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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.
The first application to option pricing was by Phelim Boyle in 1977 (for European options). In 1996, M. Broadie and P. Glasserman showed how to price Asian options by Monte Carlo. An important development was the introduction in 1996 by Carriere of Monte Carlo methods for options with early exercise features.
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 ...
%If Unchanged Potential Return = (call option price - put option price) / [stock price - (call option price - put option price)] For example, for stock JKH purchased at $52.5, a call option sold for $2.00 with a strike price of $55 and a put option purchased for $0.50 with a strike price of $50, the %If Unchanged Return for the collar would be:
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 ...
Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option on a portfolio of assets as a portfolio of options. It was developed by Farshid Jamshidian in 1989. The trick relies on the following simple, but very useful mathematical observation.
The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call option, the option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price.