Pricing with Passion: The Local Occupied Volatility (LOV) Model

Battle Count: 59

Highly relevant for quantitative trading desks involved in options market-making, volatility trading, and derivatives pricing. The LOV model directly addresses the practical problem of jointly calibrating American and European options on single-name equities, which is a daily challenge for equity derivatives desks. The path-dependent volatility captures realistic spot-vol dynamics (leverage effect, volatility clustering) important for hedging exotic options and managing gamma/vega risk. The neural calibration approach enables fast re-calibration for trading systems.

High complexity due to: (1) path-dependent SDE simulation requiring occupation measure tracking across M=63 corridors, (2) McKean-type dynamics requiring particle method for projected occupation measures, (3) LSMC for American option pricing with occupation-time regressors, (4) neural network calibration with stochastic gradient descent over full option chain, (5) careful handling of positivity constraints on variance, (6) antithetic variates and multiple path generation. However, the paper provides complete pseudocode (Algorithms 1-2) and specific hyperparameters, reducing implementation ambiguity. Training takes ~10 minutes on CPU, pricing ~20 seconds.

The paper provides detailed algorithms (Algorithm 1 for simulation, Algorithm 2 for neural calibration), explicit parameter choices (M=63 corridors, κ=12, δt=1/252, 2 hidden layers with 64 nodes, ReLU/softplus activations), and specific market data (AMZN, Sept 15 2025, r=3.7%). However, no code repository is provided, market data is from Bloomberg (proprietary), and the neural network initialization details are not fully specified. The mathematical framework is complete and well-defined.