Dear Experts -- Happy Sunday :-)  Typically when calibrating an interest rate model (e.g. Cox-Ingersoll-Ross) for multiple short rates (e.g. 3-month, 6-month, 1 year etc.), do practitioners use Cholesky decomposition and take the product of the lower triangular from the Cholesky and the vector of ra...

Thanks bearish. Either my historical returns data is too small and/or my mean-variance optimization logic is flawed. I share aspects of both below, and would be most grateful if you can provide me with any pointers as to where the blunder is! (1) On the data I'm using, please see below data. This sh...

@bearish -- Simple question on your comment "....  In a model with stochastic interest rates under the standard risk neutral measure you also need to discount with the money market account inside the expectation, which gives rise to a covariance term between the short rate and the change in the...

About 20% of my current role involves building predictive models using time series analysis. But I am a million miles away from being an expert at this, although most of the forecasts I make come "reasonably" close to reality when we look back 6 months from the time of the forecast. Also f...

Thanks Katastrofa. No, I didn't use any historical data. The delta-hedging is assumed to be carried out 90 days into the future. But yes, on day one of the delta hedging setup, I used historical (realized) volatility and not implied volatility in coming up with a value for the call premium (from Bla...

Bearish -- For each 30-day performance window, I am using the covariance matrix from 223 historical monthly returns in optimizing the portfolio. How is that a short window, please? For each window, I look back 252 days and get the rolling 30-day returns, and I get 223 of such rolling 30-day returns....

Fundamental question on mean-variance optimization, please. For the historical period 2016 through 2023, I picked 30 day windows and have 300 such windows. At the start of each of those windows, I construct 2 portfolios, both containing the same exact assets (shown down below in the form of a Python...

Thanks Alan and Katastrofa. There's no model involved here.

Thanks Katastrofa. I spent more time on this and came up with below. It's true I'm not accounting for transaction costs, but compared to the magnitude of negative P&L on below Exhibits I and IV, transaction costs should rachet up to only a relatively small number. So, that shouldn't be a factor....

Okay -- fixed a small bug. I wasn't actually changing the volatility factor and the hedging frequency in my nested for-loop. After the fix, there is a slight pattern. Any other thoughts / comments anyone, please?

Please see below graph showing the average hedging P&L from periodically delta hedging a short call position on SPY using a long SPY ETF position and cash. I varied the volatility by multiplying it with factors ranging from 0.5 to 2, and varied the hedging frequency from 1 day (i.e. everyday) to...

Makes sense. Thanks Bearish. You're right it can happen for fractions of a second and high frequency trading shops presumably take advantage of those autocorrelations in the micro/nano second time duration.

Thanks much! As a general rule when computing N(d1), should I use the spot price or the forward price i.e. ln(S/K) or ln((S*exp(-rT))/K)? P.S. That volatility of 0.8% is real! That's the S&P500 volatility of daily returns over the past 30 days, where I computed returns as computed as ln(P_t+1 / ...

That was amazing! I re-computed the N(d1) using ln((S*exp(-r * T)) / K) instead of ln(S/K) and the delta is now 0.492 =~ 0.5! Thanks Bearish -- that really helped! So is it the case that when anyone mentions money-ness in the options space, it's ALWAYS with respect to the forward and not the spot pr...

Are returns autocorrelations really close to zero? Doesn't momentum in a stock's ascent or descent that we commonly see mean returns could be autocorrelated, albeit for a short while?