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The Black-Scholes formula plays a central role in Mathematical Finance; it gives the right price at which buyer and seller can agree with, in the geometric Brownian framework, when strike K and maturity T are given. This yields an explicit well-known formula, obtained by Black and Scholes in 1973. The present volume gives another representation of this formula in terms of Brownian last passages times, which, to our knowledge, has never been made in this sense. The volume is devoted to various extensions and discussions of features and quantities stemming from the last passages times representation in the Brownian case such as: past-future martingales, last passage times up to a finite horizon, pseudo-inverses of processes... They are developed in eight chapters, with complements, appendices and exercises.

Distribution (Probability theory). --- Finance. --- Options (Finance) -- Prices -- Mathematics. --- Options (Finance) --- Distribution (Probability theory) --- Mathematics --- Finance --- Investment & Speculation --- Mathematical Statistics --- Physical Sciences & Mathematics --- Business & Economics --- Prices --- Mathematics. --- Call options --- Calls (Finance) --- Listed options --- Options exchange --- Options market --- Options trading --- Put and call transactions --- Put options --- Puts (Finance) --- Distribution functions --- Frequency distribution --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Derivative securities --- Investments --- Characteristic functions --- Probabilities --- Distribution (Probability theory. --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology --- Social sciences --- Probability Theory. --- Mathematics in Business, Economics and Finance.