Stochastic Expansion for the Pricing of Asian and Basket Options

ArXiv ID: 2402.17684 “View on arXiv”

Authors: Unknown

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.

Keywords: Basket Options, Asian Options, Stochastic Taylor Expansion, Black-Scholes Model, Analytical Approximations, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: 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.

  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"]