28

A quick google search retrieves the syllabus for the Stanford STATS 242 class. You can find it here. Just in case it's taken down at some point I'll copy-paste the source material. Keep in mind that I have no idea if this material is good or bad -- I didn't make this list. Also keep in mind that it contains treatments of what does and does not work. With ...


24

These are all examples on Ito Formula in its general form (with quadratic variations):


24

You can't make any concrete statements about the monotonicity, convexity or even sign of the yield curve. Yields are almost always positive, and in the past (2007 and earlier) you could find people who would argue that yields must be positive, typically using a no-arbitrage argument. But recent history has shown us that it is possible for even 10Y yields to ...


17

Here are some resources that I found useful when learning about this subject, in which I'm very interested. (Some may be more general ESG than just just climate.) Citigroup. Environmental and Social Policy Framework (March 2021) UBS. Suni Harford. Investing in an ESG world - A practitioner’s guide (2020) AQR. Clearing the Air: Responsible Investment (...


16

Find the topic of model-independent properties of option prices very interesting as well. Here are some results that I am aware of and the respective references in the literature. Some are already contained in your initial list as well. Plain Vanilla Prices are Convex in the Strike Theorem 4 in Merton (1973). Delta is Bounded by the Slopes of the Payoff ...


16

Along with Gatheral's book, I'd recommend reading Lorenzo Bergomi's "Stochastic Volatility Modelling". The first 2 chapters are available for download on his website. That being said, let me try to give you the basic picture. Below we assume that the equity forward curve $F(0,t)=\Bbb{E}_0^\Bbb{Q}[S_t]$ is given for all $t$ smaller than some relevant ...


10

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 ...


8

The first book that comes to mind that is written in the style of Definition - Proposition - Proof is: Bjork - Arbitrage Theory in Continuous Time It's pretty well written and can get quite technical. Probably a more common reference is the two-volume set: Shreve - Stochastic Calculus for Finance I & II The first part deals with the binomial model, ...


8

Stochastics are usually applied in the field of derivatives pricing. In this setting the task is to price a derivative such that it fits into the landscape of tradable instruments (no-arbitrage). We work using the risk-neutral measure - usually denoted by $Q$. The measure is derived from other traded instruments. In risk analysis (e.g. calculate the VaR, ES ...


8

I discuss the books I mentioned in the comments. They all deal with standard (theoretical) asset pricing (starting with one period utility maximisation and then branch off). Other books like Björk, Shreve or Jarrow focus more on time continuous models and/or derivatives pricing and I do not discuss them here. They use more advanced maths. Cochrane (2005): ...


7

I think a good book to start in your case is: Attilio Meucci: Risk and Asset Allocation I once had a seminar held by Attilio that was based on the book and it blew my mind. The book is very intuitive yet rigorous.


7

Elements of Statistical Learning by Hastie, Tibshirani and Friedman is one of the most-cited books for your purpose. Although it does not have any direct applications to Finance, this is definitely a good book to have in your professional library and can be used as a reference for most topics. If you want to use a book with more financial applications, I ...


7

Tsay's Analysis of Financial Time Series should be what you're looking for.


7

A lot has happened since Markowitz and Sharpe. While their work is still considered foundational, the empirical/practical relevance of their models has been questioned by later work. Here are a few more recent articles about portfolio theory, in no particular order (all accessible online): Jorion: Bayes-Stein Estimation for Portfolio Analysis, JFQA, 1986 ...


7

I have also currently started to learn about the subject. This is some of the material I have encountered: Many people recommend the book "The Volatility Surface: A Practitioner's Guide" by Jim Gatheral. It is a standard reference in the area (even though I personally found it a bit confusing and a bit unclear at some parts). The author also have ...


6

I thought this was an interesting example to add. It concerns a "ratio model" of habit (as opposed to a "difference" model of habit). See, for example, Abel (1990, American Economic Review). Let $$ x_t = \lambda \int_{-\infty}^t e^{-\lambda(t-s)} c_s ds. $$ (For context, $x_t$ is a log habit index that is given by a geometric average of past consumption, ...


6

One of the best pieces ever written on this topic is Salomon's "Principles of Principal Components," which is readily available on the Internet. I won't go into the details, since this paper is ridiculously comprehensive, but the fundamental idea is straightforward -- if you run a PCA based on yields, the first three components capture most of the variances, ...


