Pricing vulnerable options with stochastic liquidity risk

In this paper, we consider vulnerable options with stochastic liquidity risk. We employ liquidity-adjusted pricing models to describe the underlying stock price and option issuer’s assets. In addition, the correlation between these assets is stochastic, depending on the market liquidity measures. In the proposed framework, we derive closed forms of vulnerable European options with stochastic liquidity risk and then use them to illustrate the effects of stochastic liquidity risk on vulnerable option prices. Numerical results show that the effects of liquidity risk on the prices of out-of-the-money options or the options with a short maturity are not negligible.     

Pricing of vulnerable exchange options with early counterparty credit risk

The exchange option is one of the most popular options in the over-the-counter (OTC) market, which enables the holder of two underlying assets to exchange one with another. In OTC markets, with the increasing apprehension of credit default risk in the case of option pricing since the global financial crisis, it has become necessary to consider the counterparty credit risk while evaluating the option price. In this study, we combine the vulnerable exchange option and early counterparty default risk to obtain the closed-form formula for the vulnerable exchange option with early counterparty credit risk by using the method of dimension reduction, Mellin transform, and the method of images. Moreover, we examine the pricing accuracy of the option value by comparing our closed-form solution with the formula derived by the Monte-Carlo simulation.     

The pricing of credit risk derivatives

This paper considers the pricing of derivatives that protect holders of corporate bonds from a reduction in their value because of a deterioration in their credit quality. These derivatives are structured as either puts on the bond price or calls on the bond spread (above the risk free rate) in the context of models developed by Merton (1974) and Black and Cox (1976). The pricing properties of these options are derived using both analytical and numerical methods.     

Pricing basket spread options with default risk under Heston–Nandi GARCH models

In this paper, we investigate basket spread options under the Heston–Nandi GARCH model. Moreover, we adopt the reduced-form model to capture default risk, which is correlated with all underlying assets. Because of the nonexistence of the analytical fair values, we obtain a closed-form approximated pricing formula of basket spread options with default risk. Finally, we examine the accuracy of approximations and then use the proposed formulae to illustrate the effect of the number of the underlying assets and default risk as well.     

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.     

Pricing European continuous-installment currency options with mean-reversion

In this paper, we consider European continuous-installment currency option under the mean-reversion environment. Specifically, we provide efficient pricing formula of installment currency put option via a partial differential equation (PDE) approach when the exchange rate follows the mean reverting lognormal model. Using the Mellin transform techniques, we derive the integral equation representation for the optimal stopping boundary from the PDE for pricing of the option. To verify the efficiency and accuracy of our approach, we provide computational results with the least square Monte Carlo method proposed by Longstaff and Schwartz (2001). We also present some numerical examples to examine the characteristics of the optimal boundaries and prices.     

Corporate credit risk prediction under stochastic volatility and jumps

This paper examines the impact of allowing for stochastic volatility and jumps (SVJ) in a structural model on corporate credit risk prediction. The results from a simulation study verify the better performance of the SVJ model compared with the commonly used Merton model, and three sources are provided to explain the superiority. The empirical analysis on two real samples further ascertains the importance of recognizing the stochastic volatility and jumps by showing that the SVJ model decreases bias in spread prediction from the Merton model, and better explains the time variation in actual CDS spreads. The improvements are found particularly apparent in small firms or when the market is turbulent such as the recent financial crisis.     

Forecasting and stress testing credit card default using dynamic models

We present discrete time survival models of borrower default for credit cards that include behavioural data about credit card holders and macroeconomic conditions across the credit card lifetime. We find that dynamic models which include these behavioural and macroeconomic variables provide statistically significant improvements in model fit, which translate into better forecasts of default at both account and portfolio levels when applied to an out-of-sample data set. By simulating extreme economic conditions, we show how these models can be used to stress test credit card portfolios.     

Corporate bond market interdependence: Credit spread correlation between and within U.S. and Canadian corporate bond markets

This study investigates the correlation and interdependence between and within the U.S. and Canadian corporate bond markets. The empirical framework adopted allows credit spreads to depend on common systematic risk factors derived from structural models and incorporates dynamic conditional correlations (DCC) between spreads. Results show that there is a surprisingly weak correlation between the two markets in normal times. However, during crises, there is a sudden and strong increase in the correlation between U.S. and Canadian credit spreads. The analysis of credit spread correlation within each market also shows an unusual increase in credit spread correlations between sectors and between risk classes in the U.S. during the 2007–2009 global financial crisis. This increase persists over the post-crisis period. By contrast, in Canada, credit spread correlations between sectors remain remarkably stable over time, suggesting an interdependence of credit spreads within the Canadian market.     

