No purchaser of a sovereign debt instrument today does so in the hope and expectation that when the debt matures the borrower will have the money to repay it. The purchaser does so in the hope and expectation that when the instrument matures the borrower will be able to borrow the money from somebody else in order to repay it. This is a crucial distinction. If by sovereign creditworthiness we mean that a sovereign is expected to be able to generate enough revenue fromn taxes or other sources to repay its debts as they fall due, then most countries are utterly insolvent.
Little experiment to validate that absolute variation tends to infinity, mean squared variation tends to 1 (for standard normal), and the cubic, quartic etc variations tend to 0 (as delta t tends towards 0). This, if I am not mistaken, is why we can do all the tricks we do in Ito calculus.
MATLAB code (my first ever):
function drawExpectationConvergence = drawExpectationConvergence(nstepsmax, moment)
results = zeros(0, nstepsmax);
parfor n = 1:nstepsmax
results(n) = expectation(n, moment);
function expectation = expectation(nsteps, moment)
T = 1.0;
dt = T / nsteps;
sqrt_dt = dt^0.5;
V = 0;
for i = 0:nsteps
V = V + abs((normrnd(0,1)*sqrt_dt)^moment);
expectation = V;