Andrea Roncoroni

A new measure of cross-sectional risk and its empirical implications for portfolio risk management

Litterman, Scheinkman, and Weiss (1991) and Engle and Ng (1993) provide empirical evidence of a relation between yield curve shape and volatility. This study offers theoretical support for that finding in the general context of cross-sectional time series. We introduce a new risk measure quantifying the link between cross-sectional shape and market risk. A simple econometric procedure allows us to represent the risk experienced by cross-sections over a time period in terms of independent factors reproducing possible cross-sectional deformations. We compare our risk measure to the traditional cross-yield covariance according to their relative performance. Empirical investigation in the US interest rate market shows that 1) cross-shape risk factors outperform cross-yield risk factors (i.e., yield curve level, slope, and convexity) in explaining the market risk of yield curve dynamics; 2) hedging multiple liabilities against cross-shape risk delivers superior trading strategies compared to those stemming from cross-yield risk management.

Handbook Of Multi-Commodity Markets and Products : Structuring, Trading, and Risk Management

The comprehensive guide to working more effectively within the multi-commodity market. The Handbook of Multi-Commodity Markets and Products is the definitive desktop reference for traders, structurers, and risk managers who wish to broaden their knowledge base. This non-technical yet sophisticated manual covers everything the professional needs to become acquainted with the structure, function, rules, and practices across a wide spectrum of commodity markets. Contributions from a global team of renowned industry experts provide real-world examples for each market, along with tools for analyzing, pricing, and risk managing deals. The discussion focuses on convergence, including arbitrage valuation, econometric modeling, market structure analysis, contract engineering, and risk, while simulated scenarios help readers understand the practical application of the methods and models presented.

Asian Options with Jumps

We derive a closed-form formula for the fair value of call and put options written on the arithmetic average of security prices driven by jump diffusion processes displaying (possibly periodical) trend, time varying volatility, and mean reversion. The model allows one for jointly fitting quoted futures curve and the time structure of spot price volatility. Our result extends the no-jump case put forward in [Fusai, G., Marena, M., Roncoroni, A. 2008. Analytical Pricing of Discretely Monitored Asian-Style Options: Theory and Application to Commodity Markets. Journal of Banking and Finance 32 (10), 2033-2045]. A few tests based on commodity price data assess the importance of introducing a jump component on the resulting option prices.

Theory and Calibration of HJM with Shape Factors

We construct arbitrage free dynamics for the term structure of interest rates driven by infinitely many factors, each one representing a basic shape for the instantaneous forward rate curve in a given market. The consistency between a finitc-dimeusioual space of polynomials where the curve is day-to-day recovered and the proposed evolution equation is investigated. The main result is the developemeut of a historical-implicit hybrid calibration procedure for our infinite-dimensional shape factor model. In this context, we also derive a pricing formula for caplets.

Electricity forward curves with thin granularity: Theory and empirical evidence in the hourly EPEXspot market

We propose a constructive definition of electricity forward price curve with cross-sectional timescales featuring hourly frequency on. The curve is jointly consistent with both risk-neutral market information represented by baseload and peakload futures quotes, and historical market information, as mirrored by periodical patterns exhibited by the time series of day-ahead prices. From a methodological standpoint, we combine nonparametric filtering with monotone convex interpolation such that the resulting forward curve is pathwise smooth and monotonic, cross-sectionally stable, and time local. From an empirical standpoint, we exhibit these features in the context of EPEX Spot and EEX Derivative markets. We perform a backtesting analysis to assess the relative quality of our forward curve estimate compared to the benchmark market model of Benth, Koekebakker, and Ollmar (2007).

Hedging Size Risk: Theory and Application to the US Gas Market

Many corporate commitments exhibit a combined financial exposure to both market prices and idiosyncratic size components (e.g., volume, load, or business turnover). We design a customized contract to optimally mitigate the risk of joint fluctuations in price and size terms. The hedge is sought out among contingent claims written on price and any quoted index that is statistically dependent on commitment size. Closed-form solutions are derived for the optimal custom hedge pay-off and for the asset holdings of two market strategies, one based on price-linked forwards, the other based on price-linked and index-linked forwards. Analytical hedges are obtained using a stylized lognormal market model. Detailed comparative statics provide a thorough analysis of optimal hedging pay-off functions. Performance assessment is conducted in the context of the US gas market and a prototypical urban region. Results suggest that hedging through suitable custom claims written on price and an additional index significantly outperforms standard pricebased as well as mixed price-index forward hedging alternatives. Our optimal custom hedge could be adopted as a benchmark for the relative assessment of any risk management solution.

Static Mitigation of Volumetric Risk

We consider the problem of designing a financial instrument aimed at mitigating the joint exposure of energy-linked commitments to random price and volume delivery fluctuations. We formulate a functional optimization problem over a set of regular payoff functions: one is written on energy price, while the other is issued over any index exhibiting statistical correlation to volumetric load. On theoretical grounds, we derive closed-form expressions for both payoff structures under suitable conditions about the statistical properties of the underlying variables; we pursue analytical computations in the context of a lognormal market model and deliver explicit formulas for the optimal derivative instruments. On practical grounds, we first develop a comparative analysis of model output through simulation experiments; next, we perform an empirical study based on data quoted at EPEX SPOT power market. Our results suggest that combined price-volume hedging performance improves along with an increase of the correlation between load and index values. This outcome paves the way for a new class of effective strategies for managing volumetric risk upon extreme temperature waves.

Monetary Measurement of Risk: A Critical Overview - Part II: Coherent Measures of Risk

In Lecesne and Roncoroni (2013), we introduce the notion of monetary measure of risk borne by any financial claim. Our presentation moves from general definitions to concrete instances, including the benchmark measure Value-at-Risk (VaR). Part II develops a treatment of the class of coherent (monetary) measures of risk put forward by Artzner et al. (1999). Our goal is to illustrate the main features of this class of measures in light of application to practical cases. In this respect, we put our focus on the ambiguity of the term “coherent” and show that the connotation of consistency it naturally embeds is more an issue of lexical interpretation than actual meaning. As an example, we show that lack of subadditivity of VaR (which prevents from it to being a “coherent” measure of risk) is more a desirable property than a drawback, as is claimed in most of existing sources in the specialized literature.

Monetary Measurement of Risk: A Critical Overview - Part I: General Definitions and Value-at-Risk

We develop a self-contained pedagogical introduction to monetary measures of risk. This part deals with general definitions and a treatment of Value-at-Risk.