There is a big interest for alternative investment strategies than investing in traditional asset classes. Commodities are having a boom dynamic with increasing prices. This thesis is therefore based on applying Modern Portfolio Theory concept to this alternative asset class. In this paper we manage to create optimal portfolios of commodities for investors with known and unknown risk preferences. When comparing expected returns to actual returns we found that for the investor with the known risk preference almost replicated the return of the markets. The other investor with unknown risk preference also profited but not as efficient as the market portfolio.

Asian options are an important family of derivative contracts with a wide variety of applications in commodity, currency, energy, interest rate, equity and insurance markets. In this master's thesis, we investigate methods for evaluating the price of the Asian call options with a fixed strike. One of them is the Monte Carlo method. The accurancy of this method can be observed through variance of the price. We will see that the variance with using Monte Carlo method has to be decreased. The Variance Reduction technique is useful for this aim. We will give evidence of the efficiency of one of the Variance Reduction thechniques - Control Variate method - in a mathematical context and a numerical comparison with the ordinary Monte Carlo method.

In this thesis, I study the variance risk premium in Gold VIX market. Using synthetically created variance swaps, I quantify the variance risk premium to be average -0.068 in absolute terms and -0.358 in log return terms, meaning that purchasing volatility in Gold VIX is generally unprofitable. Although the average negative risk premium is not statistically significant, the mean log return of risk premium is robust with Newey-West test. Furthermore, I attempt to test whether risk premium vary with time or the level of the swap rate, but obtain unclear results.

Volunteer canola (<i>Brassica napus</i> L.) has become an abundant weed in western Canadian cropping systems. Modern canola cultivars are strong competitors and produce large seed yields, however seed shattering during harvest creates large volunteer seedbanks. The segregation of hybrid trait and changes in variability of traits may allow successive generations of volunteer <i>B. napus</i> weeds to display different levels of fitness and other traits. Three cultivars: 2 hybrid, and 1 open-pollinated at three consecutive generations: G1, the initial crop; G2, first generation of volunteers; and G3 the second generation of volunteers, were used to evaluate the competitive ability, fitness and population dynamics of volunteer canola when grown as a weed in wheat (<i>Triticum aestivum</i> L.). Traits including seed, biomass, and pod production, plant height, seed weight, dormancy, and competitive ability were measured. In all traits but height and seed weight, hybrid breakdown occurred, as the hybrid G1displayed greater mean values than the G2 generation. Hybrids commonly showed the highest mean values of various traits in the G1, lowest mean values in the G2. Hybrid G3 populations produced mean values not different from the G1 or G2 generations for many traits. The open-pollinated cultivar displayed mean values for all traits which did not vary across generations. Generational differences in <i>B. napus</i> seedlings resulted in differences in wheat yield losses. <i>B. napus</i> densities at maturity provided a more robust model of wheat yield loss, as there were differences in wheat yield losses due to the interaction of generation and cultivar of <i>B. napus</i>. Commercial seed generations were the most competitive and fit plants, while volunteer generations were less competitive, and not as fit.

This thesis uses synthetically created variance swaps on VIX futures to quantify the variance risk premium in VIX options. The results of this methodology suggest that the average premium is -3.26%, meaning that the realized variance on VIX futures is on average less than the variance implied by the swap rate. This premium does not vary with time or the level of the swap rate as much as premiums in other asset classes. A negative risk premium should mean that VIX option strategies that are net credit should be profitable. This thesis tests two simple net credit strategies with puts and calls, and finds that the call strategy is profitable while the put strategy is not.

Volunteer canola (<i>Brassica napus</i> L.) has become an abundant weed in western Canadian cropping systems. Modern canola cultivars are strong competitors and produce large seed yields, however seed shattering during harvest creates large volunteer seedbanks. The segregation of hybrid trait and changes in variability of traits may allow successive generations of volunteer <i>B. napus</i> weeds to display different levels of fitness and other traits. Three cultivars: 2 hybrid, and 1 open-pollinated at three consecutive generations: G1, the initial crop; G2, first generation of volunteers; and G3 the second generation of volunteers, were used to evaluate the competitive ability, fitness and population dynamics of volunteer canola when grown as a weed in wheat (<i>Triticum aestivum</i> L.). Traits including seed, biomass, and pod production, plant height, seed weight, dormancy, and competitive ability were measured. In all traits but height and seed weight, hybrid breakdown occurred, as the hybrid G1displayed greater mean values than the G2 generation. Hybrids commonly showed the highest mean values of various traits in the G1, lowest mean values in the G2. Hybrid G3 populations produced mean values not different from the G1 or G2 generations for many traits. The open-pollinated cultivar displayed mean values for all traits which did not vary across generations. Generational differences in <i>B. napus</i> seedlings resulted in differences in wheat yield losses. <i>B. napus</i> densities at maturity provided a more robust model of wheat yield loss, as there were differences in wheat yield losses due to the interaction of generation and cultivar of <i>B. napus</i>. Commercial seed generations were the most competitive and fit plants, while volunteer generations were less competitive, and not as fit.

A survey is conducted through an event study on the Stockholm Stock Exchange based on 119 historical stocks splits with a split factor of at least two, for the years between 1997 and 2012. This study has tested if there is an increase in return variance and systematic risk followed by a stock split. This is a quantitative study with the deductive approach and the positivistic epistemological standpoint. By matching 8925 squared daily returns for 75 days of pre- and post- split data, the sample of stock splits showed an increased return variance 0.515 of the matched squared daily returns, this number is significant at the 1% level in our binomial z-statistics. If the returns are compared on a 15 week interval instead of 75 days, the change in variance disappears; this confirms Dubofsky (1991) findings. When 52 weeks of pre- and post- split data is used, there is an increased variance in a proportion if 0.55 of the 6186 matched observations, this proportion is far greater than our daily sample and tells us that there is a long term effect on the return variance. The systematic risk measured as beta derived from the CAPM, did not show any increase in any of the three different time periods (75days, 16weeks and 52 weeks); the results confirms Wiggins (1992) findings; beta changes are just illusory.  The results suggest that there is an average increase in returns variance in the short and long term after a stock split, that confirms some existing studies by Ohlson and Penman (1985) and Dubofsky (1991). The increase in returns variance can be viewed as the management’s success of signaling the market, enhancing liquidity and reducing information asymmetry without any additional cost of capital. Our findings also contradict the theory of economic irrelevance of shares outstanding. This study is expanding Ohlson and Penman (1985) and Dubofsky (1991) studies, on a European stock market.

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Detecting both the majors genes that control the phenotypic mean and those controlling phenotypic variance has been raised in quantitative trait loci analysis. In order to mapping both kinds of genes, we applied the idea of the classic Haley-Knott regression to double generalized linear models. We performed both kinds of quantitative trait loci detection for a Red Jungle Fowl x White Leghorn F2 intercross using double generalized linear models. It is shown that double generalized linear model is a proper and efficient approach for localizing variance-controlling genes. We compared two models with or without fixed sex effect and prefer including the sex effect in order to reduce the residual variances. We found that different genes might take effect on the body weight at different time as the chicken grows.

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