Abstract Title: Options Based on CO2 Emissions: A Comparison with Traditional Options Seminar date: 2009-06-17 Course: Bachelor thesis in business administration, 15 ECTS Authors: Gustaf Kristiansson, Martin Nilsson Instructor: Bengt Kjellgren Key words: Black & Scholes, Certified Emission Reductions, emission markets, European Union Allowances, options, pricing Purpose: This study intends to compare traditional options with the CO2 based instruments EUAs and CERs options in the fields of pricing, cap and trade, political influence, economical effects and market function. Methodology: A combined research methodology is used in this study, which includes both a quantitative and a qualitative approach. A deductive research approach is brought out over the whole study. Theoretical perspectives: The theoretical framework is based upon previous empirical research concerning the fields in this study. The Black & Scholes formula for option pricing has a central position. Empirical foundation: Market data has been used to analyse the field of pricing. Interviews have been conducted with actors on the European emission trading market for a further understanding of cap and trade, political influence, economical effects and market function. Conclusions: We have in this research identified that the CO2 based market differs from the financial market when it comes to political decisions and price fluctuation. We have also identified that the CO2 based market is not mature enough for a complete internationalisation. / En formell presentation utfördes ej pga utlandsstudier.

Made available in DSpace on 2016-04-28T20:19:21Z (GMT). No. of bitstreams: 1 2003 - Tereza de Jesus Ramos da Silva.pdf: 1614568 bytes, checksum: 0272fd51b3a45e19c0bbf132f65427e4 (MD5) Previous issue date: 2003-03-13 / Options in future markets is a theme still with little exploration by the studious, concerned to practical work published, mainly in Brazilian Literature. In this work it has been tried to show the importance of volatility in pricing of options when applied to Black & Scholes Model. A first analysis was taken, a study of derivatives, defined as titles which values depend on other more basic variables, where the four more used types were concieved: forward contracts, swap contracts, the future and the options ones. A future contract consists in the obrigation of buying and selling an active in certain future time for a certain price. There are two types of options: call and put. A call gives its holders the right to buy an active in a settled date for a certain price and one put, the right to sell. We ve emphasized the options markets, defining a future option as an option about a future contract. The partners of these markets are the hedgers, the speculators and the arbitrators. The options have been defined inside the money, on money and out of money, which shows as differential an intrinsic value definition. The basic factors that affect the price of options about futures are, besides the volatility of future price, the future price itself, the price of exercise and the time for due date. The volatility is a very important factor, because it measures the variation of future prices with the time. It has been presented an equation of Black to the use in pricing of future contracts and it has been used the Arabic Coffee as the farming commodity object of our investigation. The calculus of premium, defined as price paid by the buyer of the options contract, has been calculated according to the results found in the application of the three methods of volatility calculus: the historic volatility which is the one that uses historic series of prices; the volatility by moving average which is the one found through an aritimetic average in a certain period of time (n days of negotiation and the implicit volatility that is an estimation of volatility which is on the level with market price. Chapter 3 has analysed all the calculus process, through treatment of data in annexes 04 to 12, describing all the mechanism used in preparing these spread sheets. From the results found, it has been concluded that the best way to be used in option pricing in Black & Scholes Model is the one of implicit volatility. / Op??es em mercados futuros ? um tema ainda pouco explorado pelos estudiosos, no que concerne a publica??o de trabalhos pr?ticos, principalmente na literatura brasileira. Neste trabalho procurou-se mostrar a import?ncia da volatilidade dentro da precifica??o de op??es quando aplicada ao modelo de Black & Scholes. Fez-se em uma primeira an?lise, um estudo dos derivativos, definidos como t?tulos cujos valores dependem de outras vari?veis mais b?sicas, onde foram conceituados os quatro tipos mais utilizados: os contratos a termo, os contratos de swaps, os futuros e os de op??es. Um contrato futuro consiste na obriga??o de comprar ou vender um ativo em certa ?poca futura por determinado pre?o. H? dois tipos de op??es: call e put. Uma call d? ao seu detentor o direito de comprar um ativo em determinada data por pre?o certo e uma put, o direito de vender. Enfatizamos os mercados de op??es, definindo uma op??o futura como uma op??o sobre um contrato futuro. Os participantes desses mercados s?o os hedgers, os especuladores e os arbitradores. Foram definidas as op??es dentro do dinheiro, no dinheiro e fora do dinheiro, que apresenta como diferencial a defini??o de valor intr?nseco. Os fatores b?sicos que afetam o pre?o das op??es sobre futuros s?o, al?m da volatilidade do pre?o futuro, o pr?prio pre?o futuro, o pre?o de exerc?cio e o tempo para o vencimento. A volatilidade ? um fator muito importante, pois ela mede a oscila??o dos pre?os futuros com o tempo. Foi apresentada a equa??o de Black quando para a utiliza??o na precifica??o de contratos futuros e utilizou-se o caf? ar?bica como a commodity agropecu?ria objeto da nossa investiga??o. O c?lculo do pr?mio, definido como o pre?o pago pelo comprador do contrato de op??es, foi calculado segundo os resultados encontrados quando da aplica??o dos tr?s m?todos de c?lculo da volatilidade: a volatilidade hist?rica que ? a que se utiliza de s?ries hist?ricas dos pre?os; a volatilidade por m?dia m?vel que ? aquela encontrada atrav?s de uma m?dia aritm?tica no lapso de um per?odo certo(n dias de negocia??o e a volatilidade impl?cita que ? uma estimativa de volatilidade que se iguala ao pre?o de mercado. O cap?tulo 3 analisou todo o processo de c?lculo, atrav?s do tratamento dos dados constantes dos anexos 04 a 12, descrevendo todo o mecanismo utilizado na confec??o dessas planilhas. A partir dos resultados encontrados, concluiu-se que o melhor m?todo a ser utilizado na precifica??o de op??es no modelo de Black & Scholes ? o da volatilidade impl?cita.

Theaim of this master-thesis is to study the impact of uncertainty in the local-and implied volatility surfaces when pricing certain structured products suchas capital protected notes and autocalls. Due to their long maturities, limitedavailability of data and liquidity issue, the uncertainty may have a crucialimpact on the choice of valuation model. The degree of sensitivity andreliability of two different valuation models are studied. The valuation models chosen for this thesis are the local volatility model of Dupire and the implied volatility model of Black&Scholes. The two models are stress tested with varying volatilities within an uncertainty interval chosen to be the volatilities obtained from Bid and Ask market prices. The volatility surface of the Mid market prices is set as the relative reference and then successively scaled up and down to measure the uncertainty.The results indicates that the uncertainty in the chosen interval for theDupire model is of higher order than in the Black&Scholes model, i.e. thelocal volatility model is more sensitive to volatility changes. Also, the pricederived in the Black&Scholes modelis closer to the market price of the issued CPN and the Dupire price is closer tothe issued Autocall. This might be an indication of uncertainty in thecalibration method, the size of the chosen uncertainty interval or the constantextrapolation assumption.A further notice is that the prices derived from the Black&Scholes model areoverall higher than the prices from the Dupire model. Another observation ofinterest is that the uncertainty between the models is significantly greaterthan within each model itself. / Syftet med dettaexamensarbete är att studera inverkan av osäkerhet, i prissättningen av struktureradeprodukter, som uppkommer på grund av förändringar i volatilitetsytan. I dennastudie värderas olika slags autocall- och kapitalskyddade struktureradeprodukter. Strukturerade produkter har typiskt långa löptider vilket medförosäkerhet i värderingen då mängden data är begränsad och man behöver ta tillextrapolations metoder för att komplettera. En annan faktor som avgörstorleksordningen på osäkerheten är illikviditeten, vilken mäts som spreadenmellan listade Bid och Ask priset. Dessa orsaker ligger bakom intresset attstudera osäkerheten för långa löptider över alla lösenpriser och dess inverkanpå två olika värderingsmodeller.Värderingsmodellerna som används i denna studie är Dupires lokala volatilitetsmodell samt Black&Scholes implicita volatilitets modell. Dessa ställs motvarandra i en jämförelse gällande stabilitet och förmåga att fånga uppvolatilitets ändringar. Man utgår från Mid volatilitetsytan som referens ochuppmäter prisändringar i intervallet från Bid upp till Ask volatilitetsytornagenom att skala Mid ytan. Resultaten indikerar på större prisskillnader inom Dupires modell i jämförelsemot Black&Scholes. Detta kan tolkas som att Dupires modell är mer känslig isammanhanget och har en starkare förmåga att fånga upp förändringar isvansarna. Vidare notering är att priserna beräknade i Dupire är relativtbilligare än motsvarande från Black&Scholes modellen. En ytterligareobservation är att osäkerheten mellan värderingsmodellerna är av högre ordningän inom var modell för sig. Ett annat resultat visar att CPN priset beräknat iBlack&Scholes modell ligger närmast marknadspriset medans marknadsprisetför Autocallen ligger närmare Dupires. Detta kan vara en indikation påosäkerheten i kalibreringsmetoden eventuellt det valda osäkerhetsintervalletoch konstanta extrapolations antagandet.