Write-down bonds,credit risk and imperfect information

A structural model of pricing Write-Down (hereafter WD) bonds under imperfect information has been developed to investigate the effect of WD bonds issuance on credit risk. Information is not only delayed but also asymmetrically distributed between managers and outside investors. We derive analytical solutions for corporate securities prices and find the issuance of WD bonds could significantly improve firm value via reducing bankruptcy cost. Our numerical results further demonstrate that the WD bonds issuance increases corporate risk tolerance and reduces the risk of bankruptcy and credit spreads under imperfect information.     

Nowcasting and forecasting global financial sector stress and credit market dislocation

We introduce a new international model for the systematic distress risk of financial institutions from the US, the European Union, and the Asia-Pacific region. Our proposed dynamic factor model can be represented as a nonlinear, non-Gaussian state space model with parameters that we estimate using Monte Carlo maximum likelihood methods. We construct measures of global financial sector risk and of credit market dislocation, where credit market dislocation is defined as a significant and persistent decoupling of the credit risk cycle from macro-financial fundamentals in one or more regions. We show that, in the past, such decoupling has preceded episodes of systemic financial distress. Our new measure provides a risk-based indicator of credit conditions, and as such, complements earlier quantity-based indicators from the literature. In an extensive comparison with such quantity-based systemic risk indicators, we find that the behaviour of the new indicator is competitive with that of the best quantity-based indicators.     

Sequential optimization three-way decision model with information gain for credit default risk evaluation

To categorize credit applications into defaulters or non-defaulters, most credit evaluation models have employed binary classification methods based on default probabilities. However, while some loan applications can be directly accepted or rejected, there are others on which immediate accurate credit status decisions cannot be made using existing information. To resolve these issues, this study developed an optimized sequential three-way decision model. First, an information gain objective function was built for the three-way decision, after which a genetic algorithm (GA) was applied to determine the optimal decision thresholds. Then, appropriate accept or reject decisions for some applicants were made using basic credit information, with the remaining applicants, whose credit status was difficult to determine, being divided into a boundary region (BND). Supplementary information was then added to reevaluate the credit applicants in the BND, and a sequential optimization process was employed to ensure more accurate predictions. Therefore, the model’s predictive abilities were improved and the information acquisition costs controlled. The empirical results demonstrated that the proposed model was able to outperform other benchmarking credit models based on performance indicators.     

Prices,debt and market structure in an agent-based model of the financial market

We develop an agent-based model in which heterogeneous and boundedly rational agents interact by trading a risky asset at an endogenously set price. Agents are endowed with balance sheets comprising the risky asset as well as cash on the asset side and equity capital as well as debt on the liabilities side. A number of findings emerge when simulating the model: we find that the empirically observable log-normal distribution of bank balance sheet size naturally emerges and that higher levels of leverage lead to a greater inequality among agents. Furthermore, greater leverage increases the frequency of bankruptcies and systemic events. Credit frictions, which we define as the stickiness of debt adjustments, are able to explain a key difference in the relation between leverage and assets observed for different bank types. Lowering credit frictions leads to an increasingly procyclical behavior of leverage, which is typical for investment banks. Nevertheless, the impact of credit frictions on the fragility of the model financial system is complex. Lower frictions do increase the stability of the system most of the time, while systemic events become more probable. In particular, we observe an increasing frequency of severe liquidity crises that can lead to the collapse of the entire model financial system.     

Systemic risk in European financial and energy sectors: Dynamic factor copula approach

We perform an analysis of systemic risk in financial and energy sectors in Europe using daily time series of CDS spreads. We employ the factor copula model with GAS dynamics from Oh and Patton (2018) for the purpose of estimating dependency structures between market participants. Based on the estimated models, we perform Monte Carlo simulations to obtain future values of CDS spreads, and then measure the probability of systemic events at given time points. We conclude that substantially higher systemic risk is present in the financial sector compared to the energy sector. We also find that the most systemically vulnerable financial and energy companies come from Spain.     

