Closed-form pricing for arithmetic Asian options in Heston and Black–Scholes models

Determine whether an explicit closed-form pricing formula exists for arithmetic Asian options—options whose payoff depends on the arithmetic average A[0,T] = (1/T)∫_0^T S_u du—under the Heston stochastic volatility model and under the Black–Scholes model.

Background

The paper focuses on geometric Asian options in the Volterra–Heston framework and explicitly notes that arithmetic Asian options, whose payoff depends on the arithmetic mean of the underlying, lack known closed-form solutions in widely used models. In particular, the authors highlight that no explicit closed-form solution is known in the classical Heston model, and this is already the case for the Black–Scholes model.

Because deriving closed-form solutions enables efficient pricing and calibration, the absence of known explicit formulas for arithmetic Asian options motivates the choice to paper geometric versions, for which closed-form or semi-closed representations can be obtained via Fourier methods.