5.3European contingent claims

A key topic of mathematical finance is the analysis of derivative securities or contingent claims, i.e., of certain assets whose payoff depends on the behavior of the primary assets S0, S1, . . . , Sd and, in some cases, also on other factors.

Definition 5.19. A nonnegative random variable C on (Ω,FT , P) is called a European contingent claim. A European contingent claim C is called a derivative of the underlying assets S0, S1, . . . , Sd if C is measurable with respect to the σ-algebra generated by the price process (St)t=0,...,T.

A European contingent claim has the interpretation of an asset which yields at time T the amount C(ω), depending on the scenario ω of the market evolution. T is called the expiration ...

Get Stochastic Finance, 4th Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.