In this paper, we evaluate American-style, path-dependent derivatives with an artificial intelligence technique. Specifically, we use swarm intelligence to find the optimal exercise boundary for an American-style derivative. Swarm intelligence is particularly efficient (regarding computation and accuracy) in solving high-dimensional optimization problems and hence, is perfectly suitable for valuing complex American-style derivatives (e.g., multiple-asset, path-dependent) which require a high-dimensional optimal exercise boundary.

In this article, the authors provide a unified valuation framework under which a multicurve economy can be established and caps/floors and swaptions can be consistently priced. Furthermore, if a lognormal distribution is employed for the forward price (or 1 plus forward rate), then a “model-free” volatility calibration can be achieved, and all swaptions and caps/floors are perfectly repriced. This article leverages earlier work by Chen, Hsieh, and Huang (2017) who fix a crucial drift-adjustment problem of the traditional LIBOR market model (LMM) where the LIBOR rates follow a lognormal distribution. By assuming 1 + LIBOR to be lognormal (hence LIBOR is shifted lognormal), Chen, Hsieh, and Huang achieve an exact and deterministic drift-adjustment term. In this article, they extend the model to provide a perfect calibration to both swaptions and caps/floors (which is not doable under the traditional LMM), and by using a foreign currency analogy, they show that the model supports multiple curves, which is a key element to overnight index swap (OIS) discounting.

Predicting future price movements has always been one of the major topics in financial research, and there is no better method to predict the future prices of an asset than using its derivatives. In this paper, we propose a model-free lattice model that describes the complete price evolution of the underlying asset and simultaneously re-prices all of its European options. Given that such a lattice is consistent with market option prices, it must embed all necessary risk factors (e.g., random volatility, random interest rates, and jumps) and market restrictions (e.g., mean-reversion and liquidity) that are priced into the European options.