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Derivatives: Markets, Valuation, and Risk Management by ROBERT E. WHALEY

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CHAPTER 6

No-Arbitrage Price Relations: Options

The purpose of this chapter is to develop no-arbitrage price relations for option contracts. Unlike forwards and futures, options provide the right, but not the obligation, to buy or sell the underlying asset at a specified price. The right to buy is a call option, the right to sell is a put. The price at which the underlying asset is bought (in the case of a call) or sold (in the case of a put) is called the exercise price or strike price of the option.

In this chapter, the assumption that two perfect substitutes have the same price is again applied. In the absence of costless arbitrage opportunities, options have three types of no-arbitrage price relations—lower bounds, put-call parity relations, and intermarket relations.1 Each type of relation is developed in turn, for both European- and American-style options2 and under both the continuous rate and discrete flow net cost of carry assumptions. Before deriving the no-arbitrage price relations for options, however, we focus on clearly distinguishing between the characteristics of option and forward contracts.

OPTIONS AND FORWARDS

Options differ from forwards in two key respects. First, the net cost of carry of a forward contract is zero since it involves no investment outlay. An option, on the other hand, involves investment. An option buyer pays the option premium for the right to buy or sell the underlying asset, and, like the buyer of any other asset, faces carry costs. For an ...

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