We develop a normative framework for the optimal design, value assessment, and risk management integration of combined custom contingent claims. A risk averse firm faces a mix of financially insurable and noninsurable risk. The firm seeks optimal positioning in a pair of custom claims, one written on the insurable term, and another written on any listed index correlated to the noninsurable term. We prove that a unique optimum always exists unless the index is redundant, and show that the optimal payoff schedules satisfy a design integral equation. We assess the firm’s incremental benefit in terms of both an indifference value and an efficiency rating: this benefit increases with the correlation of the index to the noninsurable term, and it decreases with the correlation of the index to the insurable term. Our hedge proves empirically relevant for a highly risk averse firm facing a market shock (COVID-19 pandemic). In the context of a newsvendor model featuring random price and demand, we show that: (i) integrating our optimal combined custom hedge with the corresponding optimal procurement policy allows the firm to obtain a significant improvement in both risk and return; (ii) this gain may be traded off for a substantial enhancement in operational flexibility.

Inventory and capacity planning models generally take the time of sale as something that is exogenously given. For example, the story associated with the well-known newsvendor model is one of stocking for an upcoming selling season that will happen x units of time from now, where x is exogenous. In this paper, we re-visit the capacity planning decision by assuming that demand follows a stochastic process and

study what happens when both the time of sale and capacity are decisions. When the selling price is fixed, our baseline case, we find that the optimal time to sell is either now or never. In contrast, when the selling price is stochastic, the optimal time to serve demand is somewhere between now and never. Thus, we link timing preference to two primary sources: uncertainty in demand and uncertainty in the selling price. Our results are useful whenever firms have considerable control over timing, such as in events when firms launch new products or in instances when there is no apparent selling season.

We review the theoretical development of optimal positioning in financial derivatives for managing corporate exposure. Our primary focus is on one-period integrated financial-operational policies featuring a bespoke financial contingent claim (or portfolio of claims) and an operational control variable. We develop a unifying theoretical framework which (a) encompasses all of existing solutions in a static set-up across the areas of of portfolio insurance, agricultural economics, and integrated financial-operational management, (b) provides researchers with a solid ground to either fill in gaps in the current literature and move forward towards a general theory of contingent claim origination. We also put forward pathways for future development, one based on current research problem, the other focusing on new methodological issue.

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 stand- point, 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).

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 price-based 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.

We consider the problem of designing a financial instrument aimed at mitigating the joint exposure to random price and volume delivery fluctuations of energy-linked commitments. We formulate a functional optimization problem over a set of regular pay-off functions: one is written on energy price, while the other is issued over any index exhibiting statistical correlation to volumetric load. On a theoretical ground, we derive closed-form expressions for both pay-off 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 formulae for the optimal derivative instruments. On a practical ground, we first develop a comparative analysis of model output through simulation experiments; next, we perform an empirical study based on data quoted on 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 to a new class of effective strategies for managing volumetric risk upon extreme temperature waves.

Galluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We propose a theoretical framework supporting that finding, which is based on a notion of “shape factors”. This notion represents cross-sectional risk in terms of stylized analytical deformations experienced by yield curves. We provide an econometric procedure to identify shape factors, and propose a continuous-time yield curve dynamic model driven by these factors. Our proposal consists of a function-valued dynamic term structure model driven by these factors. We also propose and develop the corresponding arbitrage pricing theory. We devise three applications of the proposed framework. First, we derive interest rate derivative pricing formulas. Second, we study the analytical properties exhibited by a finite factor restriction of term structure dynamics that are cross-sectionally consistent with a family of exponentially weighed polynomials. Finally, we conduct an empirical analysis of cross-sectional risk on US swap, Euro bond and oil price data sets. Results support our conclusion that shape factors outperform the classical yield/price factors (i.e., level, slope, and convexity) in explaining the underlying market risk. The methodology can in principle be used for understanding the intertemporal dynamics of any cross-sectional data, whether it be price curves, option implied volatility smiles, or cross-sections of equity returns.

We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61–73] allows us to derive a closed-form formula for the fair value of discretely monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a “jump-reversion” component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets.

Litterman et al. [Litterman, R., Scheinkman, J., Weiss, L., 1991. Volatility and the yield curve. Journal of Fixed Income 1 (June), 49–53] and Engle and Ng [Engle, R.F., Ng, V.K., 1993. Time varying volatility and the dynamic behavior of the term structure. Journal of Money, Credit and Banking 25(3), 336–349] 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.