally estimable equation is used to estimate the risk aversion elasticities for a panel of Indian service sector (non-financial) firms over 2004-2015, using the quantile regression method.