Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees

Jagdish Gnawali; Abootaleb Shirvani; Svetlozar T. Rachev

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arXiv · 2506.12694

Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees

Jagdish Gnawali·Abootaleb Shirvani·Svetlozar T. Rachev

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Abstract

We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm's asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages: first, we calibrate the asset volatility using the Black-Scholes-Merton (BSM) formula; second, we recover implied mean return and probability surfaces under the physical measure. To achieve this, we construct a recombining binomial tree under the real-world (natural) measure, assuming a fixed initial asset value. The volatility input is taken from a specific region of the implied volatility surface - based on moneyness and maturity - which then informs the calibration of drift and probability. A novel mapping is established between risk-neutral and physical parameters, enabling construction of implied surfaces that reflect the market's credit expectations and offer practical tools for stress testing and credit risk analysis.

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Jagdish Gnawali, Abootaleb Shirvani, Svetlozar T. Rachev. 2025-06-15. Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees. https://arxiv.org/abs/2506.12694

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