Super-Replication of Financial Derivatives via Convex Programming

We give a method based on convex programming to calculate the optimal super-replicating and sub-replicating prices and corresponding hedging portfolios of a financial derivative in terms of other financial derivatives in a discrete-time setting. Our method produces a model that matches the super-replicating (or sub-replicating) price within an arbitrary precision and is consistent with the other financial derivatives prices. Applications include robust replication in terms of call prices with various strikes and maturities of forward start options, volatility and variance swaps and derivatives, cliquets calls, barrier options, lookback and Asian options. Numerical examples show that, in some cases, the best super-replicating and/or sub-replicating prices are within 10% of the price obtained by a standard model, but considerably differ from it in other cases. Our method can incorporate bid-ask spreads, interest rates and dividends and various limitations to the diffusion model