## Market-Conform Valuation of Options1. 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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2004 DAX options algorithm American call options American put options American-style options Ansatze arbitrage-free asset price Avellaneda Bakshi benchmark instruments benchmark options Bewertung bid-ask spread Black-Scholes model Brown and Toft calibration current index level Derman and Kani different maturity dates down-and-out call Dupire Eurex Euwax given market prices Heston model implied binomial tree implied multinomial trees implied tree implied volatility implizite interpolation Jackwerth 1997 Jackwerth and Rubinstein Journal of Finance knock-out options least-squares approaches Longstaff and Schwartz MAOPE market-conform maturity date median midpoint moneyness Monte Carlo approach Monte Carlo method Monte Carlo paths Monte Carlo simulation node optimization problem Option Pricing Models option quotes Optionen out-of-sample path probabilities plain-vanilla probability distributions risk-neutral measure risk-neutral probability Rubinstein 1996 sample paths Scholes squared pricing errors step stochastic volatility strike price sub-trees Threshold Approach tion traded options transition probabilities trinomial volatility function volatility smile Weighted Monte Carlo