Book Recommendation for mathematical finance

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.

Solution 1:

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.

Solution 2:

Oksendal, Stochastic Differential Equations is also a very good book to learn stochastic calculus.