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CV estimates cross validation performance when done properly. Can it “correctly” estimate it? In social sciences it is a big fat question. Unless you control regressors it is easy to overestimate oos performance with cv
CV is usually abused to become an equivalent of in sample diagnostics. It can help with overfitting when done properly but it doesn’t “solve “ the problem
@Oscar, nothing truly solves the lack of data problem. Ledoit-Wolf shrinkage addresses a different issue, when your covariance matrix is not PD. The latter happens when you estimate it pair-wise, and some of your stocks have missing data. Missing data is extremely common issue though, so this issue will arise too.
the main issue with pricing options was the discount factor. if you knew the discount rate, then it would have been a trivial exercise of estimating appropriate drift and volatility, then discounting the payout $\max(0,V(s,T))$. however, it is not at all clear what should be the discount factor. that's what is this all about. the simulation or integration is easy if you know the distribution.
We don't know the $S(T)$ but we made a lognormal assumption already, and plug the variance of $\sigma^2$ of the distribution. So, the value today would have been expectation, i.e. you use could that lognormal distribution
Because we trade options. Suppose, I want to buy a put on SPX to protect my SPY position. How much should I pay for the option? Options were traded before BS, but once traders figured how to calc the value the trading volume exploded
you need to structure your question better. too many questions interspersed with statements. extract one or maybe two questions and post here. explain what you understand, what you read etc. focus, in other words
why? consider this, if you have 50 stocks, then covariance matrix has approximately (50x50-50)/2 cells, that's how many parameters you need to estimate, in this case it's 1225. That's a lot of parameters given that you may have used daily observations and there's only 250 trading days in a year. it becomes very difficult to get a stable covariance matrix estimate when the number of stocks increase. so if you use a crappy matrix, your simulations will be lousy and your optimal portfolio will not be so optimal. in simulations you have to simulate your cov matrix too, if want to be realistic
it's actually not as scary as it may seem at first sight. consider this: you obtained some daily returns, then calculated the covariance matrix. your data set was random, i.e. if you obtain the same series in different period you get a different set of values, and (!) a different covariance matrix. hence, your covariance matrix is itself a random object. you're lucky if it's a good estimate of a true covariance matrix. now, when you build your portfolio from this matrix as in textbooks, they rarely tell you that the results is most likely a garbage if the set of stock is large.
