Titlebook: Mathematical Finance; Theory Review and Ex Emanuela Rosazza Gianin,Carlo Sgarra Textbook 2023Latest edition The Editor(s) (if applicable) a

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Mathematical Finance978-3-031-28378-9Series ISSN 2038-5714 Series E-ISSN 2532-3318

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https://doi.org/10.1007/978-3-031-28378-9Option Pricing; Arbitrage Theory; Derivatives Hedging; Mathematical Finance; Stochastic Financial Models

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Short Review of Probability and of Stochastic Processes,Given a probability space ., where . denotes a non-empty set, . a .-algebra and . a probability measure on

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American Options,An . is a contract giving the buyer the right to buy (Call) or sell (Put) a financial underlying asset for a strike price . at every instant between the agreement date and the maturity. The main difference between American and European options consists thus in the . feature.

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Exotic Options, underlying value at maturity, but also on one or more values that it can assume during its lifetime. Although the two option classes do not coincide, many exotic options exhibit path-dependence features. Among the most popular Exotic options that are not path-dependent we just recall ., . and ..