Paper: arXiv 2402.17684

Abstract

We present closed analytical approximations for the pricing of basket options, also applicable to Asian options with discrete averaging under the Black-Scholes model with time-dependent parameters. 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 options in practice as well as for vanilla options with discrete dividends.

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 presents advanced mathematical derivations using stochastic Taylor expansions and measure changes, resulting in complex analytical approximations, but lacks empirical validation through backtests or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Accurate pricing for Asian/Basket options"] --> B{"Methodology"}
  B --> C["Log-normal proxy model"]
  B --> D["Stochastic Taylor expansion"]
  C & D --> E["Closed analytical approximations"]
  E --> F["Verification / Computation"]
  F --> G["Key Outcomes<br>High accuracy for Asian options &<br>Discrete dividends"]