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The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at or before a certain time (the expiration date) for a certain price (the strike price). This effectively gives the buyer a long position in the given ...
The long position of the volatility option, like the vanilla option, has the right but not the obligation to trade the annualized realized volatility interchange with the short position at some agreed price (volatility strike) at some predetermined point in the future (expiry date). The payoff is commonly settled in cash by some notional amount.
For example, a bull spread constructed from calls (e.g., long a 50 call, short a 60 call) combined with a bear spread constructed from puts (e.g., long a 60 put, short a 50 put) has a constant payoff of the difference in exercise prices (e.g. 10) assuming that the underlying stock does not go ex-dividend before the expiration of the options.
In financial applications, each of the random variables () represents an asset value, the number is the strike of the option on the portfolio of assets. We can therefore express the payoff of an option on a portfolio of assets in terms of a portfolio of options on the individual assets f i ( W ) {\displaystyle f_{i}(W)} with corresponding ...
A long butterfly options strategy consists of the following options: Long 1 call with a strike price of (X − a) Short 2 calls with a strike price of X; Long 1 call with a strike price of (X + a) 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:
The formulas used above to convert returns or volatility measures from one time period to another assume a particular underlying model or process. These formulas are accurate extrapolations of a random walk, or Wiener process, whose steps have finite variance. However, more generally, for natural stochastic processes, the precise relationship ...
In mathematical finance, Margrabe's formula [1] is an option pricing formula applicable to an option to exchange one risky asset for another risky asset at maturity. It was derived by William Margrabe (PhD Chicago) in 1978. Margrabe's paper has been cited by over 2000 subsequent articles.
In mathematical finance, the asset S t that underlies a financial derivative is typically assumed to follow a stochastic differential equation of the form = +, under the risk neutral measure, where is the instantaneous risk free rate, giving an average local direction to the dynamics, and is a Wiener process, representing the inflow of randomness into the dynamics.