In a one price economy, the Fundamental Theorem of Asset Pricing (FTAP) establishes that no-arbitrage is equivalent to the existence of an equivalent martingale measure. Such an equivalent measure can be derived as the normal unit vector of the hyperplane that separates the attainable gain subspace and the convex cone representing arbitrage opportunities. However, in two-price financial models (where there is a bid-ask price spread), the set of attainable gains is not a subspace anymore. We use convex optimization, and the conic property of this region to characterize the “No-Arbitrage” principle in financial models with the bid-ask price spread present. This characterization will lead us to the generation of a set of price factor random variables. Under such a set, we can find the lower and upper bounds (supper-hedging and sub-hedging bounds) for the price of any future cash flow. We will show that for any given cash flow, for which the price is outside the above range, we can build a trading strategy that provides one with an arbitrage opportunity. We will generalize this structure to any two-price finite-period financial model.

Renewable energy sources are increasingly crucial for meeting global energy demands in an eco-friendly manner, particularly as the world shifts away from fossil fuels and faces higher volatility of the market prices. Portugal, a country with limited fossil fuel reserves and high energy dependency, has heavily invested in renewables in recent years. However, renewables like sunlight, wind, and water are inherently unsteady due to climate influences, resulting in energy production fluctuations. To mitigate this issue, energy storage systems are being deployed to stabilize renewable energy supply during production lulls. This project aims to assess an energy storage system and define technical specification in order to maximize profitability at the Finerge-owned Alto Douro wind farm. To achieve this, we've conducted an energy demand analysis, followed by simulations to assess system performance in relation to energy use and profit, while varying parameters such as power and efficiency. We've also compared commercial proposals from different battery manufacturers utilizing various technologies. Our findings suggest that high-power, quick charge-discharge lithium-ion batteries are the most suitable solution, given their efficiency and modularity. These attributes are vital for achieving current and future profitability.

A regularization approach to model selection, within a generalized HJM framework, is introduced which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. General theoretical results are derived and then specialized to affine term-structure models where new types of arbitrage-free machine learning models for the forward-rate curve are estimated numerically and compared to classical short-rate and the dynamic Nelson-Siegel factor models.

By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise by several orders of magnitude. In order to maximize the sensitivity to volatility, a simple formulation of Merton’s model is proposed that employs deep out-of-the-money option implied volatilities. The methodology also eliminates the use of historic data to specify the default barrier thereby leading to a full risk neutral calibration. Subsequently, a new technique for identifying and hedging capital structure arbitrage opportunities is illustrated. The approach seeks to hedge the volatility risk, or vega, as opposed to the exposure from the underlying equity itself, or delta. The results question the efficacy of the common arbitrage strategy of only executing the delta hedge.

Integrating a grid-connected battery into a Renewable Energy Community boosts Collective-Self-Consumption of photovoltaic produced energy and allow to perform Energy Arbitrage in the day-ahead and intraday electricity market. However, is it a cost-effective investment? The proposed analysis relay on Net Present Value assessment. Ageing affects are integrated and sensitivity analyses are conducted: considering community customers number, electricity mar-ket prices, battery cost, size and the decision to engage in energy arbitrage. Each scenario under-goes a 20-year hourly simulation using an ageing aware rolling-horizon 24-hours-looking-ahead scheduling, optimized with Mixed-integer linear Programming. Forecast errors, provid-ing of ancillary services, real time control and grid constrains are not taken into account. Simulations conducted on the Italian market indicates that a battery dedicated solely to collec-tive self-consumption is not economically appealing. However, integrating Energy Arbitrage, despite impact on battery lifespan, halves the payback period and enhances the attractiveness of larger battery investments. The Net Present Value is contingent upon battery size, customer number and market prices. However, if battery cost does not exceed 200 €/kWh the investment become cost-effective across all scenarios.

Semantic rules link purely theoretical terms like “price” and “electron” to things we can measure. Without them, theories cannot be tested empirically. When inappropriate, they produce false rejections. Economists routinely ignore semantic rules. Empirical journal articles essentially never mention them. More to the point, the conventional tests that reject the Law of One Price and Purchasing Power Parity never consider them. As a result, those rejections are unwarranted because such tests use inappropriate semantic rules. Both theories should be restored to not rejected and then retested using the more appropriate semantic rules described here. By using appropriate semantic rules, this paper is able to combine Covered Interest Parity and Purchasing Power Parity into a single theory that links auction markets for financial assets and commodities to auction markets for exchange rates. Using appropriate semantic rules for both theories also explains several puzzles in open economy macroeconomics and opens up broad new vistas for research.