Fast-excursion limit of the Heston model

Battle Count: 56

Highly relevant for exotic derivatives pricing desks, particularly for continuously monitored barrier options in FX and equity markets. The paper demonstrates that ignoring excursion risk can lead to ~10% underestimation of hitting probabilities for one-month EURUSD options. This has direct P&L implications for banks selling barrier options. However, the model is primarily theoretical and the practical implementation (simulation, calibration) is still developing. Most relevant for structured products desks and exotic derivatives pricing rather than high-frequency trading or algorithmic execution.

The FEH model itself is simpler to define than classical Heston (Equation 1.1), but the underlying mathematics (random closed sets, Effros σ-algebra, Fell topology, Attouch-Wets metric, subordinated Lévy processes) is highly advanced. Simulation requires working with price-time parametric representations and Brownian bridges. The classical Heston simulation scheme for visualization purposes is complex (random ODEs, adaptive time grids). For practical derivative pricing, the model reduces to NIG Lévy process pricing for vanillas (already available via Mechkov 2015/Numerix), but barrier options require simulating OHLC processes which is more involved.

Code repository is openly available at https://github.com/rmcrkd/fast-excursion-limit. All numerical results are produced by simulation with stated parameters. The mathematical framework is fully specified with proofs. However, the theoretical depth (random closed sets, Effros topology, Attouch-Wets metric) requires significant mathematical background to verify independently. No empirical market data is used.