Dependence-sensitive price bounds for compatible block gluings

Compute robust lower and upper price bounds for cross-period payoffs over the set of globally feasible laws sharing the same compatible monthly SPX–VIX calibration blocks, thereby quantifying dependence risk left unidentified by monthly calibration instruments.

Background

The paper shows that monthly calibration blocks determine adjacent laws of the form $(S_i,V_i,S_{i+1})$ but do not determine the dependence structure across multiple volatility windows. A globally feasible law and its SPX-Markovization can therefore agree on every block-local payoff while assigning different prices to cross-period claims.

For compatible local block laws, the authors define a class of global gluings and the infimum and supremum of the expected value of a cross-period payoff over that class. These bounds would measure the model-risk interval generated solely by unidentified temporal dependence; the paper provides a finite-tree example showing that this interval can be non-degenerate but does not compute such bounds for market portfolios.