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.
A long butterfly options strategy consists of the following options:
where X = the spot price (i.e. current market price of underlying) and a > 0.
Using put–call parity a long butterfly can also be created as follows:
where X = the spot price and a > 0.
All the options have the same expiration date.
At expiration the value (but not the profit) of the butterfly will be:
The maximum value occurs at X (see diagram).
A short butterfly position will make profit if the future volatility is higher than the implied volatility.
A short butterfly options strategy consists of the same options as a long butterfly. However now the middle strike option position is a long position and the upper and lower strike option positions are short.
In the United States, margin requirements for all options positions, including a butterfly, are governed by what is known as Regulation T. However brokers are permitted to apply more stringent margin requirements than the regulations.
The price of a butterfly centered around some strike price can be used to estimate the implied probability of the underlying being at that strike price at expiry. This means the set of market prices for butterflies centered around different strike prices can be used to infer the market's belief about the probability distribution for the underlying price at expiry. This implied distribution may be different from the lognormal distribution assumed in the popular Black-Scholes model, and studying it can reveal ways in which real-world assets differ from the idealized assets described by Black-Scholes. [1]
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return. The equation and model are named after economists Fischer Black and Myron Scholes; Robert C. Merton, who first wrote an academic paper on the subject, is sometimes also credited.
In finance, a put or put option is a financial market derivative instrument that gives the holder the right to sell an asset, at a specified price, by a specified date to the writer of the put. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.
In financial mathematics, put–call parity defines a relationship between the price of a European call option and European put option, both with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to a single forward contract at this strike price and expiry. This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract.
In finance, a straddle strategy involves two transactions in options on the same underlying, with opposite positions. One holds long risk, the other short. As a result, it involves the purchase or sale of particular option derivatives that allow the holder to profit based on how much the price of the underlying security moves, regardless of the direction of price movement.
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting.
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. Collectively these have also been called the risk sensitivities, risk measures or hedge parameters.
In finance, moneyness is the relative position of the current price of an underlying asset with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification: if the derivative would have positive intrinsic value if it were to expire today, it is said to be in the money; if it would be worthless if expiring with the underlying at its current price it is said to be out of the money, and if the current underlying price and strike price are equal, it is said to be at the money. There are two slightly different definitions, according to whether one uses the current price (spot) or future price (forward), specified as "at the money spot" or "at the money forward", etc.
In finance, the time value (TV) of an option is the premium a rational investor would pay over its current exercise value, based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market, thus an option is always worth more than its current exercise value. As an option can be thought of as 'price insurance', TV can be thought of as the risk premium the option seller charges the buyer—the higher the expected risk, the higher the premium. Conversely, TV can be thought of as the price an investor is willing to pay for potential upside.
Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics; Financial engineering for the implementation; as well as Financial modeling § Quantitative finance generally.
The iron condor is an option trading strategy utilizing two vertical spreads – a put spread and a call spread with the same expiration and four different strikes. A long iron condor is essentially selling both sides of the underlying instrument by simultaneously shorting the same number of calls and puts, then covering each position with the purchase of further out of the money call(s) and put(s) respectively. The converse produces a short iron condor.
In finance an iron butterfly, also known as the ironfly, is the name of an advanced, neutral-outlook, options trading strategy that involves buying and holding four different options at three different strike prices. It is a limited-risk, limited-profit trading strategy that is structured for a larger probability of earning smaller limited profit when the underlying stock is perceived to have a low volatility.
Option strategies are the simultaneous, and often mixed, buying or selling of one or more options that differ in one or more of the options' variables. Call options, simply known as Calls, give the buyer a right to buy a particular stock at that option's strike price. Opposite to that are Put options, simply known as Puts, which give the buyer the right to sell a particular stock at the option's strike price. This is often done to gain exposure to a specific type of opportunity or risk while eliminating other risks as part of a trading strategy. A very straightforward strategy might simply be the buying or selling of a single option; however, option strategies often refer to a combination of simultaneous buying and or selling of options.
Options spreads are the basic building blocks of many options trading strategies. A spread position is entered by buying and selling options of the same class on the same underlying security but with different strike prices or expiration dates. An option spread shouldn't be confused with a spread option. The three main classes of spreads are the horizontal spread, the vertical spread and the diagonal spread. They are grouped by the relationships between the strike price and expiration dates of the options involved -
The backspread is the converse strategy to the ratio spread and is also known as reverse ratio spread. Using calls, a bullish strategy known as the call backspread can be constructed and with puts, a strategy known as the put backspread can be constructed.
In finance, an option is a contract which conveys to its owner, the holder, the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price on or before a specified date, depending on the style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction. Thus, they are also a form of asset and have a valuation that may depend on a complex relationship between underlying asset value, time until expiration, market volatility, and other factors. Options may be traded between private parties in over-the-counter (OTC) transactions, or they may be exchange-traded in live, orderly markets in the form of standardized contracts.
In finance, a strangle is a trading strategy involving the purchase or sale of two options, allowing the holder to profit based on how much the price of the underlying security moves, with minimal exposure to the direction of price movement. A strangle consists of one call and one put with the same expiry and underlying but different strike prices. Typically the call has a higher strike price than the put. If the put has a higher strike price instead, the position is sometimes called a guts.
In finance, a synthetic position is a way to create the payoff of a financial instrument using other financial instruments.
A condor is a limited-risk, non-directional options trading strategy consisting of four options at four different strike prices. The buyer of a condor earns a profit if the underlying is between or near the inner two strikes at expiry, but has a limited loss if the underlying is near or outside the outer two strikes at expiry. Therefore, long condors are used by traders who expect the underlying to stay within a limited range, while short condors are used by traders who expect the underlying to make a large move in either direction. Compared to a butterfly, a condor is profitable at a wider range of potential underlying values, but has a higher premium and therefore a lower maximum profit.
In finance, a ladder, also known as a Christmas tree, is a combination of three options of the same type at three different strike prices. A long ladder is used by traders who expect low volatility, while a short ladder is used by traders who expect high volatility. Ladders are in some ways similar to strangles, vertical spreads, condors, or ratio spreads.