This workshop discusses a general, arbitrage free share market modelling framework. The prices and hedging strategies for derivatives are obtained without any measure transformation. An analytically tractable share market model is proposed which models the equal value weighted share price index and the index benchmarked spot share prices by powers of square root processes. The resulting share prices have consequently leptokurtic log-return distributions which match those observed in reality. Stochastic volatility with realistic properties arises naturally. For instance, indices are negatively correlated with their volatilities which potentially explains the leverage effect. Furthermore, the pricing and hedging of derivatives under the proposed model will be considered. It turns out that the risk neutral pricing methodology fails for this model class. By an alternative, more direct approach derivatives can be priced. The pricing of European call and put options on indices leads to implied volatility skews as typically observed in reality. European options on share prices exhibit implied volatility smiles that match those in the market.

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