Time‐changed Lévy jump processes with GARCH model on reverse convertibles

For decades, financial institutions have been very motivated in creating structured high-yield financial products, especially in the economic environment of lower interest rates. Reverse convertible notes (RCNs) are the type of financial instruments, which in recent years first in Europe and then in the US – have become highly desirable financial structured products. They are complex financial structured products because they are neither plain bonds nor stocks. Instead, they are structured products embedding equity options, which involve a significant amount of asset returns' uncertainty. Given this fact, pricing of reverse convertible notes becomes a really big challenge, where both the general Black–Scholes option pricing model and the compound Poisson jump model which are designed to catch large crashes, are not suitable in valuing these kinds of products. In this paper, we propose a new asset-pricing framework for reverse convertible notes by extending the pure Brownian increments to Lévy jump risks for the underlying stock return movements. Our framework deals with time-changing volatilities of stock options with Lévy jump processes by considering the stocks' infinite-jump possibilities. We then use a discrete-time GARCH with time-changed dynamics Lévy Jump processes in order to derive the assets' valuations. The results from our new model are close to the market's valuations, especially with the normal-inverse-Gaussian model of the Lévy jump family.     

Valuation of certain CMS spreads

In this paper, we derive an approximate lognormal process for the swap rate under the multifactor LIBOR market model using a Levy approach. Using the approximate dynamics for the swap rate, the constant maturity swap spread digital range notes with different strike rates are valued in analytic and semi-analytic form. The CMS spread digital range notes are widely traded in the marketplace, or embedded in structure notes.     

An Analysis of Yield Curve Notes

This paper analyzes a new type of security, the yield curve note, which pays interest at a rate that varies inversely with short-term interest rates. A valuation model for yield curve notes is presented, the parameters of the model are estimated empirically, and the estimated model is used to explore, in simulation, the price behavior and risk characteristics of yield curve notes in comparison with fixed-rate notes. The risk of a yield curve note is approximately twice as great as a fixed-rate note with the same maturity. The unique risk characteristics of yield curve notes make them useful (as liabilities) in immunization strategies for financial institutions. Their usefulness in this regard may be the chief rationale for their development.     

Jump risk premia across major international equity markets

We decompose the non-diversifiable market risk into continuous and discontinuous components and jump systematic risks into positive vs. negative and small vs. large components. We examine their association with equity risk premia across major equity markets. We show that developed markets jumps are more closely linked to the aggregate market index than emerging and frontier ones. The reward for bearing both the continuous and downside jump risks is positive during the pre-crisis period whereas the reward for bearing the upside and large jump risks is negative during the crisis and post-crisis periods. We also provide evidence of significant continuous and discontinuous leverage effects during the pre-crisis period, suggesting that both continuous and discontinuous price and volatility risks share compensations for common underlying risk factors.     

Float on a note

From 1863-1914, banks in the U.S. could issue notes subject to full collateral, a tax on outstanding notes, redemption of notes on demand, and a clearing fee per issued note cleared through the Treasury. The system failed to satisfy a purported arbitrage condition: the yield on collateral exceeded the tax rate plus the product of the clearing fee and the average clearing rate of notes. The failure is explained by a model in which note issuers choose to issue notes only in trades that produce a low clearing rate (high float), but in which there are diminishing returns to additional note issue.     

Expected returns, risk premia, and volatility surfaces implicit in option market prices

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. A non-zero correlation between jumps and diffusive risks is necessary in order to resolve the positively sloped implied volatility term structure inherent in traditional jump diffusion models. Our evidence is consistent with a negative covariance, producing a non-monotonic term structure. For the proposed market structure, we present a closed form asset pricing model that depends on the factors of the traditional jump-diffusion models, and on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. We present statistical evidence that these covariances are positive. For our model the expected stock return, jump and diffusive risk premiums are non-linear functions of time.     

A bridge from ruin theory to credit risk

The structural model uses the firm-value process and the default threshold to obtain the implied credit spread. Merton’s (J Finance 29:449–470, 1974) credit spread is reported too small compared to the observed market spread. Zhou (J Bank Finance 25:2015–2040, 2001) proposes a jump-diffusion firm-value process and obtains a credit spread that is closer to the observed market spread. Going in a different direction, the reduced-form model uses the observed market credit spread to obtain the probability of default and the mean recovery rate. We use a jump-diffusion firm-value process and the observed credit spread to obtain the implied jump distribution. Therefore, the discrepancy in credit spreads between the structural model and the reduced-form model can be removed. From the market credit spread, we obtain the implied probability of default and the mean recovery rate. When the solvency-ratio process in credit risk and the surplus process in ruin theory both follow jump-diffusion processes, we show a bridge between ruin theory and credit risk so that results developed in ruin theory can be used to develop analogous results in credit risk. Specifically, when the jump is Logexponentially distributed, it results in a Beta distributed recovery rate that is close to market experience. For bonds of multiple seniorities, we obtain closed-form solutions of the mean and variance of the recovery rate. We prove that the defective renewal equation still holds, even if the jumps are possibly negative. Therefore, we can use ruin theory as a methodology for assessing credit ratings.      

