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First, my notation. $K$ is the strike price, $S$ is the stock price, $r$ is the continuously compounded risk-free rate, $T$ is time at expiration, $t$ is time at issue, $\sigma$ is volatility, $\delta$ is continuously compounded dividend rate. The Black-Scholes formula for a European call is $C = Se^{-\delta (T-t)} N(d_1) - Ke^{-r(T-t)} N(d_2)$ $d_1 = ...


In general, quantitative finance requires mathematics, finance, and numerical programming. The mix of the three and the areas of focus within the three will depend on the particular area you intend to work in. For example, option pricing, risk, and asset management are all related but derivative modeling would draw more on stochastic processes and ...


For general mathematical finance, you may start with the book Stochastic Calculus for Finance, and then the books Martingale Methods in Financial Modelling and Mathematical Methods for Financial Markets. After those preparations, you can start with some books in specialized areas such as the books Interest Rate Models by Brigo and Mercurio, Credit Risk by ...


Crouhy, Mark and Galai's book Risk Management is about all aspects of risk management for investment banks, including credit risk of course. If you need to focus on one book, it is this one.


In the case you're interested in asset management, Robbert Shiller's open fiance course is definitely a good introduction to finance, although not quantitative. In addition to that, John Cochrane's course on Coursera is a very good. Here portfolio theory and option pricing is approached from a quantitative perspective.


I used Optimisation Methods in Finance, it covers: Linear Programming Nonlinear Programming Quadratic Pogramming Conic Programming Integer Programming Dynamic Programming Stochastic Programming I haven't come across another book with such coverage or wider yet, although I've not been actively looking though.


Some suggestions:- Modern Portfolio Theory and Investment Analysis, Ch. 6 Techniques for Calculating the Efficient Frontier Original 1970 paper An analytic derivation of the efficient portfolio frontier by Merton, Robert C Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques


The following paper gives a simple derivation of the BSM (via a simple integration approach instead of the classical PDE approach) and the Greeks plus some intuition for each: Derivation and Comparative Statics of the Black-Scholes Call and Put Option Pricing Formulas by Garven, J. You find the derivation of the Greeks in chapter 4 (called "comparative ...

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