Impact of Black-Scholes assumptions on Delta Hedging

In this work we are going to evaluate the different assumptions used in the Black- Scholes-Merton pricing model, namely log-normality of returns, continuous interest rates, inexistence of dividends and transaction costs, and the consequences of using them to hedge different options in real markets, where they often fail to verify. We are going to conduct a series of tests in simulated underlying price series, where alternatively each assumption will be violated and every option delta hedging profit and loss analysed. Ultimately we will monitor how the aggressiveness of an option payoff causes its hedging to be more vulnerable to profit and loss variations, caused by the referred assumptions.

O financiamento hospitalar e a definição de preços

RESUMO - Inseridos num contexto onde as unidades prestadoras de cuidados de saúde não possuem autonomia para fixar os seus próprios preços, estuda-se através do presente documento o processo de definição de preços do internamento hospitalar português entre 1993 e 2001, no sentido de aferir o grau de sinalização proporcionado ao mercado, uma vez que, na sua essência, um sistema de preços constitui um sistema de incentivos influenciador de comportamentos produtivos ao nível prestador. Utilizou-se a base de dados nacionais do sistema de classificação de doentes Grupos de Diagnóstico Homogéneos e foi caracterizada a evolução e tendência dos pesos relativos dos produtos do internamento hospitalar português. Foi também avaliada a relação da estrutura de preços com a quantidade produzida, a eficiência técnica e as necessidades em saúde da população portuguesa durante o período considerado. Apesar de existir alguma instabilidade durante o período analisado, o ponto de partida e de chegada não diferiu significativamente. Não foi encontrado nenhum padrão de variação que explicasse a instabilidade encontrada entre os produtos mais complexos, mais produzidos ou os que apresentaram maior/menor variação ao longo da década de 90. A hipótese relativa à correlação entre a evolução de preços e as variáveis quantidade, eficiência e necessidades também foi infirmada. Conclui-se que a utilização do sistema de preços constituiu na sua essência um sistema de incentivos neutro, não foi sinalizador para os prestadores e possuiu uma forte correlação com o nível de reposição de custos históricos dos hospitais portugueses.

Growth hacking model for B2B saas startups

The following project introduces a model of Growth Hacking strategies for business-tobusiness Software-as-a-Service startups that was developed in collaboration with and applied to a Portuguese startup called Liquid. The work addresses digital marketing channels such as content marketing, email marketing, social marketing and selling. Further, the company’s product, pricing strategy, partnerships and website communication are examined. Applying best case practices, competitor benchmarks and interview insights from numerous industry influencers and experts, areas for improvement are deduced and procedures for each of those channels recommended.

A comparison analysis of the marketing strategy of Lufthansa and Emirates in Germany

The objective of this paper is to perform an analysis of the marketing strategy of Lufthansa and Emirates in Germany. Since both airlines use a similar approach to increase brand awareness an in-depth analysis is implemented in order to identify potential differences. Hereby, consumer insights about the perception and expectation travellers have in common will be analyzed and assessed with quantitative data. Both airlines are well positioned in terms of their marketing strategy, but when Emirates is strengthen its marketing campaign with that pace, the Gulf carrier will certainly make use of its economic strength and can become a frightening threat for the Lufthansa Group on long-haul destinations. Finally, recommendations for future marketing activities for both airlines will be given.

On project finance and the first road concession in Portugal

In broad sense, Project Financing1 as a mean of financing large scale infrastructural projects worldwide has had a steady growth in popularity for the last 20 years. This growth has been relatively unscathed from most economic cycles. However in the wake of the 2007 systemic Financial Crisis, Project Financing was also in trouble. The liquidity freeze and credit crunch that ensued affected all parties involved. Traditional Lenders, of this type of financial instrument, locked-in long-term contractual obligations, were severely hit with scarcity of funding compounded by rapidly increasing cost of funding. All the while, Banks were “rescued” by the concerted actions of Central Banks and other Multi-Lateral Agencies around the world but at the same time “stressed” by upcoming regulatory effort (Basel Committee). This impact resulted in specific changes to this type of long-term financing. Changes such as Commercial Banks’ increased risk aversion; pricing increase and maturities decrease of credit facilities; enforcement of Market Disruption Event clauses; partial responsibility for project risk by Multilateral Agencies; and adoption of utility-like availability payments in other industrial sectors such as transportation and even social infrastructure. To the extent possible, this report is then divided in three parts. First, it begins with a more instructional part, touching academic literature (theory) and giving the Banks perspective (practice), but mostly as an overview of Project Finance for awareness’ sake. The renowned Harvard Business School professor – Benjamin Esty, states2 that Project Finance is a “relatively unexplored territory for both empirical and theoretical research” which means that academic research efforts are lagging the practice of Project Finance. Second, the report presents a practical case regarding the first Road Concession in Portugal in 1998 ending with the lessons learned 10 years after Financial Close. Lastly, the report concludes with the analysis of the current trends and changes to the industry post Financial Crisis of the late 2000’s. To achieve this I’ll reference relevant papers, books on the subject, online articles and my own experience in the Project Finance Department at a major Portuguese Investment Bank. Regarding the latter, with the signing of a confidentiality agreement, I’m duly omitting sensitive and proprietary bank information.