Asian option valuation under price impact

Battle Count: 85

Highly relevant for quantitative trading desks dealing with Asian options in equity, FX, and commodity markets. The framework directly addresses the practical problem of hedging path-dependent derivatives when trading moves the market. The endogenous bid-ask spread analysis is directly applicable to dealer pricing and risk management. The super-linear spread growth with impact parameters and the counterintuitive finding that lower execution costs widen spreads are practically important insights. However, the paper is primarily theoretical and would require calibration and implementation work before direct trading use.

The numerical scheme requires solving a 4D backward induction problem (log-price, impact state, running average, control) with correlated Brownian increments and monotone interpolation for off-grid values. The HJB equation involves pointwise optimization over the control set at each grid node. Grid sizes of 61x41x41x51 with 30 time steps are manageable but non-trivial. The closed-form geometric Asian result is straightforward to implement. The main complexity lies in the endogenous Bellman recursion and ensuring numerical stability across the impact parameter space.

The paper provides detailed parameter tables (Table 1), explicit closed-form formulas (Theorem 3.2), full HJB equations, and a complete Bellman recursion algorithm (Algorithm 1). All numerical experiments use specified base-case parameters. However, no code repository is provided, and some numerical details (interpolation schemes, grid construction) are described at a high level. The theoretical derivations are complete and self-contained.