Oil price shocks and credit spread: Structural effect and dynamic spillover

This study analyzes the heterogeneous response of U.S. credit spread to global oil price shocks by building an extended structural vector autoregressive model (SVAR), which can distinguish among the U.S. and non-US oil supply shocks, aggregated demand shocks and oil market-specific demand shocks behind the real oil prices. Meanwhile, a spillover index model developed by Diebold and Yilmaz (2012) (hereafter D.Y. (2012)) is used to estimate the link between oil price shocks and the U.S. credit spread over time. The results show that (i) the credit spread does not respond to global oil supply shocks and non-US oil supply shocks, but has a negative reaction to the U.S. oil supply shocks, aggregate demand shocks, and oil-market-specific demand shocks. (ii) There exists a close connectedness between oil price shocks and the U.S. credit spread, and the link fluctuates cyclically and relates to the economic cycle and the U.S. shale oil revolution. (iii) The spillover from different oil price shocks to the U.S. credit spread shows significant heterogeneity over time. Our findings suggest that policymakers and investors can better track the U.S. credit spread changes using oil price information.     

Default-risky bond prices with jumps,liquidity risk and incomplete information

This paper provides a default-risky bond valuation model, which assumes that the issuer’s credit quality, modelled by the intensity of default, is driven by a continuous-time Markov chain. The model accounts for default and liquidity risk as well as incomplete information. A full-information semimartingale representation of a liquid defaultable bond price, which separates three different types of risks—default, interest-rate and credit-quality, is obtained. The illiquidity is modelled as exogenously specified stochastic reduction in the price of the bond, which adds more risks for the investors. A model of a market with partially informed investors, belonging to specific investor classes and having access to discrete information sets about credit quality, was specified. Valuations of defaultable bonds in this market were provided as well as price impacts of the new information releases.      

The Cox,Ross and Rubinstein tree model which includes counterparty credit risk and funding costs

The binomial asset pricing model of Cox, Ross and Rubinstein (CRR) is extensively used for the valuation of options. The CRR model is a discrete analog of the Black–Scholes–Merton (BSM) model. The 2008 credit crisis exposed the shortcomings of the oversimplified assumptions of the BSM model. Burgard and Kjaer extended the BSM model to include adjustments such as a credit value adjustment (CVA), a debit value adjustment (DVA) and a funding value adjustment (FVA). The aim of this paper is to extend the CRR model to include CVA, DVA and FVA and to prove that this extended CRR model coincides with the model that results from discretising the Burgard and Kjaer model. Our results are numerically implemented and we also show that as the number of time-steps increase in the derived tree structure model, the model converges to the model developed by Burgard and Kjaer.     

Hedging and pricing early-exercise options with complex fourier series expansion

We introduce a new numerical method called the complex Fourier series (CFS) method proposed by Chan (2017) to price options with an early-exercise feature—American, Bermudan and discretely monitored barrier options—under exponential Lévy asset dynamics. This new method allows us to quickly and accurately compute the values of early-exercise options and their Greeks. We also provide an error analysis to demonstrate that, in many cases, we can achieve an exponential convergence rate in the pricing method as long as we choose the correct truncated computational interval. Our numerical analysis indicates that the CFS method is computationally more comparable or favourable than the methods currently available. Finally, the superiority of the CFS method is illustrated with real financial data by considering Standard & Poor’s depositary receipts (SPDR) exchange-traded fund (ETF) on the S&P 500® index options, which are American options traded from November 2017 to February 2018 and from 30 January 2019 to 21 June 2019.     

Modeling common volatility characteristics and dynamic risk premia in European equity markets

The paper applies a Factor-GARCH model to evaluate the impact of the market portfolio, as a single common dynamic risk factor, on conditional volatility and risk premia for the returns on size-based equity portfolios of three major European markets; France, Germany and the United Kingdom. The results show that for the size-based portfolios the factor loading for the dynamic market factor is significant and positive but the association between the risk premia and the conditional market volatility is weak. However, the dynamic market factor is shown to explain common characteristics in the conditional variance such as asymmetry and persistence. This finding is consistent across markets and portfolio sizes.     

Interconnectedness and systemic risk in the US CDS market

This study assesses systemic risk in the US credit default swap (CDS) market. First, this study estimates the bilateral exposures matrix using aggregate fair value data and theoretically analyze interconnectedness in the US CDS network using various network measures. Second, this study theoretically analyzes the contagious defaults. The default analysis shows the theoretical occurrence of many stand-alone defaults and one contagious default via the CDS network during the global financial crisis. A stress test based on a hypothetical severe stress scenario predicts almost no future contagious defaults. Thus, risk contagion via the CDS network is unlikely.