A teoria sobre o custo de capital das empresas estudada desde a década de 1950 trouxe amplas contribuições aos estudos de finanças corporativas, alocação de carteiras de investimento, fusões e aquisições, ciências contábeis, entre outras aplicações. Os modelos clássicos de custo de capital compreendem modelos como o CAPM (Capital Asset Pricing Model), de Sharpe, Lintner e Mossin; o APT (Arbitrage Pricing Theory), de Ross; o modelo de 3-fatores, de Fama e French, e de 4-fatores, de Carhart, entre outros. Em virtude das diversas críticas feitas aos modelos clássicos (ELTON, 1999; FAMA; FRENCH, 2004; GRINBLATT; TITMAN, 2005; ASHTON; WANG, 2012; HOU et al., 2012), há então espaço para o surgimento de uma metodologia alternativa para estimativa do custo de capital das empresas, contexto em que surgem os modelos de Custo de Capital Implícito (ICC - Implied Cost of Capital). São cinco os principais modelos de ICC estudados e testados na literatura: Gordon e Gordon, modelo FHERM (1997), Claus e Thomas, modelo CT (2001), Gebhardt, Lee e Swaminathan, modelo GLS (2001), Ohlson e Juettner-Nauroth, modelo OJ (2005) e Easton, modelo de EASTON (2004). Todos se baseiam em expectativas sobre resultados futuros projetados, e as pesquisas que os aplicam fundamentam-se majoritariamente em projeções de analistas. Há, no entanto, diversos problemas levantados pela literatura quanto ao uso de dados produzidos por analistas (GUAY et al., 2011; HOU et al., 2012; KARAMANOU, 2012). Hou et al. (2012) propõem então uma metodologia cross-sectional de projeções de resultados das empresas, com base em dados contábeis, alternativa às projeções dos analistas e aplicável aos modelos de ICC, a qual se mostrou eficiente para os testes desenvolvidos. O objetivo desta tese foi verificar se a metodologia de projeção de lucros proposta por Hou et al. (2012), com as devidas considerações e ajustes, é válida para aplicação no mercado brasileiro e, em caso positivo, verificar qual a magnitude do Custo de Capital Implícito esperado pelos investidores para aplicação de recursos no Brasil, através da aplicação dos cinco principais modelos de ICC. Analisou-se também se os modelos de ICC podem ser considerados eficientes como ferramenta para prever os ativos que terão maiores ou menores retornos futuros e, por fim, verificou-se como o prêmio pelo risco implícito se compara com o prêmio pelo risco do CAPM, e qual das duas abordagens é mais eficiente como ferramenta de precificação de ativos. Para tanto, foi analisada uma janela de dados de 1994 a 2014. As principais conclusões obtidas foram: (i) o modelo de Hou et al. (2012) ajustado tem desempenho muito positivo para fins de projeção de lucros no Brasil, com capacidade de prever 69,8% dos lucros futuros; (ii) o prêmio pelo risco implícito apurado para o Brasil para o período de 1994 a 2014 é da magnitude de 7,5% a.a., em linha com a literatura internacional e nacional; (iii) identificou-se a importância de se efetuarem ajustes e controles inflacionários, em especial, para aplicar os modelos GLS e CT, sob risco de subestimar o ICC nesses modelos; (iv) verificou-se que o único modelo, entre os testados, contraindicado para aplicação no Brasil é o FHERM, cujas simplificações teóricas e de premissas levam a resultados muito voláteis e pouco capazes de prever os retornos futuros das ações; e (v) na análise comparativa entre os modelos de ICC e os modelos clássicos de custo de capital, concluiu-se que as metodologias de ICC testadas são eficientes como ferramenta para previsão da performance futura dos ativos, diferentemente do CAPM tradicional que apresentou resultados inferiores e não conclusivos para tais fins. Por fim, salienta-se a potencial contribuição