Forecasting risk with Markov-switching GARCH models:A large-scale performance study

We perform a large-scale empirical study in order to compare the forecasting performances of single-regime and Markov-switching $\text{GARCH}$ ($\text{MSGARCH}$) models from a risk management perspective. We find that $\text{MSGARCH}$ models yield more accurate Value-at-Risk, expected shortfall, and left-tail distribution forecasts than their single-regime counterparts for daily, weekly, and ten-day equity log-returns. Also, our results indicate that accounting for parameter uncertainty improves the left-tail predictions, independently of the inclusion of the Markov-switching mechanism.     

Model risk and option hedging

This paper presents a theoretical approach to option hedging and valuation when traders are facing model risk. Model risk is restrictively defined as the financial risk resulting from the choice of an approximating model to proxy for the true but ex-ante unknown state space of the underlying security process. A generalized model is defined for estimating the appropriate volatility markup, which is dependent on the noisiness of the volatility estimate over time. Delta neutral hedge portfolios are created using simulated S&P 500 option prices to demonstrate that using a volatility markup in the traditional binomial model reduces model risk.     

Determinants of corporate hedging: A (statistical) meta-analysis

While literature provides several hedging theories, evidence on the corporate incentives to hedge remains ambiguous. We synthesize data of empirical studies via statistical meta-analysis to test different hedging hypotheses. To our knowledge, this constitutes the first application of such a methodology in financial economics. Our results imply that financial distress costs induce firms to hedge. We find weak evidence that the underinvestment problem and the dependence on costly external financing influence hedging behavior. Taxes and agency conflicts do not show explanatory power. Because statistical and narrative reviews yield different outcomes, we see various other application possibilities for meta-analysis in financial economics.     

Cross-sectional quantile regression for estimating conditional VaR of returns during periods of high volatility

Evaluating value at risk (VaR) for a firm’s returns during periods of financial turmoil is a challenging task because of the high volatility in the market. We propose estimating conditional VaR and expected shortfall (ES) for a given firm’s returns using quantile regression with cross-sectional (CSQR) data about other firms operating in the same market. An evaluation using US market data between 2000 and 2020 shows that our approach has certain advantages over a CAViaR model. Identification of low-risk firms and a reduction in computing times are additional advantages of the new method described.     

On pricing and hedging options in regime-switching models with feedback effect

We study the pricing and hedging of European-style derivative securities in a Markov, regime-switching, model with a feedback effect depending on the economic condition. We adopt a pricing kernel which prices both financial and economic risks explicitly in a dynamically incomplete market and we provide an equilibrium analysis. A martingale representation for a European-style index option's price is established based on the price kernel. The martingale representation is then used to construct the local risk-minimizing strategy explicitly and to characterize the corresponding pricing measure.     

Retrieving the implicit risk neutral density of WTI options with a semi-nonparametric approach

This paper contributes to the literature on the estimation of the Risk Neutral Density (RND) function by proposing a log-semi-nonparametric (log-SNP) distribution as the implicit RND when the Gram-Charlier model is used for option pricing. The performance of the model is compared to the lognormal (Black Scholes) benchmark for a sample of option prices for West Texas Intermediate (WTI) crude oil that were traded in the period between January 2016 and December 2017. Results show that the lognormal specification tends to systematically undervalue option prices and that the proposed log-SNP distribution, which explicitly adjusts for negative skewness and excess kurtosis, results in markedly improved accuracy, especially in periods of market instability. As a result, the implied skewness and excess kurtosis are relevant sources of information on market expectations that should be used for hedging and risk management purposes.     

