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J. M. Schumacher introduces the mathematical models used to analyse derivative contracts in finance and insurance. The book develops a continuous-time approach, beginning with the ideas behind the Black-Scholes formula and the relationship between the price of a contingent claim, the assets used to hedge it and the assumptions placed on a financial market.
An introduction to stochastic calculus supplies the tools needed for the later models. The discussion connects concepts such as self-financing strategies, absence of arbitrage and market completeness with analytical and numerical methods for valuation. Programming exercises and mathematical problems encourage readers to work through the calculations as well as understand their interpretation.
The text grew out of a master's-level course at Tilburg University and assumes familiarity with calculus, linear algebra and probability. Its progression is designed to make the modelling framework and its technical machinery accessible without starting from a full measure-theoretic treatment. Readers will find a sustained mathematical account of pricing and hedging, supported by examples, exercises and references for further study.