dos modelos de ICC para análises relacionadas às finanças comportamentais e prêmios de liquidez. / The theory on companies\' cost of capital has been studied since the 1960s, bringing forward extensive contributions to the study of corporate finance, allocation of investment portfolios, mergers and acquisitions, accounting, among other several applications. The classical models of cost of capital include, for example, the CAPM (Capital Asset Pricing Model) of Shrape, Lintnet and Mossin, the APT (Arbitrage Pricing Theory) of Ross, the 3-factor model of Fama and French and the 4-factor model of Carhart. Due to the several criticisms directed at the classical models and its limitations (ELTON, 1999; FAMA; FRENCH, 2004; GRINBLATT; TITMAN, 2005; ASHTON; WANG, 2012; HOU et al., 2012), this context made room for the emergence of an alternative methodology for estimating the firms\' cost of capital, represented by the Implied Cost of Capital models (ICC). There are five main models of ICC studied and tested in the literature: Gordon and Gordon, FHERM Model (1997), Claus and Thomas, CT Model (2001), Gebhardt Lee and Swaminathan, GLS Model (2001), Ohlson and Juettner-Nauroth, OJ Model (2005) and Easton, EASTON Model (2004). All such models are based on expectations about projected future earnings, and studies that apply these methods are predominantly based on analysts\' estimates. There are, however, several problems raised by the literature regarding the use of analysts projections (GUAY et al., 2011; HOU et al., 2012; KARAMANOU, 2012). Hou et al. (2012) then proposed a cross-sectional approach to estimate the firms\' future earnings, as an alternative methodology to apply in the ICC models, which was proved very efficient. Given this context, the objective of this thesis is to verify whether the cross-sectional methodology proposed by Hou et al. (2012) to estimate future earnings, with due adjustments to the local market\'s characteristics, is valid for application in Brazil. If so, we should then verify what the magnitude of the ICC expected by investors in Brazil is, estimated using the five main ICC models. Also, this thesis should analyse if the ICC models can be considered efficient as a tool to predict which assets should have larger or smaller future returns. Finally, we should compare the risk premium estimated by the ICC models and risk premium estimated by the CAPM, and identify which of the two approaches is more efficient for asset pricing. In order to achieve such goals, a window of data from 1994 to 2014 was analysed. The main results achieved were: (i) the adjusted model of Hou et al. (2012) has shown very positive performance for projecting earnings in Brasil, with power to predict 69,8% of future earnings; (ii) the implicit risk premium for the Brazilian market from 1994 to 2014 is of 7,5% per year, which corroborates the national and international literature; (iii) it was identified the need of controlling for inflation effects, specially when implementing the GLS and CT models, at risk of underestimating the ICC if not taking the due precautions; (iv) the only model, among the tested, which was identified as unfit for applying to the Brazilian market was FHERM, since its theorical simplifications lead to too volatile results, which are poorly capable of predicting future returns; and (v) when comparing the ICC to the classical models, it was concluded that the ICC methodologies are efficient as a tool to infer future asstes\' performance, while the traditional CAPM presents poor and unconclusuve results for such purpose. At last, we stress the potencial contribution of the ICC models to the study of behavioral finance and liquidity premiums.

