6

Physicists typically know PDEs but not stochastic calculus I have a masters in physics, so have a reasonable idea of the usual skillsets a physicist will know (at least at undergraduate level), and also then a masters in mathematical finance, so learnt the hard way the bits of maths physicists typically don't know but will need to know for quantitative ...


5

here is how to get covariance matrix from correlations:


3

The first observation I make is that the proportion of variance is not very high for the first PCs, with the implication that I would hypothesise that the PCs are not very stable, nor reliable. (You can test this by varying the sample period and analysing the consistency of the PCs) If the PCs are not stable from period to period then information you can ...


3

In the Black Scholes (1973) model, the stock price is assumed to follow a geometric Brownian motion $\mathrm{d}S_t=S_t\mu \mathrm{d}t + S_t \sigma \mathrm{d}W_t$. If you solve the SDE, $(S_t)$ is log-normally distributed for every $t$. Alternative, you can model the returns by a normal distribution and then take the exponential function to obtain the stock ...


2

Here is a nice survey of how this model and its alternatives are used by the central banks: https://www.bis.org/publ/bppdf/bispap25a.pdf


2

If I am reading this correctly, ie you are compounding -1x the daily returns, this is exactly what inverse ETFs do. The obvious catch is that you have to rebalance your short holdings every day, killing you in transaction costs. The less obvious, but very significant, risk is that this strategy also invokes "variance drag". Imagine a hypothetical stock ...


2

The relationship between covariance, standard deviation and correlation is: $$ corr(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}$$ So to construct your matrix you will have the variances in the diagonal: $$ cov(x,x) = corr(x,x) \times \sigma_x \times \sigma_x = 1 \times \sigma_x^2 = \sigma_x^2 $$ And for the covariances: $$ cov(x,y) = corr(x,y) \times \...


2

IIRC, the signs of the PC are meaningless. +/-'ive doesn't itself tell you anything. Rather, the cross-sectional, absolute max of the PCs will tell you which one is most important per item (eg: PC6 looks most important for Beta: M-3). I think 6.6a and 6.6b in Cochrane's asset pricing touch on this (https://www.youtube.com/playlist?list=...


2

It's not a great book, but Jan Dash. Quantitative Finance and Risk Management: A Physicist's Approach. World Scientific Publishing Company (2004) takes the approach that you might like - not too much formal math, and not too elementary.


2

The standard error for an estimate of a mean like a mean return - is: $$SE(\bar{r}) = \frac{\sigma}{\sqrt{T}}$$ Now for the stock market, if σ=0.2 and you have 100 years of data, then the confidence interval for the mean is fairly wide (approx +/- 2%). To expand on @noob2 comment above, yes it was indeed Merton. A summary of Merton's insight below: Log ...


2

As a long practicing plasma physicist who moved into quantdom (now retired), I suggest focusing on stochastic calculus and modeling. How deep you go down the rabbit hole of measure theory will depend on what you do. Simulation will be your friend and help you in many situations. To the excellent suggestions above, I add Paul Glasserman's Monte Carlo Methods ...


1

As a former physicist you will certainly enjoy Jean-Philippe Bouchaud’s approach. Pragmatic and empirical with simple models that are sophisticated enough to be useful. Check out “Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management” and “Trades, Quotes and Prices: Financial Markets Under the Microscope” in that ...


1

Since you didn't study measure theoretic probability, that would be the first thing I recommend. In my opinion that's the main gap that many physicists on math side, because stochastic calculus is not in mainstream physics curriculum. Whether you first study measure theory in calculus then take on probability, or jump right into measure theoretic ...


1

It looks like $Z(t)$ is dependent on $t$ through $X_t$ and not directly on $t$, loosely speaking. Assume that $Z_t = f(X_t)$ and use Ito's formula with just one variable. $$dZ_t = \frac{df}{dX} dX_t + \frac{1}{2} \frac{d^2f}{dX^2} d[X_t,X_t] $$ Can you proceed and finish it?


1

Probably the simplest place to start is to pick some binarized features and targets and stay very low dimensional. You can look at mutual information or other distributional estimates to test for causal linkages. I think typically most causal network discovery is either a full sweep or some heuristic basiced on Lasso in higher dimensions. Prado has a lot ...


1

Let’s put it this way. Classic MV is still used, but its shortcomings are universally appreciated. In its favour, the process is logical, conceptually intuitive, and non-quants easily understand it. But the optimisation produces some very unintuitive results, no different to multicollinearity effects in regression analysis. That’s a harder one for the non-...


1

In a CAPM framework, the Beta of Y to X = Correlation * Y Volatility/X Volatility. Which alternatively is Covariance / X Volatility So to (1) above, it's your latter formulation not the reciprocal. To (2) above, you could use prices rather than returns, but this can be problematic depending on the precise thing you want to measure. It's generally ...


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