2019/11/26 by Vikranth Lokeshwar, Lokeshwar, Vikranth, Vikram Bhardawaj +3
Economics, Econometrics and Finance · #Computational Finance (q-fin.CP) #FOS: Economics and business #Monetary Policy and Economic Impact #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1911.11362
openalex publication_date 2019/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present here a regress later based Monte Carlo approach that uses neural\nnetworks for pricing high-dimensional contingent claims. The choice of specific\narchitecture of the neural networks used in the proposed algorithm provides for\ninterpretability of the model, a feature that is often desirable in the\nfinancial context. Specifically, the interpretation leads us to demonstrate\nthat any contingent claim -- possibly high dimensional and path-dependent --\nunder the Markovian and the no-arbitrage assumptions, can be semi-statically\nhedged using a portfolio of short maturity options. We show how the method can\nbe used to obtain an upper and lower bound to the true price, where the lower\nbound is obtained by following a sub-optimal policy, while the upper bound by\nexploiting the dual formulation. Unlike other duality based upper bounds where\none typically has to resort to nested simulation for constructing\nsuper-martingales, the martingales in the current approach come at no extra\ncost, without the need for any sub-simulations. We demonstrate through\nnumerical examples the simplicity and efficiency of the method for both pricing\nand semi-static hedging of path-dependent options\n