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In the Black–Scholes model, the price of the option can be found by the formulas below. [27] In fact, the Black–Scholes formula for the price of a vanilla call option (or put option) can be interpreted by decomposing a call option into an asset-or-nothing call option minus a cash-or-nothing call option, and similarly for a put – the binary options are easier to analyze, and correspond to ...
A binary call option is, at long expirations, similar to a tight call spread using two vanilla options. One can model the value of a binary cash-or-nothing option, C , at strike K , as an infinitesimally tight spread, where C v {\displaystyle C_{v}} is a vanilla European call: [ 35 ] [ 36 ]
Martingale pricing is a pricing approach based on the notions of martingale and risk neutrality.The martingale pricing approach is a cornerstone of modern quantitative finance and can be applied to a variety of derivatives contracts, e.g. options, futures, interest rate derivatives, credit derivatives, etc.
A martingale is a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails.
A convex function of a martingale is a submartingale, by Jensen's inequality. For example, the square of the gambler's fortune in the fair coin game is a submartingale (which also follows from the fact that X n 2 − n is a martingale). Similarly, a concave function of a martingale is a supermartingale.
From the viewpoint of the option issuer, e.g. an investment bank, the gamma term is the cost of hedging the option. (Since gamma is the greatest when the spot price of the underlying is near the strike price of the option, the seller's hedging costs are the greatest in that circumstance.)
The last image we have of Patrick Cagey is of his first moments as a free man. He has just walked out of a 30-day drug treatment center in Georgetown, Kentucky, dressed in gym clothes and carrying a Nike duffel bag.
The trinomial tree is a lattice-based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the binomial options pricing model, and is conceptually similar. It can also be shown that the approach is equivalent to the explicit finite difference method for option ...
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