国际商业票据市场的发展与借鉴

发行商业票据已经成为很多公司短期资金的重要来源.本文回顾了国际商业票据市场的发展,对票据市场的风险及防范进行了总结,在此基础上结合我国票据市场的发展实际,提出应通过加强资信评级、商业银行积极参与、监管不断完善等措施,来推进我国商业票据市场的健康发展.     

Pricing mortgage insurance contracts under housing price cycles with jump risk: evidence from the U.K. housing market

Previous studies have investigated the determinants of housing price cycles in the housing market; however, we observed the phenomenon of housing price jumps in the 2007 subprime crisis. This paper presents a discussion on the housing price cycle and abnormal price jumps to describe the behavior of housing prices in the United Kingdom. The empirical results show that the impact factors of housing cycles are market risk and the switching factor. Furthermore, the impact factors of jump risks include the bursting of the housing bubble and financial crises. Therefore, in this paper, we employ the Markov switching model with jump risks to value the MI contracts and analyze the influences of housing price cycles, jump risks, risks of market interest rate, and the prepayment risks on MI premiums. The results of sensitivity analysis show that more volatile housing price index returns, as well as longer periods of higher volatility in housing prices, raise MI premiums. Moreover, the MI premium is positively related to the absolute value of the average jump amplitude and the shock frequency of abnormal events. There is the tradeoff between the market interest rate and the prepayment risk. The influences of market interest rate are different on MI premium with/without prepayment risks.     

Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks

Recent variable annuities offer participation in the equity market and attractive protection against downside movements. Accurately quantifying this additional equity market risk and robustly hedging options embedded in the guarantees of variable annuities are new challenges for insurance companies. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black–Scholes model is inadequate in preventing excessive liabilities. A model which realistically describes the real world price dynamics over a long time horizon is essential for the risk management of the variable annuities. In this article, both jump risk and volatility risk are considered for risk management of lookback options embedded in guarantees with a ratchet feature. We evaluate relative performances of delta hedging and dynamic discrete risk minimization hedging strategies. Using the underlying as the hedging instrument, we show that, under a Black–Scholes model, local risk minimization hedging can be significantly better than delta hedging. In addition, we compare risk minimization hedging using the underlying with that of using standard options. We demonstrate that, under a Merton's jump diffusion model, hedging using standard options is superior to hedging using the underlying in terms of the risk reduction. Finally, we consider a market model for volatility risks in which the at‐the‐money implied volatility is a state variable. We compute risk minimization hedging by modeling at‐the‐money Black–Scholes implied volatility explicitly; the hedging effectiveness is evaluated, however, under a joint model for the underlying price and implied volatility. Our computational results suggest that, when implied volatility risk is suitably modeled, risk minimization hedging using standard options, compared to hedging using the underlying, can potentially be more effective in risk reduction under both jump and volatility risks.     

Price Dynamics and Information Flows in Strategically-Linked Debt Instruments: The NOB and MOB Constituents

We examine information flows between the constituents of the NOB (notes-over-bonds) and MOB (municipals-over-bonds) futures spreads. The results suggest a bicausal relationship between notes and bonds and a unicausal relationship from bonds to municipals. Shocks in the bond market have a large impact on the municipal and note markets, whereas shocks in the municipal or note markets have a smaller impact on the bond market. Volatility spillover from bonds to notes and municipals is detected. We also find significant volatility persistence in all three markets. Spread trades are found to have an asymmetric influence on notes and municipal futures variance.     

The price impact of order book events: market orders,limit orders and cancellations

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective impact on future price changes. We define and extract from the data the ‘bare’ impact these events would have if they were to happen in isolation. For large tick stocks, we show that a model where the bare impact of all events is permanent and non-fluctuating is in good agreement with the data. For small tick stocks, however, bare impacts must contain a history-dependent part, reflecting the internal fluctuations of the order book. We show that this effect can be accurately described by an autoregressive model of the past order flow. This framework allows us to decompose the impact of an event into three parts: an instantaneous jump component, the modification of the future rates of the different events, and the modification of the jump sizes of future events. We compare in detail the present formalism with the temporary impact model that was proposed earlier to describe the impact of market orders when other types of events are not observed. Finally, we extend the model to describe the dynamics of the bid–ask spread.     

The world price of jump and volatility risk

We study international integration of markets for jump and volatility risk, using index option data for the main global markets. To explain the cross-section of expected option returns we focus on return-based multi-factor models. For each market separately, we provide evidence that volatility and jump risk are priced risk factors. There is little evidence, however, of global unconditional pricing of these risks. We show that UK and US option markets have become increasingly interrelated, and using conditional pricing models generates some evidence of international pricing. Finally, the benefits of diversifying jump and volatility risk internationally are substantial, but declining.     

Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices

This paper examines the empirical performance of jump diffusion models of stock price dynamics from joint options and stock markets data. The paper introduces a model with discontinuous correlated jumps in stock prices and stock price volatility, and with state-dependent arrival intensity. We discuss how to perform likelihood-based inference based upon joint options/returns data and present estimates of risk premiums for jump and volatility risks. The paper finds that while complex jump specifications add little explanatory power in fitting options data, these models fare better in fitting options and returns data simultaneously.     

