Quantitative Finance

Mathematical method based on a direct or indirect analysis of growth rates is described. It is shown how simple assumptions and a relatively easy analysis can be used to describe mathematically complicated trends and to predict growth. Only rudimentary knowledge of calculus is required. Projected trajectories based on such simple initial assumptions are easier to accept and to understand than alternative complicated projections based on more complicated assumptions and on more intricate computational procedures. Examples of the growth of population and of the growth of the Gross Domestic Product are used to illustrate the application of this method of forecasting.

This paper presents a framework capable of accurately forecasting future sales in the retail industry and classifying the product portfolio according to the expected level of forecasting reliability. The proposed framework, that would be of great use for any company operating in the retail industry, is based on Facebook's Prophet algorithm and backtesting strategy. Real-world sales forecasting benchmark data obtained experimentally in a production environment in one of the biggest retail companies in Bosnia and Herzegovina is used to evaluate the framework and demonstrate its capabilities in a real-world use case scenario.

This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront that several of the examples reviewed in this chapter were already discussed in book form. Still, they are here accompanied with discussions of, and references to, works which appeared over the last three years. Moreover, several completely new sections are added to show how recent developments in financial engineering and economics can benefit from being viewed through the lens of the Mean Field Game paradigm. The new financial engineering applications deal with bitcoin mining and the energy markets, while the new economic applications concern models offering a smooth transition between macro-economics and finance, and contract theory.

Volatility is a key variable in option pricing, trading and hedging strategies. The purpose of this paper is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training-subset selection methods. These methods manipulate the training data in order to improve the out of sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models which are not adapted to some out of sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training-subset selection methods are proposed based on random, sequential or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases errors. Using real data from SP500 index options, these techniques are compared to the static subset selection method. Based on MSE total and percentage of non fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, specially those obtained from the adaptive random training subset selection method applied to the whole set of training samples.

There has been limited success applying the Nash Bargaining Solution (NBS) in assigning intellectual property damages due to the difficulty of relating it to the specific facts of the case. Because of this, parties are not taking advantage of Georgia-Pacific factor fifteen. This paper intends to bring clarity to the NBS so it can be applied to the facts of a case. This paper normalizes the NBS and provides a methodology for determining the bargaining weight in Nash's solution. Several examples demonstrate this normalized form, and a nomograph is added for computational ease.

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. Some approximation methods date back over 80 years and most take one of two approaches, either: 1) an approximate probability distribution is derived mathematically, or 2) the sum is approximated by a single lognormal random variable. In this research, we take the latter approach and review a fairly recent approximation procedure proposed by Mehta, Wu, Molisch, and Zhang (2007), then implement it using C++. The result is applied to a discrete time model commonly encountered within the field of financial economics.

In the domain of technology startups, biotechnology has often been considered as specific. Their unique technology content, the type of founders and managers they have, the amount of venture capital they raise, the time it takes them to reach an exit as well as the technology clusters they belong to are seen as such unique features. Based on extensive research from new databases, the author claims that the biotechnology startups are not as different as it might have been claimed: the amount of venture capital raised, the time to exit, their geography are indeed similar and even their equity structure to founders and managers have similarities. The differences still exist, for example the experience of the founders, the revenue and profit level at exit.

During times of extreme market turmoil, it is acknowledged that there is a tendency towards "flight to safety". A strong (weak) safe haven is defined as an asset that has a significant positive (negative) return in periods where another asset is in distress, while hedge has to be negatively correlated (uncorrelated) on average. The Bitcoin's surge alongside the aftermath of Trump's win in the 2016 U.S. presidential elections has strengthened its status as the modern safe haven. This paper uses a truly noise-assisted data analysis method, termed as Ensemble Empirical Mode Decomposition-based approach, to examine whether Bitcoin can act as a hedge and safe haven for U.S. stock price index. The results document that the Bitcoin's safe-haven property is time-varying and that it has primarily been a weak safe haven in the short term and the long-term. We also demonstrate that precious metals lost their safe haven properties over time as the correlation between gold/silver and U.S. stock price declines from short-to long-run horizons.

Are cryptocurrency traders driven by a desire to invest in a new asset class to diversify their portfolio or are they merely seeking to increase their levels of risk? To answer this question, we use individual-level brokerage data and study their behavior in stock trading around the time they engage in their first cryptocurrency trade. We find that when engaging in cryptocurrency trading investors simultaneously increase their risk-seeking behavior in stock trading as they increase their trading intensity and use of leverage. The increase in risk-seeking in stocks is particularly pronounced when volatility in cryptocurrency returns is low, suggesting that their overall behavior is driven by excitement-seeking.

A crypto coin designed to provide a stabilization instrument backed up by minded like financial investments instruments to maintain the purchase value of savings across time, in order to construct new tools for unstable economies.