A Hybrid Conditional Quadratic-Form and Broadie–Kaya Approach to Arithmetic Asian Option Pricing Under the Heston Model

We develop a hybrid framework for pricing discretely monitored arithmetic Asian options under the Heston stochastic volatility model by extending a positive quadratic-form approximation of correlated lognormal sums. Conditioning on variance endpoints and integrated variances yields a Gaussian representation of the monitored log-prices. Applying the quadratic-form approximation to this conditional distribution produces Laguerre-series formulas for approximate call and put prices. These formulas integrate out the independent stock price randomness, avoiding inner stock path simulation and leaving an outer average over the variance state. A central advantage is that the approximation is accompanied by explicit conditional remainder moments, yielding a strike-independent absolute pricing error bound under a stock price second-moment condition. The framework distinguishes the quadratic approximation error from series truncation, numerical evaluation and input errors, and sampling uncertainty, providing a systematic basis for assessing computed prices. Two implementations combine the conditional formulas with Broadie–Kaya simulation or quadrature based on exactly simulated variance endpoints. Numerical experiments illustrate the error diagnostics and demonstrate how quadrature refinement reduces the additional pricing discrepancy in the tested configuration. The resulting framework combines semi-analytical payoff evaluation with explicit error assessment and alternative variance input implementations for arithmetic Asian option pricing under stochastic volatility.