Pricing an European gas storage facility using a continuous-time spot price model with GARCH diffusion

In this article we present both a theoretical framework and a solved example for pricing an European gas storage facility and computing the optimal strategy for its operation. As a representative price index we choose the Dutch TTF day-ahead gas price. We present statistical evidence that the volatility of this index is time-varying, so we introduce a new continuous-time model by incorporating GARCH diffusion into an Ornstein-Uhlenbeck process. Based on this price process we use dynamic programming methods to derive partial differential equations for pricing a storage facility. As an example we apply our methodology to a storage site located in Epe at the German-Dutch border. In this context we investigate the effects of multiple contract types, and perform a sensitivity analysis for all model parameters. We obtain a value surface displaying the properties of a financial straddle. Both volatility and mean reversion influence the facility value - but only around the long-run mean of the gas price. The terminal condition, which includes information about the contract provisions, is of importance if it contains e.g. penalty terms for low inventory levels. Otherwise its influence is diminishing for increasing lease periods. --TTF gas price,GARCH diffusion,natural gas storage,dynamic computing

Equilibrium and Real Options in the Ethanol Industry: Modelling and Empirical Evidence

In the last twenty years a large number of competitive ethanol rms have estab- lished operations in the US. Ethanol, produced from corn, is blended with pure gasoline to produce fuel. Producers hold an option to turn o unpro table plants. Blenders choose to substitute ethanol for gasoline at or beyond the minimum ratio set by the government. We propose and test an equilibrium model for blenders and producers that accounts for the real optionality embedded in the industry. The model, driven by corn and gasoline prices, leads to analytical expressions for the price and physical output of ethanol, and for the value of an ethanol producer. We confront the model with data between 2000 and 2017. In line with the model, we con rm that ethanol was largely priced as the maximum of rescaled gasoline and corn prices. Historical output levels between the mandate and installed capacity were explained by the model. Finally, the share price dynamics for the largest public ethanol producer in the US was consistent in some aspects with the value of a real option.Journal of Commodity Markets (JCM

An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms

Program Evaluation in Medical Education: An Overview of the Utilization-focused Approach

Medical school administrators, educators, and other key personnel must often make difficult choices regarding the creation, retention, modification, or termination of the various programs that take place at their institutions. Program evaluation is a data-driven strategy to aide decision-makers in determining the most appropriate outcome for programs within their purview. The purpose of this brief article is to describe one program evaluation model, the utilization-focused approach. In particular, we address the focus of this model, the personal factor, the role of the evaluator, and the evaluation process. Based on the flexibility of this model as well as its focus on stakeholder involvement, we encourage readers to consider the utilization-focused approach when evaluating programs

Blockin: Multi-Chain Sign-In Standard with Micro-Authorizations

The tech industry is currently making the transition from Web 2.0 to Web 3.0, and with this transition, authentication and authorization have been reimag- ined. Users can now sign in to websites with their unique public/private key pair rather than generating a username and password for every site. How- ever, many useful features, like role-based access control, dynamic resource owner privileges, and expiration tokens, currently don’t have efficient Web 3.0 solutions. Our solution aims to provide a flexible foundation for resource providers to implement the aforementioned features on any blockchain through a two-step process. The first step, authorization, creates an on-chain asset which is to be presented as an access token when interacting with a resource. The second step, authentication, verifies ownership of an asset through querying the blockchain and cryptographic digital signatures. Our solution also aims to be a multi-chain standard, whereas current Web 3.0 sign-in standards are limited to a single blockchain