Income Uncertainty and the Decision to Invest in Bulk Shipping

We develop a coherent framework for the valuation of real assets and determination of the optimal time to invest. To this end, we model the stochastic nature of income and develop methodologies for valuing traded derivatives to facilitate model calibration and for assessing real investment projects. A valuation paradigm for freight-linked assets is presented and the effects of uncertainty in the key parameters are examined by means of a sensitivity analysis. Using a real option approach, we demonstrate its usefulness in investment appraisal and optimal timing of entry. We accompany our theoretical results with illustrative examples from the shipping industry

Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market

In this paper we examine the importance of mean reversion and spikes in the stochastic behaviour of the underlying asset when pricing options on power. We propose a model that is flexible in its formulation and captures the stylized features of power prices in a parsimonious way. The main feature of the model is that it incorporates two different speeds of mean reversion to capture the differences in price behaviour between normal and spiky periods. We derive semi-closed form solutions for European option prices using transform analysis and then examine the properties of the implied volatilities that the model generates. We find that the presence of jumps generates prominent volatility skews which depend on the sign of the mean jump size. We also show that mean reversion reduces the volatility smile as time to maturity increases. In addition, mean reversion induces volatility skews particularly for ITM options, even in the absence of jumps. Finally, jump size volatility and jump intensity mainly affect the kurtosis and thus the curvature of the smile with the former having a more important role in making the volatility smile more pronounced and thus increasing the kurtosis of the underlying price distribution

A Simulation Approach to Optimal Stopping Under Partial Information

We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional diffusion with correlated noise. Such models where the controller is not fully aware of her environment are of interest in applied probability and financial mathematics. We propose a new approximate numerical algorithm based on the particle filtering and regression Monte Carlo methods. The algorithm maintains a continuous state-space and yields an integrated approach to the filtering and control sub-problems. Our approach is entirely simulation-based and therefore allows for a robust implementation with respect to model specification. We carry out the error analysis of our scheme and illustrate with several computational examples. An extension to discretely observed stochastic volatility models is also considered

Gas Storage Valuation: A Comparative Simulation Study

The purpose of this paper is the comparative analysis of four natural gas storage valuation approaches. In competitive natural gas markets the optimal valuation and operation of natural gas storages is a key task for natural gas companies operating storages. Within this paper, four spot based valuation approaches are analyzed regarding computational time and accuracy. In particular, explicit and implicit finite differences, multinomial recombining trees, and Least Squares Monte Carlo Simulation are compared. These approaches are applied to the valuation of a gas storage facility considering three different underlying price processes. Major characteristics of historical natural gas prices are: seasonality, mean reversion and jumps. Therefore, we consider a mean reversion process as underlying price process. In a first step, we extend this mean reversion process to a mean reversion jump diffusion process, to account for jumps, occurring in historical gas spot price time series. Moreover, we consider a more general price process accounting for mean reversion as well as seasonal patterns as observed in the historical time series. Besides the analysis of the numerical results, the benefits and drawbacks of the methodologies are discussed

Decision-support tool for assessing future nuclear reactor generation portfolios

Capital costs, fuel, operation and maintenance (O&M) costs, and electricity prices play a key role in the economics of nuclear power plants. Often standardized reactor designs are required to be locally adapted, which often impacts the project plans and the supply chain. It then becomes difficult to ascertain how these changes will eventually reflect in costs,which makes the capital costs component of nuclear power plants uncertain. Different nuclear reactor types compete economically by having either lower and less uncertain construction costs, increased efficiencies, lower and less uncertain fuel cycles and O&M costs etc. The decision making process related to nuclear power plants requires a holistic approach that takes into account the key economic factors and their uncertainties. We here present a decision-support tool that satisfactorily takes into account the major uncertainties in the cost elements of a nuclear power plant, to provide an optimal portfolio of nuclear reactors. The portfolio so obtained, under our model assumptions and the constraints considered, maximizes the combined returns for a given level of risk or uncertainty. These decisions are made using a combination of real option theory and mean\xe2\x80\x93variance portfolio optimization