Paper: arXiv 2407.02901

Abstract

The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of the multivariate process of constituents with a copula model and propose an efficient method to extract the dependency structure from the market. The proposed method generates coherent sets of samples of the constituents process through systematic sampling rearrangement. These samples are then utilized to calibrate a local volatility model (LVM) of the basket process, which is used to price basket derivatives. We show that the method is capable of efficiently pricing basket options based on a large number of basket constituents, accomplishing the calibration process within a matter of seconds, and achieving near-perfect calibration to the index options of the market.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper involves advanced mathematics including copulas, local volatility models, Dupire’s formula, and rearrangement algorithms with heavy LaTeX derivations. It lacks empirical validation such as backtests, code, or statistical metrics, focusing instead on theoretical calibration methods and numerical approximations.

Research Flowchart

  flowchart TD
  A["Research Goal: Efficient Pricing of Basket Options with Volatility Skew"] --> B["Input: Market Data on Basket Constituents"]
  B --> C["Methodology: Construct Samples via Copula-Based Rearrangement"]
  C --> D["Computational Process: Calibrate Local Volatility Model LVM"]
  D --> E["Outcome: Fast Pricing of Basket Derivatives"]
  E --> F["Key Finding: Near-Perfect Calibration to Index Options"]

Cited References (25)

  1. Efficient pricing and calibration of high-dimensional basket options (2023)
  2. The stochastic collocation Monte Carlo Sampler: Highly efficient sampling from “expensive” distributions (2014)
  3. Correlation skew via product copula (2012)
  4. A dynamic model for correlation (2010)
  5. Breaking correlation breaks (2010)
  6. Correlation skew via stochastic correlation and jumps (2015)
  7. On the distribution of sums of random variables with copula-induced dependence (2014)
  8. Smile-consistent basket skew (2023)
and 17 more
  1. Mathematical Modeling and Computation in Finance: With exercises and Python and MATLAB computer codes (2019)
  2. Pricing basket options with skew (2010)
  3. The smile calibration problem solved (2011)
  4. Calibration of local correlation models to basket smiles (2016)
  5. A pairwise local correlation model (2019)
  6. Why is the index smile so steep? (2004)
  7. Euronext Fact Book 2022 (2023) — link
  8. Pricing multiasset equity options: How relevant is the dependence function? (2010)
  9. Pricing multivariate currency options with copulas (2007)
  10. Bivariate option pricing using dynamic copula models (2005)
  11. Prices of state-contingent claims implicit in option prices (1978)
  12. Basket options valuation for a local volatility jump–diffusion model with the asymptotic expansion method (2010)
  13. A generalization of the G livenko- C antelli theorem (1959)
  14. Machine learning: a probabilistic perspective (2012)
  15. Volatility interpolation (2011)
  16. Model uncertainty and VaR aggregation (2013)
  17. A model-free approach to multivariate option pricing (2021)

0 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.