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Based on comparative analysis, we first discuss different kinds of Greek letters in terms of Black–Scholes option pricing model, then we show how these Greek letters can be applied to perform hedging and risk management. The relationship between delta, theta, and gamma is also explored in detail.

This paper presents arbitrage and risk arbitrage betting strategies for Team Jai Alai. This game is the setting for the analysis and most results generalize to other sports betting situations and some financial market applications. The arbitrage conditions are utility free while the risk arbitrage wagers are constructed according to the Kelly criterion/capital growth theory that maximizes asymptotically long-run wealth almost surely.

I consider the Black–Scholes–Merton option-pricing model from several angles, including personal, technical and, most importantly, from the perspective of a paradigm-shifting mathematical formula.

Starting from humble beginnings, the use of financial options has substantially increased as an important financial tool for both speculation and hedging over the last 50 years. This chapter discusses both the theoretical and practical applications of financial options and related models. While the content is somewhat technical, we provide illustrations of their applications in simple settings. We address particular stylized features of option pricing models.

Based upon comparative analysis, we first discuss different kinds of Greek letters in terms of Black–Scholes option pricing model, then we show how these Greek letters can be applied to perform hedging and risk management. The relationship between delta, theta, and gamma is also explored in detail.

During the past couple of months, the pandemic situation raised the need for assessment of the impact on derivatives, particularly weather and freight derivatives, as an innovative financial product. There are several issues and challenges faced by weather and freight derivatives in the financial market. This chapter aims to appreciate innovative financial derivatives and also address issues relating to the functioning of weather and freight derivatives. We have also examined the pricing models of weather derivatives across the globe. In addition, we examine the impact of the COVID-19 pandemic situation on weather derivatives.

This research discusses the role of cryptocurrencies in portfolio investment and observes the timing within which the cryptos provide benefit to investors in a traditional financial market. We first use a mean-variance spanning test to check for any improvement that cryptos bring to a well-diversified portfolio and find a significant difference between port-folios with and without cryptos. Second, we analyze the weight dynamics of cryptos in the minimum-variance portfolio and the tangent portfolio to examine if cryptos present a hedging property in the mean-variance viewpoint. The finding shows that the optimal weights of cryptos increase distinctly in a market distress period, which shows their hedging property in a mean-variance view. Finally, we include cryptos in a well-diversified portfolio composed of common assets to check their weight dynamics in both tangent portfolio and minimum-variance portfolio. Consequently, we found that the cryptos take more weights in the tangent portfolio rather than in the minimum-variance portfolio, while the weights of cryptos increased in both portfolios during the COVID-19 pandemic; we thus conclude that cryptocurrencies can bring some hedging effect even in a portfolio with very common traditional assets. We also compare gold and cryptos and find that they have a similar pattern of weight dynamics, although gold has a slightly better effect in eliminating the downside risk of a minimum-variance portfolio.

The objective of this paper is to estimate the hedge ratios of foreign-listed single stock futures (SSFs) and to compare the performance of risk reduction of different methods. The OLS method and a bivariate GJR-GARCH model are employed to estimate constant optimal hedge ratios and the dynamic hedging ratios, respectively. Data of the SSFs listed on the London International Financial Future and Options Exchange (LIFFE) are used in this research. We find that the data series have high estimated constant optimal hedge ratios and high constant correlation in the bivariate GJR-GARCH model, except for three SSFs with their underlying stocks traded in Italy. Our findings provide evidence that distance is a critical factor when explaining investor's trading behavior. Results also show that in general, of the three methods examined (i.e., naïve hedge, conventional OLS method and dynamic hedging) the dynamic hedging performs the best and that naïve hedge is the worst.

