隨著醫療技術進步、環境衛生改善與人類追求健康生活的趨勢，全世界人類的死亡率不斷地下降。在死亡率不斷的改善的情形下，保險公司可能在壽險商品上獲利，但在年金部份卻會因長壽風險而有所虧損。 自然避險則是保險公司可行的避險策略之一，即透過公司整體保單的組合，來達到規避死亡率風險和利率風險。此外，不同於之前的相關研究，我們所使用的資料，是由臺灣所有的保險公司提供的經驗死亡率，而不是國民生命表。目前保險公司在定價年金和壽險商品時，使用的死亡率是國民生命表，即假設買年金商品的被保險人和買壽險商品的被保險人的死亡率是相同的。但是從經驗死亡率的資料，我們發現購買年金商品的被保險人，其死亡率會低於買壽險商品的被保險人的死亡率。上述情形，會造成保險商品定價有誤;因此，我們考慮不同性別的年金、壽險的死亡率，並研究這些死亡率之間隨機變動項的相關性，以期在未來死亡率和利率變動下，可以藉由死亡率間的相關性，而抵消總價值變動的變異數和定價差異。 根據經驗資料，我們提出一個模型，可透過調整賣出年金和壽險的比例(年齡、性別)，使得保險公司能夠針對公司整體保單組合，找到並有效地運用的自然避險策略。文中最後進行模型敏感度分析，以及提出可能採用的保險商品配置策略，可作為目前保險公司進行死亡率和利率避險的參考。 / The mortality rate of human being has decreased year by year due to the improvement of medical and hygienic techniques. With the mortality improvement over time, life insurers may gain a profit and annuity insurers may suffer losses because of longevity risk. However, natural hedging is a feasible strategy to hedge mortality risk and interest risk at the same time. In this paper, we investigate the natural hedging strategy and try to find an optimal collocation of insurance products to deal with longevity risks for the insurance companies. Different from previous literatures, we use the experienced mortality rates from life insurance companies rather than population mortality rates. This experienced mortality data set includes more than 50,000,000 policies which are collected from the incidence data of the whole Taiwan life insurance companies. In general, insurance companies use population mortality rates to price life insurance and annuity products. Nevertheless, the mortality rate of annuity purchasers is averagely lower than that of life insurance purchasers. This situation leads to mispricing problem of both life insurance and annuity products. So in this paper, we can construct four mortality tables (gender, product) and investigate the correlation of these stochastic variation terms of four mortality rates. According to the correlation relation between these four mortality rates, we can offset the variance of portfolio’s change and difference of mispricing. On the basis of the experienced mortality rates, we demonstrate that the proposed model can lead to an optimal collocation of insurance products and effectively apply the natural hedging strategy to a more general portfolio for life insurance companies.

<p>Recently, both company executives as well as national media have claimed that short currency exchange rate fluctuations are negatively affecting the stock returns of certain firms. However, most previous studies focusing on companies in the US and Asia have been unable to find empirical support for a statistically significant linkage between firm value and exchange rate risk. By using a quantitative method with a deductive approach,the present research investigates if currency exchange rate movements impact the stock return of European based car companies with market interests in the US. By selecting French Renault and Peugeot, German Audi and BMW and Swedish Saab and Volvo, we were able to analyze three currencies exchange rates in our study: SEK/USD, SEK/Euro and Euro/USD. In addition, we included three macroeconomic factors: GDP, stock market index and Oil price to perform a multiple regression analysis. In consistency with the earlier studies, our results indicate that for five out of the six investigated companies, short movements in the three exchange rates do not significantly affect the stock returns of the companies investigated. By analyzing the annual report of the investigated companies, we found that derivatives instruments such as currency option, foreign exchange forwards, currency futures and currency swaps were used to hedge exchange risk. This might be one of the reasons why it was difficult to capture exchange rate risk. The fact that BMW was the only company showing a significant effect could indicate that the company is not applying the accurate hedging strategy. Another reason might be that the company is more exposed to exchange risk due to its large exporting activity compared to the other investigated companies.</p>

