The double-mean-reverting model by Gatheral is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. Using the method by Pagliarani and Pascucci, we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

This thesis aims to back-test the ability of implied volatility carry trade strategies to outperform the carry trade strategies in the FX markets. Recent research has shown that the profitability of the strategies is partly attributable to the market mispricings of the forward volatility agreements and a tendency of the forward implied volatility to overestimate the future spot implied volatility. This thesis uses a similar approach to construct portfolios containing 10 developed as well as 9 emerging market currencies. Our approach is based on the assumption that Uncovered Interest rate Parity (UIP), Forward Unbiasedness Hypothesis (FUH) and Forward Volatility Unbiasedness Hypothesis (FVUH) do not hold and therefore providing investors with several opportunities to construct trading strategies taking advantage of these market mispricings. In this thesis, we show that the foreign exchange carry trade strategy composed of the specific developed and emerging country's currencies can be outperformed by portfolio consisting of the implied volatility carry trade strategies in the FX market over the analysed period. The portfolios are adjusted to the riskiness which is accounted for by the VIX and VXY-G7 index for developed and VIX and VXY-EM index for emerging economies. The strong performance of the strategies outlined in this thesis can be of significant value to FX traders and portfolio managers.

Problem: Investors are dependent on the issuers’ valuation of covered warrants because the issuers also act as market makers. Hence it is crucial that the issuers value each of the five variables used in the Black & Scholes pricing formula in the same way at both the buying and selling occasion. For a covered warrant investor the most important is-sue is the volatility and how it changes over time. This thesis will therefore search for differences in changes of implied volatility between the different issuers. Purpose: The purpose of this thesis is to analyze differences and similarities between the issuers’ changes of their covered warrants implied volatility. Method: The authors have calculated the implied volatility for a sample of warrants with H&M and Ericsson as underlying assets. Black & Scholes formula has been used and this part of the thesis is made with a quantitative approach. After the implied volatility had been calculated correlation tests to the mean as well as to the stock were made. When analyzing the results the authors, in addition to the calculation, used a qualitative method by interviewing market makers. This was made in order to find better explanations to the results. Conclusions: The differences in changes of implied volatility found between different warrants were small. In general, one warrant changed in the same way as the other ones from one day to another. These results reject the rumors that single issuers adjust their implied volatility in order to make more money. When single events in form of reports were analyzed, the authors found that the issuers changed their volatility in the same way to adjust for the changed uncertainty about the stocks future price. Further, these events clarifies that the basic dynamics of implied volatility is followed by the market. The analysis of how the implied volatility changes with respect to the stock price movements indicates a negative correlation. This implies that an increase in the stock price will lower the implied volatility and vice verse.

Little research has been done into implied correlations, and the small literature grows even smaller when referring to currency options. The existing literature has established that implied correlation is a good if not the best forecaster of future realized correlation, and that this ability to forecast is not necessarily universal. This paper will establish that the forecasting ability of implied correlations in currency options varies across currency pairs, thus proving that not all implied correlations are created equal. Using two different proxies for the quality of the forecaster, the paper attempts to explain which characteristics of an option on a currency pair affect the variation in forecasting ability.

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The study use preparing the 2011¡¦s pro forma financial statements of China Construction Bank (CCB) at first, and use market stock price as given result, conjecture the Non-Performance Loan ratio of the market investors. And then, using implied Non-Performance Loan ratio, adjust the original financial statements, prepare the 2012¡¦s pro forma financial statements of CCB. In the end, using Copeland, Koller, and Murrin¡]2000¡^¡¦s equity DCF method and Preinreivh¡BEdwards and Bell¡BOhlson¡¦s EBO method to estimate the intrinsic value of the common stock for the China Construction Bank. Based on my analysis, it is suggested that, after preparing the pro forma financial statements by carefully considering economic environment¡Blaws and regulations¡Bindustrial structure and lending proportion¡Bmarket position, and future strategies of the specific bank, use two valuation model by considering implied Non-Performance Loan ratio. The intrinsic value of the common stock is higher than its market price, that is, the market price of the China Construction Bank is undervalued. Therefore, I hope the result of this business evaluation research, will help the investors making more rational decisions.

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This paper has two researches direction, one is in the pricing and application of a probation option, the other is in the pricing and application of an American option. In the research of a probation option, this paper used the concept of the marketing strategy to be the source of financial innovation, and therefore decision a new exotic option. We call this option is a probation option. We introduce the application of this option, and further more to device the value of this option. Beside, this option also can apply to the field of marketing, and to calculate the cost of marketing strategy. In the research of an American, this paper proposes a new method- the implied belief model, to obtain a closed-form solution of the value of the American option. We analyze the value of the American option through the view point of the sellers of the options. By adopting this method, we derive the upper bound for the value of an American option. Then we define the belief value of seller to obtain a closed-form solution of the value of an American option. Finally, we apply the method to S&P 100 American option and deduce the implied belief value.

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<p>Problem: Investors are dependent on the issuers’ valuation of covered warrants because the issuers also act as market makers. Hence it is crucial that the issuers value each of the five variables used in the Black & Scholes pricing formula in the same way at both the buying and selling occasion. For a covered warrant investor the most important is-sue is the volatility and how it changes over time. This thesis will therefore search for differences in changes of implied volatility between the different issuers.</p><p>Purpose: The purpose of this thesis is to analyze differences and similarities between the issuers’ changes of their covered warrants implied volatility.</p><p>Method: The authors have calculated the implied volatility for a sample of warrants with H&M and Ericsson as underlying assets. Black & Scholes formula has been used and this part of the thesis is made with a quantitative approach. After the implied volatility had been calculated correlation tests to the mean as well as to the stock were made. When analyzing the results the authors, in addition to the calculation, used a qualitative method by interviewing market makers. This was made in order to find better explanations to the results.</p><p>Conclusions: The differences in changes of implied volatility found between different warrants were small. In general, one warrant changed in the same way as the other ones from one day to another. These results reject the rumors that single issuers adjust their implied volatility in order to make more money. When single events in form of reports were analyzed, the authors found that the issuers changed their volatility in the same way to adjust for the changed uncertainty about the stocks future price. Further, these events clarifies that the basic dynamics of implied volatility is followed by the market. The analysis of how the implied volatility changes with respect to the stock price movements indicates a negative correlation. This implies that an increase in the stock price will lower the implied volatility and vice verse.</p>