Does anyone know a book which covers topics on:
Brownian Motion
Martingales
Stochastic Calculus
Stochastic Differential Equations
Options pricing. Black-Scholes model
Fundamental Theorems. Interest Rates
Random Walk
Applications in Insurance
Simulations. Convergence
Simulation methods
I would like something in-depth, but at an undergraduate level.
Best Answer
A recommended book which covers most of your topics is Options, Futures and Other Derivatives - John Hull. Regarding simulation methods, I would suggest Monte Carlo Methods in Financial Engineering - Paul Glasserman..
Both books are a good starting point.