<p>Background: As a result of the financial markets ever ongoing product innovation a new derivative was introduced in the USA in 1997. A derivative that derived it's value, not from the price of an underlying asset, but instead from a climate factor. It's been known for a long time that revenue in certain industries are affected by weather conditions. The suppliers of weather derivatives claim that these weather sensitive businesses can user weather derivatives in order to lessen weather risk. </p><p>Purpose: To do a critical evaluation of how weather derivatives can be used by companies as a risk management tool. </p><p>Results & Realization: The usefulness of weather derivatives have been evaluated by studies of the effect on the revenue of constructed example businesses in different situations andby using different types of weather derivatives. A collection of problems related to weather derivatives have been collected from the existing theoretical framework on weather derivatives. This thesis offers an in dept description of how different types of weather derivatives function and how they can be used by business in order to reduce weather risk. We conclude that weather derivatives do perform a function as a risk management tool. Although it's important that the end is aware of the problems concerning weather derivatives in order to be able to manage weather risk in a proper fashion.</p>

<p>In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.</p>

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Background: As a result of the financial markets ever ongoing product innovation a new derivative was introduced in the USA in 1997. A derivative that derived it's value, not from the price of an underlying asset, but instead from a climate factor. It's been known for a long time that revenue in certain industries are affected by weather conditions. The suppliers of weather derivatives claim that these weather sensitive businesses can user weather derivatives in order to lessen weather risk. Purpose: To do a critical evaluation of how weather derivatives can be used by companies as a risk management tool. Results &amp; Realization: The usefulness of weather derivatives have been evaluated by studies of the effect on the revenue of constructed example businesses in different situations andby using different types of weather derivatives. A collection of problems related to weather derivatives have been collected from the existing theoretical framework on weather derivatives. This thesis offers an in dept description of how different types of weather derivatives function and how they can be used by business in order to reduce weather risk. We conclude that weather derivatives do perform a function as a risk management tool. Although it's important that the end is aware of the problems concerning weather derivatives in order to be able to manage weather risk in a proper fashion.

Introduction: Companies that are dependent on different commodities as input or output are exposed to price risk in these commodities. The price changes can be expressed as volatility and higher volatility results in higher risk. Hedging the commodity contracts with futures can offset this risk. One of the most important questions in this field is to what extent the risk exposure should be hedged with futures contract, i.e. the optimal hedge ratio. Purpose: The study aims to conduct an analysis of the variance in different commodities contracts and provide evidence of the optimal hedge ratio in the respective commodities. Method: We used a quantitative study with daily spot and futures price changes of Copper, Gold, Cotton and Oil. We investigated the 6-month hedging behaviour where timeseries were created for the period January-June each year during 2001-2004. We used a simple linear regression of the futures and spot price changes and a minimum variance model in order to calculate the optimal hedge ratio. Conclusion: Companies that are dependent on Copper, Gold, Cotton and Oil can significantly reduce the risk by engaging in futures contracts. The optimal hedge ratio for Copper is (96%), Gold (52%), Cotton (96%) and Oil (88%). By applying the optimal hedge ratio, a company may reduce their risk exposure up to 90% compared to an unhedged position.

