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Show that the probability that a European call option will be exercised in a risk-neutral world is,

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Show that the probability that a European call option will be exercised in a risk-neutral world is, with the notation introduced in this chapter, N(d2). What is an expression for the value of a derivative that pays off $100 if the price of a stock at time T is greater than K?
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Fundamentals of Futures and Options Markets

Fundamentals of Futures and Options Markets

ISBN: 978-0132993340

8th edition

Authors: John C. Hull

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A call option is a type of financial contract that gives the holder the right, but not the obligation, to buy an underlying asset (such as a stock, commodity, or currency) at a specified price (called the strike price) within a specified period of time. When an investor purchases a call option, they are essentially betting that the price of the underlying asset will rise above the strike price before the option\'s expiration date. If the price of the asset does rise above the strike price, the investor can exercise the option by buying the asset at the strike price and then selling it at the higher market price, thereby earning a profit. Call options are often used as a speculative investment strategy, as they allow investors to potentially profit from the upward movement of an asset without having to actually own the asset itself. They are also commonly used as a hedging tool to protect against potential losses in a portfolio.

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