I am going to complete a continuous time finance course in the upcoming semester. Although all my higher education is in economics I have not encountered a financial economics setting of contingent markets,i.e, of the geometric representation of the state space of the aforementioned. I have a solid knowledge on investments, financial markets and financial products such as derivatives but I was looking for the mathematical finance formulation of contingent markets. What introductory book would be good for an introduction in the simpler settings before jumping to the Black-Scholes setting for example which is the end-goal of the class I am going to take. Cochrane's book "Asset Pricing" is similar to what I am looking for but I would like to know if there are any alternatives.
Financial Asset Pricing Theory, by Claus Munk.
This book takes a nice approach in that each chapter repeats the material 3 times: in discrete time with a discrete state space, in discrete time with a continuous state space, and in continuous time with a continuous state space. This makes it easy to see how each relates to the others. Also, it helps the reader to focus on the underlying concepts rather than the mathematical artifacts of each individual setting.
I like Cochrane's book a lot for the intuitions that it provides. In my opinion, Munk's book is very useful as a complement to Cochrane's book. Munk's book provides a lot of the mathematical clarity that I feel is less clear in Cochrane's book.
Dynamic Asset Pricing Theory, by Darrell Duffie.
This book seems to be referred to a lot. It's very thorough. In my experience, it might be a little to difficult for a introduction to the topic. However, it is a good reference.
If you are looking for something simpler before jumping to Black-Scholes, consider the textbook "Investments" from Bodie, Kane, and Marcus.
You can look at the table of contents. The book assumes that the reader does not know stochastic calculus and continuous time finance, but it still gets to the Black-Scholes formula.