由於隱含波動度具有前瞻性的特質，以往有許多學者探討隱含波動度與標的股價指數間的關聯性，但多利用線性模型。而本研究與其他文獻不同之處在於，本文利用馬可夫轉換模型分析隱含波動度VIX和VXN(VIX為S&P500指數的隱含波動度，而VXN為Nasdaq-100指數的隱含波動度)，馬可夫轉換模型為非線性模型，可捕捉不同區間轉換與不規則跳動，隱含波動度在特殊金融事件發生時會突然竄高，馬可夫轉換模型相對於一般線性模型更可捕捉此跳動，並將隱含波動度分為兩個區間。 　　經由多變量迴歸分析後，本研究也發現隱含波動度的變動以及技術指標的趨勢（偏離五天移動平均值）皆會影響標的股價指數的報酬，但隱含波動度變動對於股價指數報酬的影響高於技術指標，且不同區間存在不同現象。 / Implied volatility indices are forward-looking, and lots of researches discuss the relationship between the implied volatility and underlying stock market returns. Dif-ferent from other studies, we use Marcov switching model to examine the implied volatility indices: S&P 500 volatility index (VIX) and NASDAQ-100 volatility index (VXN), then we separately exploit the different regime behavior about the relationship between implied volatility change, technical indicators and stock market returns. As a result, S&P 500 index and NASDAQ-100 index respond in opposite direc-tions to positive and negative S&P 500 volatility index (VIX) and NASDAQ volatility index (VXN) changes, where technical indicators do not have that much influence on stock market returns. In addition, the impact of implied volatility change, technical indicators to stock market returns indeed depend on different regimes.

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

由選擇權價格反推求算出的隱含波動率，可表示市場對未來波動的預期，亦間接反映出該選擇權的價值高低，成為投資者在制定交易策略時重要的依據。經由實證研究發現，CBOE VXO及VIX都可反應投資人的恐慌心理，因此能作為標的走勢的逆向指標，所以又稱為「投資人恐慌指標」。而台指市場並沒有波動率的指標可供投資人參考，所以本研究的目的，是依照臺灣指數選擇權之市場特性，修改多種隱含波動率的估計方法。依照下列比較基準，找出適合台指市場的波動率指數。 1. 報酬反向指標： 分析波動率指數變動與市場報酬之間的關係，觀察「反向非對稱變動行為」，以Vega指數的表現最明顯。 2. 週期行為： 所有波動率指數，在日內行為的偏離幅度都很有限，且週內行為並沒有異常的週期性。分析到期日效果，只有ATM指數在到期日前二日及交易當日顯著下降，顯示台指報酬在到期日前並沒有大幅的異常波動。 3. 預測能力： 比較各波動指數的預測能力優劣。使用避免假性迴歸的模型、每分鐘報價來計算實際波動率，以VIX指數的解釋能力最佳。 綜觀以上分析結果，發現無法找出單一最佳的台指波動率指標。所以若需要最佳的「投資人恐慌指標」，必須使用Vega指數；若想做預測分析，則必須使用VIX指數。

