Calibration to market-implied risk measures

Vortrag von Gabriele Visentin

Datum: 03.10.24  Zeit: 12.15 - 13.45  Raum: Y27H12

Abstract: In incomplete market models the interval of arbitrage-free prices for a contingent claim is typically very wide, with different prices corresponding to radically different hedging risks. The classical approach to model calibration consists in estimating a single martingale measure for the underlying asset by matching the observed mid prices of some calibration instruments (typically a selection of ATM call/put options) and using the resulting measure as a linear pricing rule for pricing new claims. This approach does not explicitly take into account market-implied risk preferences and, when used to price exotic or bespoke contingent claims, it may yield prices that are far from realistic market valuations and hedging positions that can only be liquidated at a loss. In this work we present an alternative approach to model calibration, in which we directly estimate the market-implied risk measure that corresponds to the observed bid and ask prices of the calibration instruments. This approach is related to the literature on good deal bounds and is based on machine learning techniques, which combine deep hedging under convex risk measures with adversarial machine learning. We present empirical results on synthetic and real datasets and investigate the stability of the market-implied risk measures in time.