Este trabalho apresenta uma metodologia de cálculo de sensibilidades utilizando equa- ções analíticas, levando em a conta a correção de smile na superfície de volatilidade, que não é contemplada no modelo de Black e Scholes. Dada a diferença signicativa na mensura ção do risco as instituições nanceiras calculam suas sensibilidades incorporando esta correção, mas tal determinação tem sido realizada por métodos numéricos, que acabam sendo mais lentos que a abordagem aqui proposta. São apresentadas equações analíticas para as principais sensibilidades do modelo a partir de dados de mercado usados na constução da superfície de volatilidade implícita. Ilustramos a comparação da técnica proposta com o método numérico com base no mercado de opções sobre taxa de câmbio Brasileiro. / This work presents a study on how we should adapted the Greeks or risk factors of the Black and Scholes model. We can derive analytical equations for the main sensitivities of the model and using the market data to build an implied volatility surface and to get additional terms for the risk factors. We propose to implement this model in a scheme of analytic differential equations derived from the pricing model and from the implied volatility function. The building of this implied volatility and risk factors was based on the foreign exchange Brazilian market.

Many past literatures have examined the predictive power of implied volatility versus that of historical volatility, but they have showed divergent conclusions. One of the major differences among these studies is the methods that they used to obtain implied volatility. The VIX index, introduced in 1993, provides a model-free and directly observable source of implied volatility data. The VIX futures is an actively traded VIX derivative product, and its prices are believed to contain market’s expectation about future volatility. By analyzing the relationship between the VIX futures prices and the realized volatilities of the 30-day period that these VIX futures contracts cover, this paper finds that the VIX futures contracts with shorter maturities have predictive power on future realized volatility, but they are upwardly biased estimates. The predictive power, however, decreases as the time to maturity increases. The outstanding VIX futures contracts with the nearest expiration dates outperform GARCH estimates based on historical return data at predicting future realized volatility.

To understand and model the dynamics of the implied volatility smile is essential for trading, pricing and risk management portfolio. We suggest a  linear Kalman filter for updating of the Stochastic Volatility Inspired (SVI) model of the volatility. From a risk management perspective we generate the 1-day ahead forecast of profit and loss (P\&L) of option portfolios. We compare the estimation of the implied volatility using the SVI model with the cubic polynomial model. We find that the SVI Kalman filter has outperformed the  others.

This study develops a multi-period log-return quantile forecasting procedure to evaluate the performance of eleven nearby commodity futures contracts (NCFC) using a sample of 897 daily price observations and at-the-money (ATM) put and call implied volatilities of the corresponding prices for the period from 1/16/2008 to 7/29/2011. The statistical approach employs dynamic log-returns quantile regression models to forecast price densities using implied volatilities (IVs) and factors estimated through principal component analysis (PCA) from the IVs, pooled IVs and lagged returns. Extensive in-sample and out-of-sample analyses are conducted, including assessment of excess trading returns, and evaluations of several combinations of quantiles, model specifications, and NCFC's. The results suggest that the IV-PCA-factors, particularly pooled return-IV-PCA-factors, improve quantile forecasting power relative to models using only individual IV information. The ratio of the put-IV to the call-IV is also found to improve quantile forecasting performance of log returns. Improvements in quantile forecasting performance are found to be better in the tails of the distribution than in the center. Trading performance based on quantile forecasts from the models above generated significant excess returns. Finally, the fact that the single IV forecasts were outperformed by their quantile regression (QR) counterparts suggests that the conditional distribution of the log-returns is not normal.

The purpose of this paper is threefold. First, the paper builds on the work done previously done in the area of option implied probability distribution functions (PDFs) by extending the methods described by Breeden and Litzenberger (1978) to individual equity options. Second, it describes a closed-form, onto mapping from a two-dimensional volatility surface to the risk-neutral PDF. Lastly the paper performs an event study on the implied risk-neutral PDFs of companies which are the target of corporate takeover. While there was not sufficient data to determine any statistical relationship, there is observational evidence that option market implied PDFs may be predictive of future takeovers.

Due to the sharpen regulation of the Swedish plain vanilla warrant in 2006 and the recent increase in trade among private investors, this thesis examined the informa-tion efficiency of Swedish plain vanilla warrants. This was done in three different ways. First the theoretical Black & Scholes (B&S) price was tested against the ac-tual market price. Secondly likelihood ratio test statistics was used to see whether information regarding past returns added any information to that already captured by the implied volatility (IV) generated from observed warrant market prices via the B&S model. The third method used was a comparison of the IV´s among com-parable warrants. As the regulation of the Swedish plain vanilla warrant market states that only certified issuer are allowed short calls and puts, the self adjusting price mechanism found in the option market doesn’t exist on this market. As a con-sequence of this, investors on this market is reliant of accurate ask and bid prices from the issuers. Further, the information efficiency of a capital market is of es-sence for capital allocation, price discovery and risk management. The results from all three tests rejected the information efficiency hypothesis of the sample. Thus concluding that the included warrants in this thesis are none ideally for activities such as capital allocation, price discovery and risk management.

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This article examines the hedging positions derived from the Black-Scholes(B-S) model and the GARCH(1,1) models, respectively, when the log returns of underlying asset exhibits GARCH(1,1) process. The result shows that Black-Scholes and GARCH options deltas, one of the hedging parameters, are similar for near-the-money options, and Black-Scholes options delta is higher then GARCH delta in absolute terms when the options are deep out-of-money, and Black-Scholes options delta is lower then GARCH delta in absolute terms when the options are deep in-the-money. Simulation study of hedging procedure of GARCH(1,1) and B-S models are performed, which also support the above findings.