Equity Risk Premium (ERP) is the cornerstone in Financial Economics. It is a basic requirement in stock valuation, evaluation of portfolio performance and asset allocation. For the last decades, several studies have attempted to investigate the relationship between macroeconomic drivers of ERP. In this work, I empirically investigate the macroeconomic determinants of UK ERP. For this I parsimoniously cover a large body of literature stemming from ERP puzzle. I motivate the empirical investigation based on three mutually exclusive theoretical lenses. The thesis is organised in the journal paper format. In the first paper I review the literature on ERP over the past twenty-eight years. In particular, the aim of the paper is three fold. First, to review the methods and techniques, proposed by the literature to estimate ERP. Second, to review the literature that attempts to resolve the ERP puzzle, first coined by Mehra and Prescott (1985), by exploring five different types of modifications to the standard utility framework. And third, to review the literature that investigates and develops relationship between ERP and various macroeconomic and market factors in domestic and international context. I find that ERP puzzle is still a puzzle, within the universe of standard power utility framework and Consumption Capital Asset Pricing Model, a conclusion which is in line with Kocherlakota (1996) and Mehra (2003). In the second paper, I investigate the impact of structural monetary policy shocks on ex-post ERP. More specifically, the aim of this paper is to investigate the whether the response of UK ERP is different to the structural monetary policy shocks, before and after the implementation of Quantitative Easing in the UK. I find that monetary policy shocks negatively affect the ERP at aggregate level. However, at the sectoral level, the magnitude of the response is heterogeneous. Further, monetary policy shocks have a significant negative (positive) impact on the ERP before (after) the implementation of Quantitative Easing (QE). The empirical evidence provided in the paper sheds light on the equity market’s asymmetric response to the Bank of England’s monetary policy before and after the monetary stimulus. In the third paper I examine the impact of aggregate and disaggregate consumption shocks on the ex-post ERP of various FTSE indices and the 25 Fama-French style value-weighted portfolios, constructed on the basis of size and book-to-market characteristics. I extract consumption shocks using Structural Vector Autoregression (SVAR) and investigate its time-series and cross-sectional implications for ERP in the UK. These structural consumption shocks represent deviation of agent’s actual consumption path from its theoretically expected path. Aggregate consumption shocks seem to explain significant time variation in the ERP. At disaggregated level, when the actual consumption is less than expected, the ERP rises. Durable and Semi-durable consumption shocks have a greater impact on the ERP than non-durable consumption shocks. In the fourth and final paper I investigate the impact of short and long term market implied volatility on the UK ERP. I also examine the pricing implications of innovations to short and long term implied market volatility in the cross-section of stocks returns. I find that both the short and the long term implied volatility have significant negative impact on the aggregate ERP, while at sectoral level the impact is heterogeneous. I find both short and long term volatility is priced negatively indicating that (i) investors care both short and long term market implied volatility (ii) investors are ready to pay for insurance against these risks.

Submitted by Alysson Oliveira Lima (alyssonlima@hotmail.com) on 2014-02-20T12:28:37Z No. of bitstreams: 1 DISSERTACAO FINAL - Alysson Oliveira Lima.pdf: 1422126 bytes, checksum: ea07829e7f2fef5ba62cea63d58dab7a (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2014-02-20T12:59:52Z (GMT) No. of bitstreams: 1 DISSERTACAO FINAL - Alysson Oliveira Lima.pdf: 1422126 bytes, checksum: ea07829e7f2fef5ba62cea63d58dab7a (MD5) / Made available in DSpace on 2014-02-20T13:03:40Z (GMT). No. of bitstreams: 1 DISSERTACAO FINAL - Alysson Oliveira Lima.pdf: 1422126 bytes, checksum: ea07829e7f2fef5ba62cea63d58dab7a (MD5) Previous issue date: 2014-01-28 / Desde a adoção do sistema de câmbio flutuante pelo Banco Central do Brasil, tanto a autoridade monetária quanto o governo brasileiro têm instituído medidas convencionais e não convencionais de intervenção no mercado de câmbio. Dentre essas medidas, salientam-se as compras e vendas de dólares no mercado de spot e derivativos, cujas finalidades precípuas seriam a tentativa de estabilizar os mercados em situação de 'stress' e suavizar uma determinada tendência de valorização ou desvalorização da moeda brasileira. O presente trabalho analisa os efeitos de referidas intervenções sobre a volatilidade na moeda brasileira. Utilizamos modelos econométricos da família ARCH (Autoregressive Conditional Heteroskedasticity) com o intuito de se averiguar o efeito sobre a volatilidade de curto e longo prazo, inclusive com metodologias semelhantes às empregadas em trabalhos direcionados a outras economias emergentes. Com o propósito de se estudar o efeito sinalizador das intervenções, foram utilizadas regressões simples com dados de volatilidade implícita e risk reversal do mercado de opções do dólar/real. Concluiu-se pela não relevância dos efeitos das intervenções sobre o nível da taxa de câmbio. No que concerne às volatilidades de curto e longo prazo, verificou-se que as vendas de dólares aumentam ambas as volatilidades, porém, quanto às compras, estas não apresentaram significância. No que se refere aos efeitos sinalizadores, via volatilidade implícita e risk reversal, estes também não expuseram relevância. Enfim, o que talvez possa consistir em fundamento para a não relevância dessas intervenções é o fato de o Brasil se consubstanciar em uma economia emergente e com menor credibilidade na condução de suas políticas monetárias. / Since Brazilian Central Bank adopted the floating exchange rate system, both the monetary authority and the Brazilian government have established conventional and unconventional measures to intervene in the foreign exchange market. Among these measures, it is important to emphasize the buying and selling dollars event in the spot and derivatives market, whose main purposes are to stabilize markets in distressful situations and to soften a particular trend of brazilian currency’s appreciation or depreciation. This paper exactly analyzes the effects of such interventions on the Brazilian currency volatility. We investigated the effect on the volatility of short and long terms, by means of ARCH (Autoregressive Conditional Heteroskedasticity) type models. To study the interventions signaling effect, we employed simple regressions with implied volatility and risk reversal of options market dollar/real. We are eligible that the effects of these interventions on the level of the exchange rate. Regarding the volatility of short and long term, selling dollars increases both volatilities, however, for the purchases, these did not show significant change. As for signaling effects, through implied volatility and risk reversal, effects are not relevant. We conjecture that the irrelevance of this interventions is due to the lack of credibility of the brazilian monetary policy

