Stable reconstruction of the volatility in a regime-switching local\n volatility model

2017/10/09 by Mourad Bellassoued, Bellassoued, Mourad, Raymond Brummelhuis +5
Economics, Econometrics and Finance · #35K10 #35R30 #91G80 #Analysis of PDEs (math.AP) #FOS: Mathematics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1710.03172

openalex publication_date 2017/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Prices of European call options in a regime-switching local volatility model\ncan be computed by solving a parabolic system which generalises the classical\nBlack and Scholes equation, giving these prices as functionals of the local\nvolatilities. We prove Lipschitz stability for the inverse problem of\ndetermining the local volatilities from quoted call option prices for a range\nof strikes, if the calls are indexed by the different states of the continuous\nMarkov chain which governs the regime switches.\n

Citations

• The Pricing of Options and Corporate Liabilities

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