依據中華民國證券櫃檯買賣中心公佈之新金融商品業務概況，我們可以看出債券選擇權雖然到2004年7月才核准開放，但是從年度成交金額，債券選擇權均居所有債券與利率衍生性商品之冠。由於債券選擇權市場仍處於開放初期，相關資料如債券選擇權隱含波動率取得不易，因此關於台灣債券選擇權市場並未如指數選擇權市場吸引很多學術與實務界之注目。 本研究嘗試對於台灣債券選擇權市場，從評價模型、市場實務概況描述及未來可能之發展，作進一步之研究；此外，本文亦參酌Goodman and Ho（1997）所進行之美國債券選擇權損益之實證研究，來探討賣出債券「買進選擇權」之一方，是否能同樣在台灣債券選擇權市場獲得相對等之報酬。 本實證分析方法基本上是假設，「債券買權」賣方賣出履約殖利率為一個基本點價外之「債券買權」，選擇權存續期間是以兩個星期為一個循環，以中華民國證券櫃檯買賣中心公佈之每日10年期指標公債加權平均殖利率作為相對應部位調整之依據，分別代入實際波動率與期初「債券買權」之隱含波動率，進行Delta Neutral避險，且假設債券拆借與資金融通利率為中華民國證券櫃檯買賣中心公佈之等殖成交行情表（附條件）中所揭露之附條件利率，來探討賣方是否能夠賺取一定合理之報酬率及其可能面對之風險。 從2005年4月至2005年11月底之實證期間，共計13個循環週期，我們發現下列幾個現象： ◆債券買權與賣權之隱含波動率普遍高於實際波動率，賣權隱含波動率又高於買權。 ◆以賣出債券買權為例，在不考慮交易成本下，賣出買權之一方均能獲利，但損益之變異性都相當大。 ◆在避險波動率參數之使用上，代入實際波動率，不論是從損益之絕對數值或每單位風險報酬，均優於代入期初買權隱含波動率。 ◆從等殖成交行情表（附條件）中所揭露之附條件利率，即債券融資與融券利率，其波動性遠大於債券殖利率，因此在進行債券選擇權交易時必需將此列入評價之重要考量因素。 ◆如果考慮權利金收入，由於目前稅法無法與避險損失互抵，必需被課徵25%營利事業所得稅，因此選擇權賣方均無法獲利。 / According to the fact reports of OTC derivatives released by GraTai Securities Market (GTSM) in 2005, trading value of bond option was top of all interest rate derivatives and bond derivatives, though it was opened lately in July 2004. Due to the difficulty to get the market information like implied volatility of options, we haven’t seen considerable studies on Taiwan bond option market. Owing to the writer of this paper serves in this field, we can take advantage of collecting these data from Interdealer brokers and dealers. Accordingly, we have ground to develop this research. In this paper, we begin our discussion by presenting the landscape of Taiwan bond option market and then turn to review the basic models. Lastly, we reference the empirical study of US OTC Treasury option done by Goodman and Ho (1997) to construct the framework for measuring how investors are fairly compensated by selling call in Taiwan bond option market. To evaluate the profit and risk of option writing, we assume writer can sell two-week call options on ten-year Treasury note at market implied volatility, with a strike yield at one basis point out of daily closing yield. Option writer uses daily closing yields to do the delta neutral hedge. Besides, we take overnight call loan rates of Electronic Bond Trading System in GTSM as the borrowing and lending rates of government bond. Over the empirical period of 2005.04.1-2005.11.30, several circumstances can be found from this study. 1.In average, the implied volatilities are higher than actual volatility. This is in agreement with the results of Goodman and Ho (1997). Besides, implied volatility of put option is generally higher than call option. 2.Without considering transaction cost, call option writer can have vulnerable profit from selling volatility. 3.Adoption of actual volatility can bring better absolute profit and risk-adjusted return than implied volatility in the option valuation. 4.In this article, it shows a striking effect of the borrowing and lending rates of government bonds on the movement of implied volatility spread between call and put. 5.Under current Act of Income Tax, the hedging loss of option writer cannot be offset by premium income. Therefore, call writer can not make profit after tax.