GreeceGreece, officially the Hellenic Republic, is a country in Southeast Europe, situated on the southern tip of the Balkan peninsula. Greece shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to the east. The Aegean Sea lies to the east of the mainland, the Ionian Sea to the west, and the Sea of Crete and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean Basin, featuring thousands of islands.
GreeksThe Greeks or Hellenes (ˈhɛliːnz; Έλληνες, Éllines ˈelines) are an ethnic group and nation native to Greece, Cyprus, southern Albania, Anatolia, parts of Italy and Egypt, and to a lesser extent, other countries surrounding the Eastern Mediterranean and Black Sea. They also form a significant diaspora (), with many Greek communities established around the world. Greek colonies and communities have been historically established on the shores of the Mediterranean Sea and Black Sea, but the Greek people themselves have always been centered on the Aegean and Ionian seas, where the Greek language has been spoken since the Bronze Age.
Mathematical financeMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering.
Delta neutralIn finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security. Such a portfolio typically contains options and their corresponding underlying securities such that positive and negative delta components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security.
Bond valuationBond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist.
Binomial options pricing modelIn finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting. The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (), and formalized by Cox, Ross and Rubinstein in 1979 and by Rendleman and Bartter in that same year.
Rational pricingRational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments. Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets. Where this mismatch can be exploited (i.
Risk-neutral measureIn mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure. This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure.
Mycenaean GreeceMycenaean Greece (or the Mycenaean civilization) was the last phase of the Bronze Age in Ancient Greece, spanning the period from approximately 1750 to 1050 BC. It represents the first advanced and distinctively Greek civilization in mainland Greece with its palatial states, urban organization, works of art, and writing system. The Mycenaeans were mainland Greek peoples who were likely stimulated by their contact with insular Minoan Crete and other Mediterranean cultures to develop a more sophisticated sociopolitical culture of their own.
Butterfly (options)In finance, a butterfly (or simply fly) is a limited risk, non-directional options strategy that is designed to have a high probability of earning a limited profit when the future volatility of the underlying asset is expected to be lower (when long the butterfly) or higher (when short the butterfly) than that asset's current implied volatility. A long butterfly position will make profit if the future volatility is lower than the implied volatility.
Asset pricingIn financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing.
Finite difference methods for option pricingFinite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977. In general, finite difference methods are used to price options by approximating the (continuous-time) differential equation that describes how an option price evolves over time by a set of (discrete-time) difference equations. The discrete difference equations may then be solved iteratively to calculate a price for the option.
Nassim Nicholas TalebNassim Nicholas Taleb (ˈtɑːləb; alternatively Nessim or Nissim; born 12 September 1960) is a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist whose work concerns problems of randomness, probability, and uncertainty. Taleb is the author of the Incerto, a five-volume philosophical essay on uncertainty published between 2001 and 2018 (notably, The Black Swan and Antifragile).
Greeks (finance)In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). Collectively these have also been called the risk sensitivities, risk measures or hedge parameters. The Greeks are vital tools in risk management.
Risk neutral preferencesIn economics and finance, risk neutral preferences are preferences that are neither risk averse nor risk seeking. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indifferent between choices with equal expected payoffs even if one choice is riskier. In the context of the theory of the firm, a risk neutral firm facing risk about the market price of its product, and caring only about profit, would maximize the expected value of its profit (with respect to its choices of labor input usage, output produced, etc.
Credit derivativeIn finance, a credit derivative refers to any one of "various instruments and techniques designed to separate and then transfer the credit risk" or the risk of an event of default of a corporate or sovereign borrower, transferring it to an entity other than the lender or debtholder. An unfunded credit derivative is one where credit protection is bought and sold between bilateral counterparties without the protection seller having to put up money upfront or at any given time during the life of the deal unless an event of default occurs.
Volatility arbitrageIn finance, volatility arbitrage (or vol arb) is a term for financial arbitrage techniques directly dependent and based on volatility. A common type of vol arb is type of statistical arbitrage that is implemented by trading a delta neutral portfolio of an option and its underlying. The objective is to take advantage of differences between the implied volatility of the option, and a forecast of future realized volatility of the option's underlying. In volatility arbitrage, volatility rather than price is used as the unit of relative measure, i.
Quantum financeQuantum finance is an interdisciplinary research field, applying theories and methods developed by quantum physicists and economists in order to solve problems in finance. It is a branch of econophysics. Finance theory is heavily based on financial instrument pricing such as stock option pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as computational finance.
Portfolio optimizationPortfolio optimization is the process of selecting the best portfolio (asset distribution), out of the set of all portfolios being considered, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk. Factors being considered may range from tangible (such as assets, liabilities, earnings or other fundamentals) to intangible (such as selective divestment). Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz; see Markowitz model.
Hedge fundA hedge fund is a pooled investment fund that trades in relatively liquid assets and is able to make extensive use of more complex trading, portfolio-construction, and risk management techniques in an attempt to improve performance, such as short selling, leverage, and derivatives. Financial regulators generally restrict hedge fund marketing to institutional investors, high net worth individuals, and accredited investors. Hedge funds are considered alternative investments.
