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There is nothing in simple cubic spline fitting routines that would prevent arbitrage. Even with conscientious use of knot points and smoothing techniques you may end up with simple spread and local volatility arbitrage conditions. Stochastic volatility models on the other hand can explicitly constrain your solutions to prevent call/ put spread arbitrage at ...


3

Typically, strategists run a regression of changes in implied vols against changes in rates. If rates are highly directional with implied vols (regression coefficient is positive and statistically significant), then it would imply a more lognormal relationship. If the two series are not correlated or very weakly correlated, then the relationship is ...


2

One of the most used interpolation techniques is the cubic spline interpolation. Here you can find an overview of that, while, on Mathworks.com, you can find the tutorial to implement that in Matlab directly simply by using the spline(x,Y,xx) command function. It is not difficult to implement and, moreover, it gives pretty reliable results. I never tried ...


1

I'm not sure that machine learning would lead to any practical solutions here. Do you really have enough data for that kind of techniques? I would suggest a different approach: assume that the exercise is optimal, but just based on a different cost function than the expected pay-off. If you can find a function that replicates well enough the past exercise ...


1

Your question is too broad, but I there is plenty of examples of uses of machine learning to mimic human behaviour. For instance deep learning has been used 25 years ago to read checks in banks, or support vector machines 15 years ago to implement artificial vision, or bayesian networks to mimic expert diagnosis. I guess it would not be that hard to use ...


1

American options pricing (swaption is just a kind of option) is a bit tricky due to the early exercise. Here is a page listing possible approaches, including some numeric methods, and some close form approximation formula. As I understand, lattice methods (tree, PDE discretization such as forward shooting) are fine to price American options. There're ...



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