Forecasting risk measures using intraday data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

Forecast combinations for value at risk and expected shortfall

Combining provides a pragmatic way of synthesising the information provided by individual forecasting methods. In the context of forecasting the mean, numerous studies have shown that combining often leads to improvements in accuracy. Despite the importance of the value at risk (VaR), though, few papers have considered quantile forecast combinations. One risk measure that is receiving an increasing amount of attention is the expected shortfall (ES), which is the expectation of the exceedances beyond the VaR. There have been no previous studies on combining ES predictions, presumably due to there being no suitable loss function for ES. However, it has been shown recently that a set of scoring functions exist for the joint estimation or backtesting of VaR and ES forecasts. We use such scoring functions to estimate combining weights for VaR and ES prediction. The results from five stock indices show that combining outperforms the individual methods for the 1% and 5% probability levels.     

Forecasting value at risk and expected shortfall with mixed data sampling

I propose applying the Mixed Data Sampling (MIDAS) framework to forecast Value at Risk (VaR) and Expected shortfall (ES). The new methods exploit the serial dependence on short-horizon returns to directly forecast the tail dynamics of the desired horizon. I perform a comprehensive comparison of out-of-sample VaR and ES forecasts with established models for a wide range of financial assets and backtests. The MIDAS-based models significantly outperform traditional GARCH-based forecasts and alternative conditional quantile specifications, especially in terms of multi-day forecast horizons. My analysis advocates models that feature asymmetric conditional quantiles and the use of the Asymmetric Laplace density to jointly estimate VaR and ES.     

Selective hedging with market views and risk limits: the case of Hydro-Quebec

This study presents how Hydro-Quebec manages its short-term financial risks. The quantitative hedging model is articulated over forward and volatility premia and constrained by a yearly risk limit provided by the firm's Finance Committee. The hedging solutions provide the optimal linear hedging parameters and option strike levels. The second part of the paper is devoted to a theoretical analysis of the sensitivity of the optimal solutions to changes in the premia, by means of the general implicit function theorem.     

Empirical analysis of long memory,leverage, and distribution effects for stock market risk estimates

In this study, eight generalized autoregressive conditional heteroskedasticity (GARCH) types of variance specifications and two return distribution settings, the normal and skewed generalized Student's t (SGT) of Theodossiou (1998), totaling nine GARCH-based models, are utilized to forecast the volatility of six stock indices, and then both the out-of-sample-period value-at-risk (VaR) and the expected shortfall (ES) are estimated following the rolling window approach. Moreover, the in-sample VaR is estimated for both the global financial crisis (GFC) period and the non-GFC period. Subsequently, through several accuracy measures, nine models are evaluated in order to explore the influence of long memory, leverage, and distribution effects on the performance of VaR and ES forecasts. As shown by the empirical results of the nine models, the long memory, leverage, and distribution effects subsist in the stock markets. Moreover, regarding the out-of-sample VaR forecasts, long memory is the most important effect, followed by the leverage effect for the low level, whereas the distribution effect is crucial for the high level. As for the three VaR approaches, weighted historical simulation achieves the best VaR forecasting performance, followed by filtered historical simulation, whereas the parametric approach has the worst VaR forecasting performance for all the levels. Furthermore, VaR models underestimate the true risk, whereas ES models overestimate the true risk, indicating that the ES risk measure is more conservative than the VaR risk measure. Additionally, based on back-testing, the VaR provides a better risk forecast than the ES since the ES highly overestimates the true risk. Notably, long memory is important for the ES estimate, whereas both the long memory and the leverage effect are crucial for the VaR estimate. Finally, via in-sample VaR forecasts in regard to the low level, it is found that long memory is important for the non-GFC period, whereas the distribution effect is crucial for the GFC period. On the other hand, with regard to the high level, the distribution effect is crucial for both the non-GFC and the GFC period. These results seem to be consistent with those found in the out-of-sample VaR forecasts. In accordance with these results, several important policy implications are proposed in this study.     

The role of the board and the audit committee in corporate risk management

This paper examines the impact of corporate governance on corporate risk-management activities in S&P 500 firms over the period 2004–2010 by measuring the characteristics of the board directors and audit committee. Our results show that the board of directors, especially the audit committee, plays an important role in the firm’s hedging decisions, including whether to hedge and to what extent. Such evidence is even stronger in high-leveraged firms with large risk-shifting incentives. These results are robust to the consideration of endogenous concerns, a board corporate governance index, and industrial effects. Our study contributes to the literature by showing the influential role of the audit committee on corporate risk management.     

