Paper: arXiv 2504.16011

Authors: Fabien Le Floc’h

Abstract

We present closed analytical approximations for the pricing of Asian basket spread options under the Black-Scholes model. The formulae are obtained by using a stochastic Taylor expansion around a log-normal proxy model and are found to be highly accurate for Asian and spread options in practice. Unlike other approaches, they do not require any numerical integration or root solving.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated analytical expansion technique using stochastic Taylor expansions to price Asian basket spread options under Black-Scholes. While mathematically sound with clear step-by-step derivations and proxy definitions, the excerpt lacks empirical backtesting or extensive numerical experiments in the provided text.

Research Flowchart

  flowchart TD
    A["Research Goal: Fast, closed-form pricing for Asian Basket Spread Options without numerical integration"] --> B["Inputs: Black-Scholes Model Parameters (Asset Prices, Volatilities, Correlations, Strikes)"]
    B --> C["Select Log-Normal Proxy Model as Base Approximation"]
    C --> D["Apply Stochastic Taylor Expansion around Proxy Model"]
    D --> E["Derive Analytical Formulae (No Root-Solving Required)"]
    E --> F["Outcomes: Highly Accurate Closed-Form Pricing for Complex Asian & Spread Derivatives"]

Cited References (30)

  1. Recent advances in randomized quasi-Monte Carlo methods (2002)
  2. Stochastic Expansion for the Pricing of Asian and Basket Options — → 2402.17684
  3. Pricing and hedging Asian basket spread options (2010)
  4. A general closed form approximation pricing formula for basket and multi-asset spread options (2016)
  5. An efficient approach for pricing spread options (1999)
  6. Correlation in the energy markets (1995)
  7. The value of an option to exchange one asset for another (1978)
  8. Closed form spread option valuation (2014)
and 22 more
  1. A closed form approach to the valuation and hedging of basket and spread options (2007)
  2. Asian basket spreads and other exotic averaging options (2003)
  3. Pricing Asian and basket options via Taylor expansion (2002)
  4. Basket weaving (1993)
  5. Commodity option pricing: a practitioner’s guide (2014)
  6. Matching Sensitivities to Discrete Dividends: A New Approach for Pricing Vanillas (2011)
  7. Fast Valuation for European Options With Cash Dividends (2011)
  8. Efficient pricing of derivatives on assets with discrete dividends (2006)
  9. The pricing of vanilla options with cash dividends as a classic vanilla basket option problem (2021) — link
  10. The pricing of Asian options on average spot with average strike (2003)
  11. An analysis of pricing methods for baskets options (2004)
  12. Partially exact and bounded approximations for arithmetic Asian options (2005)
  13. The pricing of an Asian option on a basket of futures (Nederlandse titel:“Het prijzen van Aziatische opties op baskets van futures”) (2013)
  14. Valuing Asian and portfolio options by conditioning on the geometric mean price (1994)
  15. Moment matching approximation of Asian basket option prices (2010)
  16. Stochastic expansion for the pricing of call options with discrete dividends (2012)
  17. More Stochastic Expansions for the Pricing of Vanilla Options with Cash Dividends (2015)
  18. Pricing European average rate currency options (1992)
  19. Unified pricing of Asian options (2002)
  20. Prices and hedge ratios of average exchange rate options (1992)
  21. Efficient pricing of European -style Asian options under exponential L 'e vy processes based on Fourier cosine expansions (2013)
  22. Accurate closed-form approximation for pricing Asian and basket options (2008)

1 of 30 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.