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- Title
Construction of a Bivariate Distribution Accounting for Correlation Skew by Alternate Projections.
- Authors
Barc, Romain
- Abstract
A method based on successive adjustments of a discrete bivariate distribution consistently with target marginal distributions is presented, with the motivation of matching the correlation skew for rates and FX markets. Each step performs a permutation of the coordinates to achieve optimal pairing consistently with the spread or cross FX distribution, by ensuring minimal perturbation using the Hoeffding-Fréchet map, as inspired by the theory of optimal transport. A proof of convergence in the special case of evenly distributed coordinates (Monte Carlo simulations) is given using alternate projections onto discrete sets results, although a more efficient version of the algorithm is introduced and investigated with numerical examples. Numerous tests are presented for the convergence speed and calibration to Constant Maturity Swap spread options and cross FX markets. The method is compared with the copula method (used as a starting point of the algorithm), and the Austing model for the FX case, to value exotic payoffs. The robustness and efficiency of the method (it requires only sorting a vector of ℝN at each iteration) makes it easy to adapt in higher dimensions (equity markets) or to use as a tool to spot arbitrage in the rates market.
- Subjects
SWAPS (Finance); MATURITY (Finance); INTEREST rates; STOCK exchanges; ALGORITHMS
- Publication
Journal of Derivatives, 2024, Vol 31, Issue 4, p126
- ISSN
1074-1240
- Publication type
Article
- DOI
10.3905/jod.2024.1.204