Asian Options

Deep Learning Option Pricing with Market Implied Volatility Surfaces ArXiv ID: 2509.05911 “View on arXiv” Authors: Lijie Ding, Egang Lu, Kin Cheung Abstract We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data for American puts and arithmetic Asian options using QuantLib. To address the high dimensionality of volatility surfaces, we employ a variational autoencoder (VAE) that compresses volatility surfaces across maturities and strikes into a 10-dimensional latent representation. We feed these latent variables, combined with option-specific inputs such as strike and maturity, into a multilayer perceptron to predict option prices. Our model is trained in stages: first to train the VAE for volatility surface compression and reconstruction, then options pricing mapping, and finally fine-tune the entire network end-to-end. The trained pricer achieves high accuracy across American and Asian options, with prediction errors concentrated primarily near long maturities and at-the-money strikes, where absolute bid-ask price differences are known to be large. Our method offers an efficient and scalable approach requiring only a single neural network forward pass and naturally improve with additional data. By bridging volatility surface modeling and option pricing in a unified framework, it provides a fast and flexible alternative to traditional numerical approaches for exotic options. ...

Path-dependent option pricing with two-dimensional PDE using MPDATA ArXiv ID: 2505.24435 “View on arXiv” Authors: Paweł Magnuszewski, Sylwester Arabas Abstract In this paper, we discuss a simple yet robust PDE method for evaluating path-dependent Asian-style options using the non-oscillatory forward-in-time second-order MPDATA finite-difference scheme. The valuation methodology involves casting the Black-Merton-Scholes equation as a transport problem by first transforming it into a homogeneous advection-diffusion PDE via variable substitution, and then expressing the diffusion term as an advective flux using the pseudo-velocity technique. As a result, all terms of the Black-Merton-Sholes equation are consistently represented using a single high-order numerical scheme for the advection operator. We detail the additional steps required to solve the two-dimensional valuation problem compared to MPDATA valuations of vanilla instruments documented in a prior study. Using test cases employing fixed-strike instruments, we validate the solutions against Monte Carlo valuations, as well as against an approximate analytical solution in which geometric instead of arithmetic averaging is used. The analysis highlights the critical importance of the MPDATA corrective steps that improve the solution over the underlying first-order “upwind” step. The introduced valuation scheme is robust: conservative, non-oscillatory, and positive-definite; yet lucid: explicit in time, engendering intuitive stability-condition interpretation and inflow/outflow boundary-condition heuristics. MPDATA is particularly well suited for two-dimensional problems as it is not a dimensionally split scheme. The documented valuation workflow also constitutes a useful two-dimensional case for testing advection schemes featuring both Monte Carlo solutions and analytic bounds. An implementation of the introduced valuation workflow, based on the PyMPDATA package and the Numba Just-In-Time compiler for Python, is provided as free and open source software. ...

Unbiased simulation of Asian options ArXiv ID: 2504.16349 “View on arXiv” Authors: Bruno Bouchard, Xiaolu Tan Abstract We provide an extension of the unbiased simulation method for SDEs developed in Henry-Labordere et al. [“Ann Appl Probab. 27:6 (2017) 1-37”] to a class of path-dependent dynamics, pertaining for Asian options. In our setting, both the payoff and the SDE’s coefficients depend on the (weighted) average of the process or, more precisely, on the integral of the solution to the SDE against a continuous function with bounded variations. In particular, this applies to the numerical resolution of the class of path-dependent PDEs whose regularity, in the sens of Dupire, is studied in Bouchard and Tan [“Ann. I.H.P., to appear”]. ...

Semi-analytical pricing of options written on SOFR futures ArXiv ID: 2409.04903 “View on arXiv” Authors: Unknown Abstract In this paper, we propose a semi-analytical approach to pricing options on SOFR futures where the underlying SOFR follows a time-dependent CEV model. By definition, these options change their type at the beginning of the reference period: before this time, this is an American option written on a SOFR forward price as an underlying, and after this point, this is an arithmetic Asian option with an American style exercise written on the daily SOFR rates. We develop a new version of the GIT method and solve both problems semi-analytically, obtaining the option price, the exercise boundary, and the option Greeks. This work is intended to address the concern that the transfer from LIBOR to SOFR has resulted in a situation in which the options of the key money market (i.e., futures on the reference rate) are options without any pricing model available. Therefore, the trading in options on 3M SOFR futures currently ends before their reference quarter starts, to eliminate the final metamorphosis into exotic options. ...

Computation of Robust Option Prices via Structured Multi-Marginal Martingale Optimal Transport ArXiv ID: 2406.09959 “View on arXiv” Authors: Unknown Abstract We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically computationally challenging due to the martingale constraint, however, by extending the state space we can identify them with problems that exhibit a certain sequential martingale structure. Our method exploits such structures in combination with entropic regularisation, enabling fast computation of optimal solutions and allowing us to solve problems with a large number of marginals. We demonstrate the method by using it for computing robust price bounds for different options, such as lookback options and Asian options. ...

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. ...