Do heterogeneous oil price shocks really have different effects on earnings management?

Under the modern corporate governance structure, there is a knowledge gap in how companies' financial reporting practices respond to oil price shocks in China. To fill this gap, we employ China's A-share listed companies and follow Kilian (2009) study to investigate how the three types of classical oil shocks affect corporate earnings management heterogeneously. We also consider the role of oil implied volatility in this relationship and further examine the possible heterogeneity between energy-related and non-energy-related subsamples. The empirical results show that there are variant effects among the heterogeneous oil price shocks on earnings management. Specifically, oil supply shocks stimulate firms to manipulate more accrual and real earnings, and firms are more likely to carry out accrual earnings management downward. Oil aggregate demand shocks weaken the degree of accrual earnings manipulation and mainly reduce the negative accrual earnings manipulation. Oil-specific demand shocks constrain the earnings management behavior of companies and improve their accounting quality. Besides, the increased uncertainty of oil price weakens the promotion effect of oil supply shocks on earnings manipulation, and the moderating effect occurs mainly in downward earnings management. Furthermore, the subsample estimated results reveal that oil price shocks do not affect the degree of accrual earnings management of energy-related companies. Instead, they impact the non-energy-related companies. Overall, our findings provide a series of targeted policy recommendations to mitigate the principal-agent problems and cope with energy price volatility risks.     

The persistence of earnings and cash flows and the role of special items: Implications for the accrual anomaly

We argue that high accruals are likely to be the outcome of rules with an income statement perspective, while low accruals are likely to be the outcome of rules with a balance sheet perspective, and that this has implications for the properties of earnings. Specifically, earnings persistence is affected both by the magnitude and sign of the accruals. Accruals improve the persistence of earnings relative to cash flows in high accrual firms, but reduce earnings persistence in low accrual firms. We show that the low persistence of earnings in low accrual firms is primarily driven by special items. We then show that special item-low accrual firms have higher future stock returns than other low accrual firms. This is consistent with investors misunderstanding the transitory nature of special items. Further analysis reveals that special item-low accrual firms have poor past performance and declines in investor recognition (analyst coverage and institutional holdings). Special items continue to explain future returns after controlling for these factors.     

Equity index variance: Evidence from flexible parametric jump–diffusion models

This paper analyzes a wide range of flexible drift and diffusion specifications of stochastic-volatility jump–diffusion models for daily S&P 500 index returns. We find that model performance is driven almost exclusively by the specification of the diffusion component whereas the drift specifications is of second-order importance. Further, the variance dynamics of non-affine models resemble popular non-parametric high-frequency estimates of variance, and their outperformance is mainly accumulated during turbulent market regimes. Finally, we show that jump diffusion models yield more reliable estimates for the expected return of variance swap contracts.     

Political risk and international valuation

Measuring the impact of political risk on investment projects is one of the most vexing issues in international business. One popular approach is to assume that the sovereign yield spread captures political risk and to augment the project discount rate by this spread. We show that this approach is flawed. While the sovereign spread is influenced by political risk, it also reflects other risks that are likely included in the valuation analysis — leading to the double counting of risks. We propose to use “political risk spreads” to undo the double counting in the evaluation of international investment projects.     

On the Stewardship and Valuation Implications of Accrual Accounting Systems

In this paper we explore the role of accruals in determining “earnings quality” from both a stewardship and a valuation perspective. We show that the valuation and stewardship qualities of accrual accounting are maximized by either an “aggressive” or a “conservative” accrual strategy. Furthermore, accrual strategy choices can be delegated to management as it does not benefit by implementing a strategy that is not in the best interests of the shareholders. We also investigate the implications of accrual strategies for standard empirical measures of “earnings quality”: regression coefficients and R²s from price‐earnings and market‐to‐book regressions. We show that such measures respond differently, and in some cases adversely, to the kind of strategies that make accounting constructs more correlated with the underlying economic activities of firms.     

The Accrual Effect on Future Earnings

Earnings manipulation has become a widespread practice for US corporations. However, most studies in the literature focus on whether certain incentives would facilitate managers to manipulate earnings and there has been little evidence documenting the consequences of earnings manipulation. This paper fills this gap by examining how current accruals affect future earnings (the accrual effect) and measuring the size of this effect. We find that the aggregate future earnings will decrease by $0.046 and $0.096, respectively, in the next one and three years for a $1 increase of current accruals. Over the very long-term (25 years), 20% of current accruals will reverse. This negative accrual effect is more significant for firms with high price-earnings ratios, high market-to-book ratios and high accruals where earnings management is more likely to occur. We show that incorporating the accrual effect is useful in improving the accuracy of earnings forecasts for these firms. Accordingly, the empirical results are consistent with the notion that earnings management causes the negative relationship between current accruals and future earnings. In addition, this paper shows that one recently developed accrual model has better performance than the popularly cited model in identifying manipulated earnings.