I am looking for an easy and well presented introduction to Black-Scholes theory and stochastic calculus aimed at undergraduate mathematics students. Please can you recommend a book?
How about Paul Wilmott on QF?
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I suggest you Arbitrage Theory in Continuous Time by Tomas Bjork. It is a standard reference introducing Stochastic Calculus, then Black-Scholes both from a hedging portfolio perspective and a martingale point of view. It has also some nice chapters on American Options, exotic options and Fixed income derivatives.
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I like Financial Calculus: An Introduction to Derivative Pricing by Baxter and Rennie. It's less technical than Shreve or Bjork, whether that's an advantage or disadvantage is up to you.