Logistics, Business & Public Policy

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Author: search.filters.author.Madan, Dilip B.

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    Arbitrage Free Approximations to Candidate Volatility Surface Quotations
    (MDPI, 2019-04-21) Madan, Dilip B.; Schoutens, Wim
    It is argued that the growth in the breadth of option strikes traded after the financial crisis of 2008 poses difficulties for the use of Fourier inversion methodologies in volatility surface calibration. Continuous time Markov chain approximations are proposed as an alternative. They are shown to be adequate, competitive, and stable though slow for the moment. Further research can be devoted to speed enhancements. The Markov chain approximation is general and not constrained to processes with independent increments. Calibrations are illustrated for data on 2695 options across 28 maturities for 𝑆𝑃𝑌 as at 8 February 2018.
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    Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices
    (MDPI, 2021-08-04) Madan, Dilip B.; Wang, King
    Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first perspective uses a geometric two-dimensional Brownian motion model. The second inverts two-dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.