You need to be a little more specific regarding your interests and background. If you are interested in theory, there are plenty of books discussing specific models. However, most practical or buzzword (e.g. HFT) books are rubbish (think about it: if you have a profitable operation, why would you write a book? Unless, like me, you have a screw loose :P )
If you want some practical discussions, "Trading and Exchanges" by Larry Harris is a bit dated, but nothing comes close. Most of the descriptions are still valid today (even if some of the mechanics have changed)
If you want something more along the lines of what a financial engineer would know:
- "Options, Futures, and other Derivatives" by John Hull (goes over basic models without delving too deeply into theoretical math aspects)
- "Stochastic Calculus for Finance II" by Steve Shreve (goes over the basic stuff but has enough stats to keep a grad student happy)
- "Monte Carlo Methods in Financial Engineering" by Paul Glasserman (much more practical, and goes over subtleties of monte carlo simulation and other stuff like low discrepancy sampling)
- "Modelling Fixed Income Securities and Interest Rate Options" by Robert Jarrow (walks through how to perform certain simulations, covers lots of little details most theoretical books skip)
If you want something more theoretical:
- "Introduction to Stochastic Calculus Applied to Finance" by Lamberton and Lapeyre (Nice little intro)
- "Arbitrage Theory in Continuous Time" by Tomas Bjork (Slower discussion, larger breadth)
- "Brownian Motion and Stochastic Calculus" and "Methods of Mathematical Finance" by Karatzas and Shreve (Solid theoretical foundation, for the more mathematically inclined)
There was a good non-measure theoretic discussion of financial models but the name escapes me ATM.
John Hull is canon. Read it, live it, love it, keep it under your pillow. It is truly superb.
Nassim Taleb's "Dynamic Hedging" is the finest book I'm aware of on the subject of actually trading/managing vol portfolios. It's REALLY good. And dense.
"Paul Wilmott on Quantitative Finance" vol 1-3 are worth having as a reference, perhaps.
"Analysis and Use of Financial Statements" by White, Sondhi and Fried.
It has nothing to do with computational finance but knowing more than nothing about financial statements and how to think about what a company actually IS can only help you in the long run. Also, it's quite interesting.
If you want some practical discussions, "Trading and Exchanges" by Larry Harris is a bit dated, but nothing comes close. Most of the descriptions are still valid today (even if some of the mechanics have changed)
If you want something more along the lines of what a financial engineer would know:
- "Options, Futures, and other Derivatives" by John Hull (goes over basic models without delving too deeply into theoretical math aspects)
- "Stochastic Calculus for Finance II" by Steve Shreve (goes over the basic stuff but has enough stats to keep a grad student happy)
- "Monte Carlo Methods in Financial Engineering" by Paul Glasserman (much more practical, and goes over subtleties of monte carlo simulation and other stuff like low discrepancy sampling)
- "Modelling Fixed Income Securities and Interest Rate Options" by Robert Jarrow (walks through how to perform certain simulations, covers lots of little details most theoretical books skip)
If you want something more theoretical:
- "Introduction to Stochastic Calculus Applied to Finance" by Lamberton and Lapeyre (Nice little intro)
- "Arbitrage Theory in Continuous Time" by Tomas Bjork (Slower discussion, larger breadth)
- "Brownian Motion and Stochastic Calculus" and "Methods of Mathematical Finance" by Karatzas and Shreve (Solid theoretical foundation, for the more mathematically inclined)
There was a good non-measure theoretic discussion of financial models but the name escapes me ATM.