Monotonic transformation and recovering the implied stock price process

Gianluca Fusai ()
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Gianluca Fusai: Bayes Business School (formerly Cass), City, University of London

Decisions in Economics and Finance, 2025, vol. 48, issue 1, No 6, 73-92

Abstract: Abstract The paper demonstrates the construction of a stock price stochastic process that aligns with observed option prices, drawing inspiration from a manuscript by Professor Erio Castagnoli that employs the concept of a non-linear monotonic transformation of a standard Brownian motion. The paper includes a detailed numerical example that illustrates the implementation of this straightforward and ingenious idea.

Keywords: Brownian motion; Implied volatility surface; Monte Carlo simulation; Black-Scholes model; 35K99; 65D05; 35K99; 65D05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10203-024-00447-z

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