<p>I denna uppsats har jag haft intentionen att försöka förklara vikten av att ha en uppfattning av volatilitet när man handlar med Optioner. Syftet har varit att analysera ifall man kan lära sig från volatilitetens historia, och ifall historisk volatilitet är bättre på att indikera framtida volatilitet än marknadens volatilitet, även kallad den implicita volatiliteten. Syftet har även varit att undersöka ifall det går att göra vinst på Optioner om man har en annan uppfatt-ning om den framtida volailiteten.</p><p>I uppsatsen har jag använt mig av Black, Scholes and Mertons epokavgörande teori om hur man prissätter Optioner, den så kallade Black-Scholes ekvationen. Från den ekvationen har jag erhålligt volailiteten i OMX index Optioner, den implicita volatiliteten. Black-Scholes ekvationen har likaså använts för att härleda denna faktiska och historiska volaliteten. För att kunna utnyttja en annan uppfattning om den framtida volaliteten än marknadens så har jag presenterat ett antal olika Options strategier.</p><p>De slutsatser som jag har kunnat dra från år 2001 OMX index Optioner är att den implicita volaliteten verkar vara bättre på att förutspå den faktiska volaliteten än den historiska vola-tiliteten. Ingen av dem är en perfekt indikator på den faktiska volatiliteten men i genomsnitt så skiljer sig den implicita mindre från den faktiska än den historiska.</p><p>För att sammanfatta volalitetens historia så kan man påstå att volatiliteten som reflekteras i Optionspriset sällan stämmer överens med den faktiska volatiliteten. Ingen sitter på Op-tionsmarknaden med en kristallkula och kan förutspå volatiliteten perfekt hela tiden. Sam-tidigt är det just skillnader i volatilitetstro mellan de olika aktörerna i en Optionsaffär som skapar handel och som gör Optioner till ett så användbart och intressant instrument.</p>

Univ., Diss. 2007--Lund, 2007.

Problem: The standard Black-Scholes framework cannot incorporate the volatility smiles usually observed in the markets. Instead, one must consider alternative stochastic volatility models such as the SABR. Little research about the suitability of the SABR model for Swedish market (swaption) data has been found. Purpose: The purpose of this paper is to account for and to calibrate the SABR model for swaptions trading on the Swedish market. We intend to alter the calibration techniques and parameter values to examine which method is the most consistent with the market. Method: In MATLAB, we investigate the model using two different minimization techniques to estimate the model’s parameters. For both techniques, we also implement refinements of the original SABR model. Results and Conclusion: The quality of the fit relies heavily on the underlying data. For the data used, we find superior fit for many different swaption smiles. In addition, little discrepancy in the quality of the fit between methods employed is found. We conclude that estimating the α parameter from at-the-money volatility produces slightly smaller errors than using minimization techniques to estimate all parameters. Using refinement techniques marginally increase the quality of the fit.

The informational content of implied volatility and its prediction power is evaluated for time horizons of one month. The study covers the period of November 2007 to November 2013 for the two indices S&amp;P500 and OMXS30. The findings are put in relation to the corresponding results for past realized volatility. We find results supporting that implied volatility is an efficient, although biased estimator of realized volatility. Our results support the common notion that implied volatility predicts realized volatility better than past realized volatility, and that it also subsumes most of the informational content of past realized volatility.

Zugl.: Augsburg, Univ., Habil.-Schr., 2002.

Universiẗat, Diss., 2004--Münster (Westfalen). / Erscheinungsjahr an der Haupttitelstelle: 2003.

