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1. 1 The Area of Research In this thesis, we will investigate the
'market-conform' 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, plain-vanilla or exotic options with
European or American-style exercise features. Market-conform
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 no-arbitrage arguments. Sometimes in
the literature other expressions are used for 'market-conform'
valuation - 'smile-consistent' valuation or 'fair-market' 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
no-arbitrage arguments. Harrison and Kreps (1979) provide a firm
mathematical foundation for the Black-Scholes- 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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