MarketConform Valuation of Options (Lecture Notes in Economics and Mathematical Systems, 571),Used

MarketConform Valuation of Options (Lecture Notes in Economics and Mathematical Systems, 571),Used

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1. 1 The Area of Research In this thesis, we will investigate the 'marketconform' pricing of newly issued contingent claims. A contingent claim is a derivative whose value at any settlement date is determined by the value of one or more other underlying assets, e. g. , forwards, futures, plainvanilla or exotic options with European or Americanstyle exercise features. Marketconform pricing means that prices of existing actively traded securities are taken as given, and then the set of equivalent martingale measures that are consistent with the initial prices of the traded securities is derived using noarbitrage arguments. Sometimes in the literature other expressions are used for 'marketconform' valuation 'smileconsistent' valuation or 'fairmarket' valuation that describe the same basic idea. The seminal work by Black and Scholes (1973) (BS) and Merton (1973) mark a breakthrough in the problem of hedging and pricing contingent claims based on noarbitrage arguments. Harrison and Kreps (1979) provide a firm mathematical foundation for the BlackScholes Merton analysis. They show that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure. Under this mea sure the normalized security price process forms a martingale and so securities can be valued by taking expectations. If the securities market is complete, then the equivalent martingale measure and hence the price of any security are unique.

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