Forecasting risk measures using intraday and overnight information

Volatility forecasts are important for a number of practical financial decisions, such as those related to risk management. When working with high-frequency data from markets that operate during a reduced time, an approach to deal with the overnight return volatility is needed. In this context, we use heterogeneous autoregressions (HAR) to model the variation associated with the intraday activity, with distinct realized measures as regressors, and, to model the overnight returns, we use augmented GARCH type models. Then, we combine the HAR and GARCH models to generate forecasts for the total daily return volatility. In an empirical study, for returns on six international stock indices, we analyze the separate modeling approach in terms of its out-of-sample forecasting performance of daily volatility, Value-at-Risk and Expected Shortfall relative to standard models from the literature. In particular, the overall results are favorable for the separate modeling approach in comparison with some HAR models based on realized variance measures for the whole day and the standard GARCH model.     

Valuing spread options with counterparty risk and jump risk

In this paper, we investigate spread options with counterparty risk in a jump-diffusion model. Due to the fact that there is no closed-form formula of spread options with counterparty risk, we obtain analytical expressions of lower and upper bounds by employing the measure-change technique. Finally, we numerically check the accuracy of the bounds and analyze the impacts of counterparty risk and jump risk on spread option prices.     

Corporate risk management and asymmetric information

We discuss the effect of information on corporate risk management decisions when the information is asymmetric between the insider and the market. We suggest an explanation for previous contradiction between existing theories and empirical findings, which state that fewer small firms choose to hedge. We consider two different scenarios of information revelation to the market, and find hedging cost is not the main reason preventing firms from hedging. Rather asymmetric information plays the decisive role in a firm's risk management policy. One of the empirical implications we find is that cash flows with high variances may discourage firms from hedging even when they face high financial distress costs.     

Supply chain risk identification with value-focused process engineering

Together with numerous benefits that were brought about by the transition from the silo enterprise perspective towards the process-based supply chain view of contemporary business, new sources of risk appeared due to the complex systemic nature of the supply chains. The need to reduce the increased level of supply chain vulnerability has been identified as a key research issue in the domain of supply chain management. In this paper, a novel value-focused process engineering methodology for process-based supply chain risk identification is proposed with the aim to increase value to supply chain members and supply chain as a whole. The proposed methodology is illustrated with a generic supply chain scenario example.     

Convergence rates of recombining trees for pricing options on stocks under GBM and regime-switching models with known cash dividends

In the literature there appear various kinds of binomial trees for pricing options on stocks under geometric Brownian motions (GBMs) with known cash dividends. The aim of this paper is to compare the performance of the existing binomial trees in aspect of the convergence rates, which are usually used to measure precisely how fast the approximate values converge to the exact one, and to give a theoretical proof of the convergence rates for the interpolation binomial trees which are based on a model that excludes the arbitrage possibilities. Also the paper extends the studies to the regime-switching models with known cash dividend payment.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Subtle price discrimination and surplus extraction under uncertainty

This paper provides a solution to Proebsting’s Paradox, an argument that appears to show that the investment rule known as the Kelly criterion can lead a decision maker to invest a higher fraction of his wealth the more unfavorable the odds he faces are and, as a consequence, risk an arbitrarily high proportion of his wealth on the outcome of a single event. The paper shows that a large class of investment criteria, including ‘fractional Kelly’, also suffer from the same shortcoming and adapts ideas from the literature on price discrimination and surplus extraction to explain why this is so. The paper also presents a new criterion, dubbed the doubly conservative criterion, that is immune to the problem identified above. Immunity stems from the investor’s attitudes toward capital preservation and from him becoming rapidly pessimistic about his chances of winning the better odds he is offered.