全球金融風暴近年來發生頻率愈來愈快，主要的原因就是許多企業不管是在發行或投資衍生性金融商品的比重都大幅地增加，卻沒有規避它們潛在的市場風險。因此，避險策略的好壞是風險管理上很重要的一個議題。本研究的目的主要是希望在一個Delta Neutral的投資組合下，加入Delta-Gamma Neutral策略能夠使間斷調整避險的效果變得比較好。故本研究透過加入相同標的物和到期日，但不同履約價的選擇權作為避險部位，使用蒙地卡羅模擬法，模擬投資組合在持有一段時間後，未來價值可能的情境，計算風險值來衡量其避險效果。實證結果發現，當原始投資組合部位為價平選擇權所組成，避險部位若能使用相同標的物，到期日也相同，但履約價不同的價平選擇權，不論在到期日長短，皆有很好的避險效果。 / The global financial storm has happened more rapidly. The most important reason is that many enterprises published or invested in the derivatives ratio which has greatly increased without evading the potential market risk. Therefore, the advantages and the disadvantages of hedging strategy is a crucial issue in risk management. This research’s primary goal is to consider Delta-Gamma Neutral strategy in the invested combination of Delta Neutral that render the effect of discretely rebalance hedge became much better. The research entered the same underlying and expiration date, and let the different strike price’s option as hedging position. Using Monte Carol Simulation to obtain the condition of the portfolio’s value after holding a period of time, and compute the value-at-risk to measure hedging effect. The outcome showed that the hedging effect will be nice no matter the date of expiration by using at-the-money options with the same underlying and expiration date but different strike price when the original portfolio was composed of at-the-money options.

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Submitted by Lucas Processi (lucasprocessi@gmail.com) on 2017-12-06T13:14:53Z No. of bitstreams: 1 Processi (2017).pdf: 1111887 bytes, checksum: 09c88a08f1d79acf1311e697cf8c14cc (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2017-12-21T11:42:42Z (GMT) No. of bitstreams: 1 Processi (2017).pdf: 1111887 bytes, checksum: 09c88a08f1d79acf1311e697cf8c14cc (MD5) / Made available in DSpace on 2017-12-27T11:50:16Z (GMT). No. of bitstreams: 1 Processi (2017).pdf: 1111887 bytes, checksum: 09c88a08f1d79acf1311e697cf8c14cc (MD5) Previous issue date: 2017-11-08 / We investigate arbitrage opportunities in the Brazilian options market. Our research consists inbacktesting several delta-gamma neutral portfolios of options traded in B3 exchange to assessthe possibility of obtaining systematic excess returns. Returns sum up to 400% of the dailyinterbank rate in Brazil (CDI), a rate viewed as risk-free. However, with bootstrap analysis,we find evidence consistent with the absence of arbitrage opportunities in the Brazilian optionsmarket.This approach is different from other studies because the analysis is taken on several options ondifferent underlying assets, which gives us the opportunity to investigate factors that influencethe magnitude of excess returns. Europeanness is the most relevant factor found.

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Submitted by Ricardo Alves Carmo Ribeiro (ricardoacrj@hotmail.com) on 2015-07-23T19:15:44Z No. of bitstreams: 1 Dissertação Ricardo Ribeiro - José Valentim - Gustavo Araujo.pdf: 507947 bytes, checksum: 29fa5a446aef99ff3676496ad8c078c1 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2015-07-29T14:20:05Z (GMT) No. of bitstreams: 1 Dissertação Ricardo Ribeiro - José Valentim - Gustavo Araujo.pdf: 507947 bytes, checksum: 29fa5a446aef99ff3676496ad8c078c1 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-07-30T12:40:19Z (GMT) No. of bitstreams: 1 Dissertação Ricardo Ribeiro - José Valentim - Gustavo Araujo.pdf: 507947 bytes, checksum: 29fa5a446aef99ff3676496ad8c078c1 (MD5) / Made available in DSpace on 2015-07-30T12:40:36Z (GMT). No. of bitstreams: 1 Dissertação Ricardo Ribeiro - José Valentim - Gustavo Araujo.pdf: 507947 bytes, checksum: 29fa5a446aef99ff3676496ad8c078c1 (MD5) Previous issue date: 2015-05-27 / Este trabalho tem como objetivo verificar se o mercado de opções da Petrobras PN (PETR4) é ineficiente na forma fraca, ou seja, se as informações públicas estão ou não refletidas nos preços dos ativos. Para isso, tenta-se obter lucro sistemático por meio da estratégia Delta-Gama-Neutra que utiliza a ação preferencial e as opções de compra da empresa. Essa ação foi escolhida, uma vez que as suas opções tinham alto grau de liquidez durante todo o período estudado (01/10/2012 a 31/03/2013). Para a realização do estudo, foram consideradas as ordens de compra e venda enviadas tanto para o ativo-objeto quanto para as opções de forma a chegar ao livro de ofertas (book) real de todos os instrumentos a cada cinco minutos. A estratégia foi utilizada quando distorções entre a Volatilidade Implícita, calculada pelo modelo Black & Scholes, e a volatilidade calculada por alisamento exponencial (EWMA – Exponentially Weighted Moving Average) foram observadas. Os resultados obtidos mostraram que o mercado de opções de Petrobras não é eficiente em sua forma fraca, já que em 371 operações realizadas durante esse período, 85% delas foram lucrativas, com resultado médio de 0,49% e o tempo médio de duração de cada operação sendo pouco menor que uma hora e treze minutos. / This work aims to verify if the Petrobras options market is ineficient on the weak form, that is, if in fact all the public information are already reflected in asset prices. So, the study tries to achieve profit systematically through the Delta-Gamma-Neutral strategy using the company's preferred stock and it’s options. This asset was chosen because it’s options were highly liquid throughout the study period (01/10/2012 to 31/03/2013). Purchase and sales orders for the underlying asset and it’s options were considered in order to reach the actual book of all instruments every five minutes. The strategy was applied when distortions between the Implied Volatility, calculated by the Black & Scholes model, and the volatility calculated by exponential smoothing (EWMA - Exponentially Weighted Moving Average) were detected. The results showed that the Petrobras options market is not efficient in it’s weak form, since in 371 transactions during this period, 85% of them were profitable, with an average result of 0,49% and the average duration of each operation being slightly smaller than an hour and thirteen minutes.

