The characteristic function of rough Heston models

It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and implied volatilities. However, due to the non‐Markovian nature of the fractional Brownian motion, they raise new issues when it comes to derivatives pricing. Using an original link between nearly unstable Hawkes processes and fractional volatility models, we compute the characteristic function of the log‐price in rough Heston models. In the classical Heston model, the characteristic function is expressed in terms of the solution of a Riccati equation. Here, we show that rough Heston models exhibit quite a similar structure, the Riccati equation being replaced by a fractional Riccati equation.     

No‐arbitrage implies power‐law market impact and rough volatility

Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that in a quite general framework, under no‐arbitrage assumption, the market impact function can only be of power‐law type. Furthermore, we prove this implies that the macroscopic price is diffusive with rough volatility, with a one‐to‐one correspondence between the exponent of the impact function and the Hurst parameter of the volatility. Hence, we simply explain the universal rough behavior of the volatility as a consequence of the no‐arbitrage property. From a mathematical viewpoint, our study relies, in particular, on new results about hyper‐rough stochastic Volterra equations.     

Knowing your boundaries: Integration opportunities in international professional service firms

This study presents three different business models (continuous, repetitious, and unique) identified in international professional service firms that pursue a transnational strategy. These business models have varying opportunities for global integration. We extend the integration–responsiveness framework by offering a framework for analyzing how to balance global integration with local responsiveness when pursuing a transnational strategy. By identifying the content, structure, and governance transactions of the three business models, we can determine when to pursue headquarters-initiated global integration and when to choose strategies that ensure local responsiveness and subsidiary competitiveness in local markets.     

How risky is a random process?

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.     

Quantification of the high level of endogeneity and of structural regime shifts in commodity markets

We propose a “reflexivity” index that quantifies the relative importance of short-term endogeneity for several commodity futures markets (corn, oil, soybean, sugar, and wheat) and a benchmark equity futures market (E-mini S&P 500), from mid-2000s to October 2012. Our reflexivity index is defined as the average ratio of the number of price moves that are due to endogenous interactions to the total number of all price changes, which also include exogenous events. It is obtained by calibrating the Hawkes self-excited conditional Poisson model on time series of price changes. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact of news and the endogenous mechanism by which past price changes may influence future price changes. Our robustness tests show that our index provides a ‘pure’ measure of endogeneity that is independent of the rate of activity, order size, volume or volatility. We find an overall increase of the reflexivity index since the mid-2000s to October 2012, which implies that at least 60–70 percent of commodity price changes are now due to self-generated activities rather than novel information, compared to 20–30 percent earlier. While our reflexivity index is defined on short-time windows (10–30 min) and thus does not capture long-term memory, we discover striking coincidence between its dynamics and that of the price hikes and abrupt falls that developed since 2006 and culminated in early 2009.     

Valuation of forward start options under affine jump-diffusion models

Under the general affine jump-diffusion framework of Duffie et al. [Econometrica, 2000, 68, 1343–1376], this paper proposes an alternative pricing methodology for European-style forward start options that does not require any parallel optimization routine to ensure square integrability. Therefore, the proposed methodology is shown to possess a better accuracy–efficiency trade-off than the usual and more general approach initiated by Hong [Forward Smile and Derivative Pricing. Working paper, UBS, 2004] that is based on the knowledge of the forward characteristic function. Explicit pricing solutions are also offered under the nested jump-diffusion setting proposed by Bakshi et al. [J. Finance, 1997, 52, 2003–2049], which accommodates stochastic volatility and stochastic interest rates, and different integration schemes are numerically tested.     

A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS

We analyze the behavior of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalization of the strike variable with the property that the implied volatility converges to a nonconstant limiting shape, which is a function of both the diffusion component of the process and the jump activity (Blumenthal–Getoor) index of the jump component. Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short‐end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter, the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the former, the wings have a constant model‐independent slope. This result gives a theoretical justification for the preference of the infinite variation Lévy models over the finite variation ones in the calibration based on short‐maturity option prices.     

On the forecasting of the challenging world future scenarios

Logistic and power law methodologies for both retrospective and prospective analyses of extended time series describing evolutionary growth processes, in environments with finite resources, are confronted. While power laws may eventually apply only to the early stages of said growth process, the Allee logistic model seems applicable over the entire span of a long range process. On applying the Allee logistic model to both the world population and the world gross domestic product time series, from 1 to 2008 AD, a projection was obtained that along the next few decades the world should experience a new economic boom phase with the world GDP peaking around the year 2020 and proceeding from then on towards a saturation value of about 142 trillion international dollars, while the world population should reach 8.9 billion people by 2050. These results were then used to forecast the behavior of the supply and consumption of energy and food, two of the main commodities that drive the world system. Our findings suggest that unless the currently prevailing focus on economic growth is changed into that of sustainable prosperity, human society may run into a period of serious economical and social struggles with unpredictable political consequences.     

What would Don Draper do? Rules for restoring the contemporary agency mojo

What are the timeless truths of advertising? How can agency leaders manage their teams, their creative talent, and clients? To answer these and other questions, the mythology of the ‘Golden Age of Advertising’ is examined and analyzed herein. Specifically, using ad man Don Draper—protagonist of the fictional, but already culturally iconic, television series Mad Men—as a mythic archetype, lessons are extracted for contemporary advertising practitioners. Ten timeless rules are proposed and explicated in the areas of (1) managing intra-agency leadership processes, (2) managing creative processes, and (3) managing client relationships.     

风险导向审计模式在新的准则体系中的应用

2006年2月15日,财政部发布了48项中国注册会计师执业准则,新的准则体系构建了崭新的风险导向审计模型,标志着风险导向审计在我国即将步人实施阶段.本文从风险导向审计模式的含义人手,研讨了新的审计准则体系对风险导向审计模式的框架构建,以及在该模式下的审计业务主要流程.