Many problems in engineering analysis and design can be cast as convex optimization problems, often non-linear and non-differentiable. Specifically, Convex optimization problems can be solved by some modern methods such as subgradient projection and interior point methods or by some old methods such as cutting plane methods, ellipsoid methods, and subgradient methods.
Optimization theory has developed from the earliest approaches of De Fermat, Lagrange, Newton, and Gauss through the formalization of Linear programming in 1939 by Kantorovich, the Simplex method of Dantzig and the Duality Theory of von Neumann in 1947, and the Karush-Kuhn-Tucker condition in 1951. Its application disrupted logistics, banking, and economics. In 1960, the…
The 1944 Bretton Woods agreement jumpstarted the dollar into its reserve currency status. While economists proposed global trust and confidence in the US ability to pay its obligations, a more compelling justitification has its roots in United States’ political influence.
With respect to the COVID-19 impact, it has not passed unobserved that the $3.3 trillion issuance of debt securities in the first half of 2020 has been purchased only by the U.S. Federal Reserve (46%) and national/international private investors (40%); instead, foreign central banks, already holding trillions of dollars of U.S. Treasuries, did not acquire a significant amount. In other terms, it seems the U.S. is substantially moving to own its debt in what we can define a Japanese way of managing the economy; probably, other developed countries will soon engage in similar practices.
The fluctuations of equity prices are attributed to the competition of firms for the limited funds of investors; as a result, demand and supply achieve the equilibrium summarized in the most competitive expected rate of return adjusted for risk.
Options are often used to reduce or eliminate the risk of holding one particular investment position by taking another position. In general, a long option position is a speculation that something will happen (bear, bull, lateral) whereas a short option is a speculation that something will NOT happen (not bear, not bull, not lateral).
CBOE Implied Correlation, Volatility of Volatility, and Skew are measures incorporating option market information and expectations about the S&P500 volatility in the near future.
Options trading is based on some rational motivation generally involving an edge or the need for hedge. An edge is what determines a trade positive expected value; usually, it is some kind of correct and not widely available information. Instead, a hedge is a trade offsetting an existing risk of another investment. Finally, trading should…
The implied volatility is generally equal to or significantly greater than the forecasted volatility; for instance, the BSM implied volatility is, in general, an upward biased estimator. Indeed, by selling implied volatility a risk premium is provided because of the many expected and unexpected events that may occur. Moreover, market microstructure posits that implied volatility should be biased high because market makers profit from the bid-ask spread in the options by slightly raising their quotes (i.e., going slight long volatility exposure particularly on the downside). However, this absolutely doesn’t mean that it is always possible to profit by selling implied volatility
Option Pricing. An option is a contract entitling the holder to buy or sell designated security at or within a certain period of time at a particular price. Options contracts are characterized by a nonlinear payoff because the price depends on a nonlinear function of the underlying. Thus, it is impossible to price without a model for the underlying but the assumptions of mathematical finance (not moving the market; liquidity, jumps; shorting; fractional quantities; no transaction costs) substantially make difficult to determine a single model always valid with the changing market conditions.