Submitted by Raniere Barreto (raniere.barros@ufvjm.edu.br) on 2018-04-16T18:07:41Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) bruno_ferreira_campos_silva.pdf: 2957468 bytes, checksum: 54576f6c332d9ba048e85d7de08b09a8 (MD5) / Rejected by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br), reason: Verificar palavras-chave, keywords. UFVJM n?o ? ag?ncia financiadora Verificar nome Carlos Alberto Mirez Tarrillo se ? espanhol. on 2018-04-20T15:06:05Z (GMT) / Submitted by Raniere Barreto (raniere.barros@ufvjm.edu.br) on 2018-05-15T19:08:56Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) bruno_ferreira_campos_silva.pdf: 2957468 bytes, checksum: 54576f6c332d9ba048e85d7de08b09a8 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2018-05-15T19:50:24Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) bruno_ferreira_campos_silva.pdf: 2957468 bytes, checksum: 54576f6c332d9ba048e85d7de08b09a8 (MD5) / Made available in DSpace on 2018-05-15T19:50:24Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) bruno_ferreira_campos_silva.pdf: 2957468 bytes, checksum: 54576f6c332d9ba048e85d7de08b09a8 (MD5) Previous issue date: 2017 / Nesta disserta??o ? apresentada a teoria que envolve o modelo de Black ? Scholes como uma alternativa de investimento para produtores rurais dos Vales do Jequitinhonha e Mucuri. Ao fazer um estudo sobre os produtores rurais dos vales, percebe-se que a produ??o no campo ? voltada para a subsist?ncia, vendendo somente o excedente. Foi constatado que a falta de investimento no campo reduz em partes o n?vel de produ??o do produtor rural. A alternativa de investimento atrav?s do modelo de Black ? Scholes na precifica??o de op??es se faz necess?rio n?o somente para se ter um maior investimento no meio rural, mas sim, ser tamb?m uma outra forma de se obter renda com t?cnicas aplicadas na Bolsa de Valores, ajudando o homem do campo em ter uma estabilidade financeira baseada n?o somente em sua produ??o. ? realizado um estudo criterioso da equa??o diferencial parcial estoc?stica advinda deste modelo, no tocante ? determina??o de poss?veis simula??es de problemas enfrentados diante das volatilidades dos mercados na precifica??o de op??es. Para que o produtor rural utilize o modelo de Black ? Scholes ? interessante se observar como se comporta os seus par?metros. Ent?o foi realizado uma an?lise do comportamento do valor da precifica??o de op??es em rela??o aos par?metros do modelo de Black ? Scholes baseados em dados reais retirados da BM&FBOVESPA. ? apresentada uma breve compara??o do modelo de Black ? Scholes com o modelo Binomial, compara??o feita com um exemplo de obten??o do valor da op??o de compra e venda via Binomial e Black ? Scholes, e neste exemplo ? observado um melhor retorno para o modelo Binomial. ? observado ao longo da pesquisa que existem dois par?metros que mais oscilam nos mercados, que s?o a volatilidade e a taxa de juros. Para se fazer bons investimentos, o produtor rural deve ficar atento e ter ci?ncia do comportamento da oscila??o desses par?metros. Para se ter uma melhor representa??o da varia??o desses par?metros, ? feito uma compara??o entre o valor das op??es de compra e venda calculados pelo modelo de Black ? Scholes e Binomial. Para a taxa de juros o modelo Binomial apresentou valores fora do esperado em rela??o ao modelo de Black ? Scholes. Devido a car?ncia de informa??es a respeito de como se investir na Bolsa de Valores, ? criado uma cartilha que se encontra nos anexos desta disserta??o voltada para o produtor rural, sobre como fazer um investimento na Bolsa de Valores e quais procedimentos iniciais deve-se tomar para obter ?xito nos mercados. Desses estudos, conclui-se que ? poss?vel o produtor rural investir pequenas quantias de dinheiro e obter retornos significativos em rela??o ao investimento inicial. Podendo assim, aplicar parte desse dinheiro em seu trabalho no campo e tamb?m ter uma forma de renda quando os retornos das produ??es no meio rural n?o forem favor?veis. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o em Tecnologia, Sa?de e Sociedade, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / In this dissertation there is presented the theory that involves the Black model ? Scholes as an alternative of investment for rural producer Jequitinhonha and Mucuri Valleys. When doing a study on the rural producers of the valleys, it is seen that the production in the field is turned for the subsistence, selling only the excess. It was noted that the lack of investment in the field reduces in parts the level of production of the rural producer. The investment alternative through Black model ? Scholes in the options pricing is made necessary not only in order that a bigger investment has been in the rural environment, but yes, to be also another form of income being obtained with techniques applied in the valuable Stock Exchange, helping the man of the field in having a financial stability based not only on his production. It is accomplished out a discerning study of the partial differential equation stochastic resulted from this model, regarding the determination of possible simulations of problems faced before the volatilities of the markets in the options pricing. For the rural producer to use the Black model ? Scholes is interesting it will notice how if it holds his parameters. Then there was accomplished out an analysis of the behavior of the value of the pricing of options regarding the parameters of the Black model ? Scholes based on retired real data of the BM&FBOVESPA. There is presented a short comparison of the Black model ? Scholes with the Binominal model, comparison done with an example of getting the value of the option of purchase and sale was seeing Binomial and Black ? Scholes, and in this example a better return is observed for the Binomial model. It is observed throughout the research that there are two parameters that more oscillate in the markets, which are the volatility and the interest rate. In order that good investments become, the rural producer must be attentive and have science of the behavior of the oscillation of these parameters. In order that there has been a better representation of the variation of these parameters, it is done a comparison between the value of the options of purchase and sale calculated by the Black model ? Scholes and Binomial. For the interest rate the Binomial model presented values out of the waited one regarding the Black model ? Scholes. Due to lack of information about how to invest in the Stock Exchange, it is created a primer that is in the annexes of this dissertation turned to the rural producer how to make an investment in the Stock Exchange and it is necessary to take which initial proceedings to obtain succeed in the markets. Of these studies, it is ended that the possible the rural producer to invest small amounts of money and to obtain significant returns regarding the initial investment. Being able so, to apply part of this money in his work in the field and also to have the form of income when the returns of the productions in the rural environment are not favorable.

