Suppose x(0) = 0 and x is observed at t=1, 2, ..., N, and x(t) = x(t-1) + z(t), where z(t) is N(0,1) (normally distributed). What is the probability that x(0) is either a minimum or maximum of x(0:N), meaning that either all N later observations are positive or all N observations are negative? For N...

https://www.bloomberg.com/news/articles/2020-04-21/negative-oil-prices-are-literally-breaking-traders-risk-models By  Alex Longley ,  Jack Farchy , and  Catherine Ngai April 21, 2020, 4:46 PM EDT   Updated on  April 22, 2020, 5:12 AM EDT   Traditional options models assume prices can’t go below zer...

Shifted Lognormal with lower bound = max storage cost? That's an interesting thought provoking approach.  Luckily, we're not looking at any more negative prices for future deliveries, so for now, threat neutralized,  but I would like to update my model for this if it happens again.  The cost of sto...

Should oil futures prices be modeled as an arithmetic brownian motion rather than a geometric one? Maybe they are arithmetic once the price falls below a certain price level?

I found a paper devoted to my question: The working paper is at http://www.lehrstab-statistik.de/download/papers/SimBrownWP.pdf . Computational Management Science January 2010, 7:1 Exact simulation of final, minimal and maximal values of Brownian motion and jump-diffusions with applications to optio...

Thanks for your help, Alan.

To simulate the terminal value of a standard Brownian motion you just need a random generator of normal deviates. What if you want to jointly simulate the high, low, and terminal values of the Brownian motion? It is known that the average maximum value up to time t = 1 is 1/sqrt(pi/2) = 0.7979. I ha...

Amazon is offering forecasting services to business, using the following models :  ARIMA, DeepAR+, Exponential Smoothing (ETS), Mixture Density Network (MDN), Multiquantile Recurrent Neural Network (MQRNN), Non-Parametric Time Series (NPTS), Prophet, and Spline Quantile Forecaster (SQF). Any thought...

Wall Street Erases the Line Between Its Jocks and Nerds By Liz Hoffman and Telis Demos Wall Street Journal Aug. 18, 2018 Meet the straders. Part risk-taking trader and part computer-whiz “strategist,” they are prowling the halls at Goldman Sachs Group Inc., erasing a once-religious line between the...

HIgh frequency quants are in demand. If you are not already working as one, how do get high-frequency data? It would be nice if there were some publicly available data sets. It is easy to get free historical *daily* data on stock prices. I understand that updated high frequency data will cost money,...

I have commonly seen hedge funds asking for track records with Sharpe ratios in excess of 2 from aspiring portfolio managers or quantitative traders. If I had a Sharpe of 2 I could make $500K on average risking only $250K per year. Why do traders with a few hundred K in savings and Sharpe's > 2 need...

Is Python 2.x or Python 3.x now more common in finance? I am thinking of brushing up my Python skills and am thinking of what to learn. In the long run, I think that finance and scientific computing will move to Python 3, and I never see job advertisements mention Python 2 or Python 3, as opposed to...

I didn't respond earlier because I have a feeling you're maybe not to interested in ML other than career-wise? On the other hand you are young and pre-career and it's very understandable that you try to figure out what to do, and so I didn't want to be negative either. I am a former hedge fund quan...

Proficiency with "machine learning" and "big data" is currently valued in the financial quant job market. What credentials can you acquire to demonstrate such proficiency? For some time there have been master's degree programs in finance that focus on stochastic calculus and deri...

<r>I read a master's thesis Value at Risk: GARCH vs. Stochastic Volatility Models: Empirical Study AbstractThe thesis compares GARCH volatility models and Stochastic Volatility (SV)models with Student's t distributed errors and its empirical forecasting performanceof Value at Risk on ve stock price ...