Titlebook: Stochastic Processes and Financial Mathematics; Ludger Rüschendorf Textbook 2023 The Editor(s) (if applicable) and The Author(s), under ex

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,Skorohod’s Embedding Theorem and Donsker’s Theorem,n be approximatively described by functionals of a continuous-time limit process. Conversely, functionals of the limit process can be simulated by those of discrete-time approximating processes. By this connection, by means of simple laws in the discrete time model, suitable continuous-time models a

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Option Prices in Complete and Incomplete Markets,e hedging principle and the risk-neutral price measure, which leads from the binomial price formula by approximation to the Black–Scholes formula. The necessary link from processes in discrete time (binomial model) to those in continuous time (Black–Scholes model) is given by approximation theorems

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,Skorohod’s Embedding Theorem and Donsker’s Theorem,losely related Skorohod embedding theorem. Hereby the simple binomial model (or more generally the Cox–Ross–Rubinstein model) can be used to approximate a geometric Brownian motion (or more generally an exponential Lévy process) as a suitable continuous-time limit model.

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Option Pricing in Discrete Time Models,ed in a simple way. This approach makes it possible to introduce essential concepts and methods with little technical effort and, allows for example, to derive the Black–Scholes formula by means of an approximation argument.

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Option Prices in Complete and Incomplete Markets, necessary link from processes in discrete time (binomial model) to those in continuous time (Black–Scholes model) is given by approximation theorems for stochastic processes in Chap. .. Theorems of this type allow an interpretation of continuous financial market models using simple discrete models such as the Cox–Ross–Rubinstein model.