Optimal stopping and mathematical finance are intimately connected since the value of an American option is given as the solution to an optimal stopping problem. Such a problem can be viewed as a game in which we are trying to maximize an expected reward. The solution involves finding the best possible strategy, or equivalently, an optimal stopping time for the game. Moreover, the reward corresponding to this optimal time should be determined. It is also of interest to know how the solution depends on the model parameters. For example, when pricing and hedging an American option, the volatility needs to be estimated and it is of great practical importance to know how the price and hedging portfolio are affected by a possible misspecification. The first paper of this thesis investigates the performance of the delta hedging strategy for a class of American options with non-convex payoffs. It turns out that an option writer who overestimates the volatility will obtain a superhedge for the option when using the misspecified hedging portfolio. In the second paper we consider the valuation of a so-called stock loan when the lender is allowed to issue a margin call. We show that the price of such an instrument is equivalent to that of an American down-and-out barrier option with a rebate. The value of this option is determined explicitly together with the optimal repayment strategy of the stock loan. The third paper considers the problem of how to optimally stop a Brownian bridge. A finite horizon optimal stopping problem like this can rarely be solved explicitly. However, one expects the value function and the optimal stopping boundary to satisfy a time-dependent free boundary problem. By assuming a special form of the boundary, we are able to transform this problem into one which does not depend on time and solving this we obtain candidates for the value function and the boundary. Using stochastic calculus we then verify that these indeed satisfy our original problem. In the fourth paper we consider an investor wanting to take advantage of a mispricing in the market by purchasing a bull spread, which is liquidated in case of a market downturn. We show that this can be formulated as an optimal stopping problem which we then, using similar techniques as in the third paper, solve explicitly. In the fifth and final paper we study convexity preservation of option prices in a model with jumps. This is done by finding a sufficient condition for the no-crossing property to hold in a jump-diffusion setting.

In this work we consider the methods of pricing and hedging an option on the forward commodity market described by the multi-factor diffusion model. In the previous research there were presented explicit valuation formulas for standard European type options and simulation schemes for other types of options. However, hedging strategies were not developed in the available literature. Extending known results this work gives analytical formulas for the price of American, Asian and general European options. Moreover, for all these options hedging strategies are presented. Using these results the dynamics of the portfolio composed of options on futures with different maturities is studied on a commodity market.

<p>In the first chapter of this dissertation I develop a flexible and estimable equilibrium model that jointly considers location decisions of heterogeneous agents across space, and their optimal portfolio decisions. Merging continuous-time asset pricing with urban economics models, I find a unique sorting equilibrium and derive equilibrium house and asset prices in closed-form. Risk premia for homes depend on both aggregate and local idiosyncratic risks, and equilibrium returns for stocks depend on their correlation with city specific income and house price risk. In equilibrium, very risk-averse households do not locate in risky cities although they may have a high productivity match with those cities. I estimate a version of this model using house price and wage data at the metropolitan area level and provide estimates for risk premia for different cities. The estimated risk premia imply that homes are on average about 20000 cheaper than they would be if owners were risk-neutral. This estimate is over 100000 for volatile coastal cities. I simulate the model to study the effects of financial innovation on equilibrium outcomes. For reasonable parameters, creating assets that correlate with city-specific risks increase house prices by about 20% and productivity by about 10%. The average willingness to pay for completing markets per homeowner is between $10000 and $20000. Productivity is increased due to a unique channel: lowering the amount of non-insurable risk decreases the households' incentive to sort on these risks, which leads to a more efficient allocation of human capital in the economy.</p><p>The second chapter of this dissertation studies ability signaling in a model of employer learning and statistical discrimination. In traditional signaling models, education provides a way for individuals to sort themselves by ability. Employers in turn use education to statistically discriminate, paying wages that reflect the average productivity of workers with the same given level of education. In this chapter, we provide evidence that graduating from college plays a much more direct role in revealing ability to the labor market. Using the NLSY79, our results suggest that ability is observed nearly perfectly for college graduates. In contrast, returns to AFQT for high school graduates are initially very close to zero and rise steeply with experience. As a result, from very beginning of the career, college graduates are paid in accordance with their own ability, while the wages of high school graduates are initially unrelated to their own ability. This view of ability revelation in the labor market has considerable power in explaining racial differences in wages, education, and the returns to ability. In particular, we find a 6-10 percent wage penalty for blacks (conditional on ability) in the high school market but a small positive black wage premium in the college labor market. These results are consistent with the notion that employers use race to statistically discriminate in the high school market but have no need to do so in the college market.</p> / Dissertation