In post-financial crisis times, new legislation in combination with banks’ changed risk aversion has to a great extent changed the proprietary trading to client driven trading, i.e. market making or client facilitation. This type of trading complicates the risk-return dynamics, as the goal is often to minimize risk and achieve profitable commission revenues. This thesis aims to disclose the risk-return tradeoff in a client driven trading environment. This is done by investigating the conditional relation between risk and realized return. As opposed from many studies which proxy the risk with beta or variance, I use a delta-gamma Value at Risk model as the risk proxy, which I also backtest. For the return proxy, I use three different measures; P&L, commission revenues and the sum of these two. A positive tradeoff exists if (i) the return is equally negatively dependent on the risk if the ex post return is negative, as it is positively dependent on the risk if the ex post return is positive and (ii) the average return is significantly positive. For three different client driven trading portfolios tested, I found a positive risk-return tradeoff in one portfolio, between the P&L plus commission revenues and the Value at Risk. However, since a symmetrical conditional relationship between risk and P&L plus commission revenues was found in all portfolios, and the average return was positive, the positive tradeoff would have existed if the average return would have been significantly positive. On the other hand, one could argue that the tradeoff exists, but is not significant. No relation between risk and commission revenues was found. A probable cause to this is the hedging strategies, which would be an interesting topic for further research. / I tiden efter finanskrisen har nya regelverk i kombination med bankers förändrade riskaptit till stor del förändrat den proprietära handeln till klientdriven handel, i.e. ”market making” eller förenklad handel för kund. Denna typ av handel komplicerar dynamiken mellan risk och avkastning, då målet ofta är att minimera risk och nå lönsamma kommissionsintäkter. Denna uppsats ämnar påvisa förhållandet mellan risk och avkastning i en klientdriven handelsmiljö. Detta görs genom att undersöka den betingade relationen mellan risk och realiserad avkastning. Till skillnad från andra studier som använder beta eller varians som riskmått, använder jag en delta-gamma Value at Risk-modell som jag också backtestar. Som avkastningsmått, använder jag tre olika mått; P&L, kommissionsintäkter samt summan av dessa två. En positiv belöning för att bära risk existerar om (i) avkastningen är lika negativt beroende av risken om den realiserade avkastningen är negativ, som den är positivt beroende av risken om den realiserade avkastningen är positiv och (ii) medelvärdet på avkastningen är signifikant positiv. För tre olika klientdrivna portföljer som testats, hittades en positiv belöning för att bära risk endast i en portfölj, mellan P&L plus kommissionsintäkter och Value at Risk. Emellertid, eftersom en symmetrisk systematisk betingad relation mellan risk och P&L plus kommissionsintäkter hittades i alla portföljer, och medelavkastningen var positiv, skulle den positiva belöningen ha funnits om medelavkastningen varit signifikant positiv. Å andra sidan skulle jag kunna hävda att den positiva belöningen finns, men inte är signifikant. Ingen relation mellan risk och kommissionsintäkter hittades. En trolig orsak till detta är hedgnings-strategierna, vilket vore ett intressant ämne för fortsatt forskning.