Submitted by Laércio Amaia (laercio_amaia@yahoo.com.br) on 2011-09-17T17:37:24Z No. of bitstreams: 1 Dissertação_LFAMAIA.pdf: 1940979 bytes, checksum: 7e6d776999403d28525c697eee220c1d (MD5) / Rejected by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br), reason: Prezado Laercio, Faltam as palavras-chave em português e inglês. Atenciosamente, Secretaria de Registro, Suzi on 2011-09-19T14:15:35Z (GMT) / Submitted by Laércio Amaia (laercio_amaia@yahoo.com.br) on 2011-09-19T14:52:47Z No. of bitstreams: 1 Dissertação_LFAMAIA.pdf: 1900930 bytes, checksum: d051a2aa7a9015bb784fe76affac8288 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2011-09-19T14:57:23Z (GMT) No. of bitstreams: 1 Dissertação_LFAMAIA.pdf: 1900930 bytes, checksum: d051a2aa7a9015bb784fe76affac8288 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2011-09-19T14:57:35Z (GMT) No. of bitstreams: 1 Dissertação_LFAMAIA.pdf: 1900930 bytes, checksum: d051a2aa7a9015bb784fe76affac8288 (MD5) / Made available in DSpace on 2011-09-19T15:00:30Z (GMT). No. of bitstreams: 1 Dissertação_LFAMAIA.pdf: 1900930 bytes, checksum: d051a2aa7a9015bb784fe76affac8288 (MD5) Previous issue date: 2011-08-19 / Muitos bancos e fundos de investimento mantêm opções de ações com pouca liquidez em suas carteiras que precisam ser apreçadas diariamente, e esta falta de liquidez gera dificuldades para o processo de apreçamento. A proposta deste trabalho para resolver este problema é utilizar um modelo derivado do CAPM para estimar a superfície de volatilidades implícitas destas opções sem liquidez através da superfície de volatilidades implícitas de opções do Índice BOVESPA, ou de outras opções com maior liquidez. O modelo testado é conhecido como modelo de um fator e é utilizado para o cálculo da variância, e conseqüentemente do risco, de uma ação, ou de uma carteira de ações. Porém, neste trabalho, testaremos a validade da aplicação deste modelo para a obtenção das volatilidades implícitas de opções ilíquidas, mas com liquidez nos ativos objeto, através dos betas obtidos pelo CAPM e de volatilidades implícitas de opções líquidas e com ativos objeto também líquidos. Para o teste, foram utilizadas séries históricas de volatilidades implícitas de opções de compra líquidas de algumas ações negociadas na BM&FBOVESPA no período de 2005 a 2010, e estas foram comparadas com as volatilidades implícitas obtidas através do modelo proposto. Com os resultados, pode-se observar que as volatilidades implícitas obtidas pelo modelo são boas estimativas para apreçarmos opções com deltas próximos de 50% e para vencimentos de até 2 meses. / Many banks and investment funds hold stock options with little liquidity in their portfolios that need to be priced daily, and this lack of liquidity creates difficulties for the pricing process. The aim of this work is to solve this problem by using a model derived from the CAPM to estimate the surface of implied volatilities of these options without liquidity obtained by the surface of implied volatilities of the BOVESPA index call options or other liquid stock options. The tested model is known as one-factor model and is used to calculate the variance, and consequently the risk of a single stock or a stock portfolio. However, in this work, we will test the validity of applying this model in order to obtain the implied volatilities of illiquid options, but whose underlying assets are liquid, through the betas obtained from the CAPM and implied volatilities of liquid options of liquid underlying assets. For the test, we used historical data of implied volatilities of call options, of some stocks traded at BM&FBOVESPA, in the period 2005 to 2010, and these were compared with the implied volatilities obtained using the proposed model. With the results, one can observe that the obtained implied volatilities are a good estimate for pricing stock options with deltas near to 50% and with maturity up to two months.