6

All the topics you've mentioned are wonderful and shouldn't be eschewed by reading some finance-oriented review book. I recommend these instead. Linear algebra: Hoffman and Kunze and Halmos Set theory: Halmos Measure theory: Rudin and Tao


6

I cannot suggest some reference particularly, since the field is going to develop day by day, but, generally, you could take a look to: Engelmann, Bernd, and Robert Rauhmeier, eds. The Basel II risk parameters: estimation, validation, and stress testing. Springer Science & Business Media, 2006. Particularly, look at the chapter 4 and 5; the ...


6

MF is linked with physics mostly because it solves the same PDEs (Black-Scholes equation is a certain type of Schrödinger equation for instance). As for the specific links you mentioned : Lie Algebra : Magnus expansion (to build fast approximation of time dependent ODEs like those arising in credit risk) Differential geometry : link with Varadhan ...


6

I think that "An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)" suggested by KarolisR could be useful but too much machine learning oriented. Moreover, such a book is for beginners. As a thorough book (PhD level) on statistics, I suggest "Statistical Inference" by Casella and Berger.


6

1: Follow the calculations in The Complete Guide to Option Pricing Formulas. The book has many formulas, sample values and outputs. Highly recommended for validating your results. Apparently, this is one of most popular books used by real-world quants (simple and fast). 2: You can still use QuantLib to price with year fractions. I have an example: ...


6

Note that, as in this question, for $s\ge t\ge 0$, \begin{align*} n_s = e^{-a_n(s-t)}n_t + \int_t^s \theta_n(u)e^{-a_n(s-u)} du + \int_t^s \sigma_n e^{-a_n(s-u)} dW^n_u, \end{align*} and \begin{align*} r_s = e^{-a_r(s-t)}r_t + \int_t^s (\theta_r(u) -\rho_{r,n}\sigma_n\sigma_r) e^{-a_r(s-u)} du + \int_t^s \sigma_r e^{-a_r(s-u)} dW^r_u. \end{align*} Moreover,...


6

As mentioned by @Adam, Stochastic Calculus for Finance by Shreve is a good start if you have a reasonably strong mathematical background. Volume I is simpler, as it presents derivative pricing methods in discrete time; Volume II tackles the continuous case. Also mentioned by @noob2, Financial Calculus: An Introduction to Derivative Pricing, by Baxter and ...


6

Status of this answer: latest update April 6, 2021. There is a new paper out which is quite interesting and which basically says that cryptocurrencies are indeed a new asset class, potentially useful as a diversifier of conventional asset classes: Corbet, Shaen and Meegan, Andrew and Larkin, Charles James and Lucey, Brian M. and Yarovaya, Larisa, Exploring ...


6

To understand the fundamentals of rates trading, I would begin by understanding the fundamentals of derivatives markets. Usually, it is easiest to understand the concepts through simple equity derivatives before moving on to the more complex interest rate derivatives. All of this is explained well in the classic Options, Futures, and Other Derivatives by ...


6

I would recommend Cochrane as well. Pros Deals with both theoretical and empirical asset pricing. Nice mix of intuition and math. Cochrane has videos from his class on Asset Pricing on Youtube, so if you get stuck on a subject you can use a video to gain some quick intuition. Great treatment of the differences between cross sectional and time series ...


6

I'm not aware of any great reference. However Peter Nash Effective product control: controlling for trading desks. Wiley (2018) chapter 10 Review of Mark-to-Market P&L is a good start. Andrew Colin Mastering Attribution in Finance: A practitioner's guide to risk-based analysis of investment returns. FT Publishing International (2015) is worth a look too. ...


6

It is covered very nicely in Iain Clark's Foreign Exchange Option Pricing, A Practitioner’s Guide (pages 98-104). The book also contains references to the relevant literature including Feller's original paper.


5

There is Monte Carlo Simulation and there is Monte Carlo Simulation. If you are referring to a simple question like simulating dice or calculation of $\pi$ or even vanilla option price calculation, it is one thing and "concisely" available. I recommend get a gist of small examples from CS books and then get on with finance. But if you are referring ...


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