Diploma thesis deals with models of asset pricing. We investigated in detail three classical models: binomial, Black-Scholes and Merton model. These models are widely used to date, although they were first published a few decades ago. It is because they are relatively simple and easy-to-use. The models were originally derived for option pricing however they can be used for the wide range of financial instruments. The theoretical part of the thesis includes an introduction to options and models derivation. The practical part consists of the sensitivity analyst and empirical test of the models. S&P 500 index options data were used for this purpose. The result is that Merton model seems to be the most accurate.

Finansų inžinerijos dėka buvo sukurti egzotiniai opcionai, kurie patrauklūs investuotojams dėl didesnio nei standartiniai opcionai pelningumo ir nestandartizacijos. Pastaraisiais metais padidėjo užbiržinėje rinkoje prekiaujamų egzotinių opcionų likvidumas, dėl ko investuotojams jie tapo dar patrauklesni. Finansų institucijos, norėdamos pasiūlyti investuotojams geriausiai jų lūkesčius atitinkančius finansinius instrumentus, konkuruoja tarpusavyje dėl naujų egzotinių opcionų kūrimo. Egzotiniai opcionai gali būti kuriami ne tik akcijų, indeksų, palūkanų normų ar valiutų pagrindu, bet netgi realiai neegzistuojančio turto pagrindu. Dėl tokios egzotinių opcionų įvairovės kyla egzotinių opcionų vertinimo problema. Darbo objektas – egzotiniai opcionai kaip kintamos vertės išvestinės finansinės priemonės. Darbo tikslas – išnagrinėjus egzotinių opcionų savybes ir įkainojimo metodus, suformuoti modelį egzotinių opcionų vertinimui ir atlikti modelio parametrų jautrumo analizę. Mokslinės finansų literatūros analizė parodė, kad opcionai gali būti naudojami apsidraudimo nuo rizikos arba spekuliaciniais tikslais. Išnagrinėjusi opcionų savybes ir egzotinių opcionų klasifikacijas, autorė pasiūlė savo sukurtą egzotinių opcionų klasifikaciją, kuri priklauso nuo opciono charakteristikų. Išnagrinėjus mokslinę literatūrą nustatyta, kad vertinant opcionus svarbiausia atsižvelgti į opcionų vertę sudarančius parametrus: bazinio turto rinkos kainą bei jos kintamumą, vykdymo kainą, nerizikingą palūkanų... [toliau žr. visą tekstą] / Financial engineering have created exotic options that are more attractive to investors for more profitability than plain-vanilla options and non-standartization. Recently years have grown liquidity on OTC tradable options, and they became even more attractive for investors. Financial institutions compete for new exotic option creation, because they want to offer investors the best financial instruments for their expectations. Exotic options could be created not only on stocks, index, interest rates or currency bases, but even on not real-existed asset. There exists a problem of exotic options valuation, because there are a big variety of exotic options. The object of the study – exotic options as variable value derivatives. The purpose of the study – after analyse of characteristics and pricing methods of options, create a model for exotic options evaluation and make model parameters sensitivity analysis. The findings of the scholar finance literature pointed, that options could be used for hedging from risks or speculation. After analysis of options characteristics and exotic options classifications, authoress offer new exotic options classification, which depends on option characteristics. To summarize of scolar literature pointed, that the most important for valuing options is their parameters: strike price, underlying spot price and volatility, risk free rate, maturity and, if it is, dividens. After comparable analysis it emerged, that exotic options greeks functions... [to full text]

In this paper, we study mathematical properties of a generalized bivariate Ornstein-Uhlenbeck model for financial assets. Originally introduced by Lo and Wang, this model possesses a stochastic drift term which influences the statistical properties of the asset in the real (observable) world. Furthermore, we generali- ze the model with respect to a time-dependent (but still non-random) volatility function. Although it is well-known, that drift terms - under weak regularity conditions - do not affect the behaviour of the asset in the risk-neutral world and consequently the Black-Scholes option pricing formula holds true, it makes sense to point out that these regularity conditions are fulfilled in the present model and that option pricing can be treated in analogy to the Black-Scholes case.