The objective of this paper is to estimate the hedge ratios of foreign-listed single stock futures (SSFs) and to compare the performance of risk reduction of different methods. The OLS method and a bivariate GJR-GARCH model are employed to estimate constant optimal hedge ratios and the dynamic hedging ratios, respectively. Data of the SSFs listed on the London International Financial Future and Options Exchange (LIFFE) are used in this research. We find that the data series have high estimated constant optimal hedge ratios and high constant correlation in the bivariate GJR-GARCH model, except for three SSFs with their underlying stocks traded in Italy. Our findings provide evidence that distance is a critical factor when explaining investor's trading behavior. Results also show that in general, of the three methods examined (i.e., naïve hedge, conventional OLS method and dynamic hedging) the dynamic hedging performs the best and that naïve hedge is the worst.

In this work we consider the problem of the approximate hedging of a contingent claim in the minimum mean square deviation criterion. A theorem on martingale representation in case of discrete time and an application of the result for semi-continuous market model are also given.

No abstract received.

The paper analyzes alternative mathematical techniques, which can be used to derive hedging strategies for credit derivatives in models with totally unexpected default. The stochastic calculus approach is used to establish abstract characterization results for hedgeable contingent claims in a fairly general set-up. In the Markovian framework, we use the PDE approach to show that the arbitrage price and the hedging strategy for an attainable contingent claim can be described in terms of solutions of a pair of coupled PDEs.

In this paper, we first present a review of statistical tools that can be used in asset management either to track financial indexes or to create synthetic ones. More precisely, we look at two important replication methods: the strong replication, where a portfolio of very liquid assets is created and the goal is to track an actual index with the portfolio, and weak replication, where a portfolio of very liquid assets is created and used to either replicate the statistical properties of an existing index, or to replicate the statistical properties of a custom asset. In addition, for weak replication, the target is not an index but a payoff, and the replication amounts to hedge the portfolio so it is as close as possible to the payoff at the end of each month. For strong replication, the main tools are predictive tools, so filtering techniques and regression play an important role. For weak replication, which is the main topic of this paper, in order to determine the target payoff, the investor has to find or choose the distribution function of the target index or custom index, as well as its dependence with other assets, and use a hedging technique. Therefore, the main tools for weak replication are modeling (estimation and goodness-of-fit) and optimal hedging. For example, an investor could wish to obtain Gaussian returns that are independent of some ETFs replicating the Nasdaq and S&P 500 indexes. In order to determine the dependence of the target and a given number of indexes, we introduce a new class of easily constructed models of conditional distributions called B-vines. We also propose to use a exible model to fit the distribution of the assets composing the portfolio and then hedge the portfolio in an optimal way. Examples are given to illustrate all the important steps required for the implementation of this new asset management methodology.

Energy-based assets are showing increased susceptibility to volatility arising out of geo-political, economic, climate and technological events. Given the economic importance of energy products, their market participants need to be able to access efficient strategies to effectively manage their exposures and reduce price risk. This chapter will outline the key futures-based hedging approaches that have been developed for managing energy price risk and evaluate their effectiveness. A key element of this analysis will be the breadth of assets considered. These include Crude and Refined Oil products, Natural Gas and wholesale Electricity markets. We find significant differences in the hedging effectiveness of the different energy markets. A key finding is that, Natural Gas and particularly Electricity futures are relatively ineffective as a risk management tool when compared with other energy assets.

We present arbitrage and risk arbitrage betting strategies for team jai alai. Most of the results generalize to other sports betting situations and some financial market applications. The arbitrage conditions are utility free. The risk arbitrage wagers use the Kelly expected log criterion.

Agricultural futures markets were the backbone of early futures trading and continue to play a vital role in today's global economy. For more than a century following the founding of the Chicago Board of Trade in 1848, the United States dominated the world's futures markets with agricultural commodities such as wheat, corn, oats, and soybeans. Today, the global agricultural futures markets include not only grains but also livestock such as cattle and hogs; dairy products such as milk, butter, and cheese; “soft” or tropical commodities such as cotton, coffee, sugar, and orange juice; and industrial products such as soybean oil, soybean meal, and lumber.

In this chapter, we shall proceed one step further to investigate how a conditional mean as mentioned in Chap. 2 could be estimated using linear statistical relationship between the two variables. The two-variable linear regression is studied and an application on financial futures hedging will be investigated later in the chapter.