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Neural network for pricing and universal static hedging of contingent claims

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  • Vikranth Lokeshwar
  • Vikram Bhardawaj
  • Shashi Jain

Abstract

We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for interpretability of the model, a feature that is often desirable in the financial context. Specifically, the interpretation leads us to demonstrate that any contingent claim -- possibly high dimensional and path-dependent -- under the Markovian and the no-arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. We show how the method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound by exploiting the dual formulation. Unlike other duality based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate through numerical examples the simplicity and efficiency of the method for both pricing and semi-static hedging of path-dependent options

Suggested Citation

  • Vikranth Lokeshwar & Vikram Bhardawaj & Shashi Jain, 2019. "Neural network for pricing and universal static hedging of contingent claims," Papers 1911.11362, arXiv.org.
  • Handle: RePEc:arx:papers:1911.11362
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    References listed on IDEAS

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    Cited by:

    1. Thibault Collin, 2023. "Using Deep Learning to Hedge Rainbow Options," Working Papers hal-04060013, HAL.
    2. Andersson, Kristoffer & Oosterlee, Cornelis W., 2021. "A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Shuaiqiang Liu & 'Alvaro Leitao & Anastasia Borovykh & Cornelis W. Oosterlee, 2020. "On Calibration Neural Networks for extracting implied information from American options," Papers 2001.11786, arXiv.org.

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