A Topological Approach to Parameterizing Deep Hedging Networks

The classical hedging problem entails replicating the payoff of a contingent claim under a certain stochastic model. While we can find a complete hedging strategy in a complete market like Black-Scholes, a market is in general incomplete, including jump diffusion, and stochastic volatility models. While there are several hedging approaches in an incomplete market, it is often very difficult to get a closed form solution or even calculate numerically. Even in a complete market like Black-Scholes, there are drawbacks to this strategy in both execution and the theory it is based on. A traditional asset pricing and hedging method assumes frictionless markets, perfect liquidity, and normally distributed returns among many other conditions.