Submitted by Marcia Bacha (marcia.bacha@fgv.br) on 2012-03-07T12:45:08Z No. of bitstreams: 1 20120306084421880.pdf: 1716342 bytes, checksum: e7f9f7df4b67ff4e12f57770620942d8 (MD5) / Approved for entry into archive by Gisele Isaura Hannickel (gisele.hannickel@fgv.br) on 2012-03-07T12:50:42Z (GMT) No. of bitstreams: 1 20120306084421880.pdf: 1716342 bytes, checksum: e7f9f7df4b67ff4e12f57770620942d8 (MD5) / Made available in DSpace on 2012-03-07T12:51:26Z (GMT). No. of bitstreams: 1 20120306084421880.pdf: 1716342 bytes, checksum: e7f9f7df4b67ff4e12f57770620942d8 (MD5) / Com origem no setor imobiliário americano, a crise de crédito de 2008 gerou grandes perdas nos mercados ao redor do mundo. O mês de outubro do mesmo ano concentrou a maior parte da turbulência, apresentando também uma explosão na volatilidade. Em meados de 2006 e 2007, o VIX, um índice de volatilidade implícita das opções do S&P500, registrou uma elevação de patamar, sinalizando o possível desequilíbrio existente no mercado americano. Esta dissertação analisa se o consenso de que a volatilidade implícita é a melhor previsora da volatilidade futura permanece durante o período de crise. Os resultados indicam que o VIX perde poder explicativo ao se passar do período sem crise para o de crise, sendo ultrapassado pela volatilidade realizada. / Started in the U.S. housing sector, the credit crisis of 2008 caused great damage in markets around the world. The effects were concentrated in October of the same year, which also showed an explosion in volatility. In mid-2006 and mid-2007, the VIX, an index of implied volatility of options on the S&P500, recorded a rise in level signaling the possible imbalance in the U.S. market. This dissertation examines whether the consensus that implied volatility is the best predictor of future volatility remains during the crisis. The results indicate that the VIX loses explanatory power to move from a period of economic stability for a period of crisis, been surpassed by the realized volatility.

Magister Scientiae - MSc / The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant. / South Africa

Implied volatility obtained from market option prices is widely regarded as an efficient predictor of future realised volatility. Implied volatility can be thought of as market's expectation of future realised volatility. We distinguish between volatility-changing events with respect to expectations - scheduled events (such as information releases) and unscheduled events. We propose a method of testing the information content of option-implied risk-neutral moments prior to volatility-changing events. Using the method introduced by Bakshi, Kapadia & Madan (2003) we extract implied volatility, skewness and kurtosis from S&P 500 options market prices and apply the proposed method in four case studies. Two are concerned with scheduled events - United Kingdom European Union membership referendum, 2016 and United States presidential election, 2016, two are concerned with unscheduled events - flash crash of August 24, 2015 and flash crash of October 15, 2014. Implied volatility indicates a rise in future realised volatility prior to both scheduled events. We find a significant rise in implied kurtosis during the last three days prior to the presidential election of 2016. Prior to unscheduled events, we find no evidence of implied moments indicating a rise in future realised volatility.