Monte Carlo simulation methods for the valuation of financial instruments have become a staple of empirical economic analysis. A specific focus is dedicated to the feasibility of the stock price losses and barrier options as well as the sensitivity of partial time barrier options in dependence...

The Chicago Board Options Exchange (CBOE) Volatility Index, often referred to as VIX Volatility Index (VIX), is considered by many market participants as a common measure of market risk and investors' sentiment. It is also sometimes called the fear index. In general, the VIX represents the...

The Chicago Board Options Exchange (CBOE) Volatility Index (VIX) is considered by many market participants as a common measure of market risk and investors' sentiment, representing the market's expectation of the 30-day-ahead looking implied volatility obtained from real-time prices of options...

In this work, I introduce a new investment strategy for long-term equity investors. In particular, my proposed portfolio relies on the mean-variance approach as in Markowitz (1952), and it requires the same input estimates and is vividly located on the efficient frontier. The analytic...

With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms...

We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly...