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

TL;DR

This paper develops a method to derive implied probabilities and volatilities in credit risk using a Merton-based model with binomial trees, linking market-implied data to real-world risk assessments.

Contribution

It introduces a novel mapping between risk-neutral and physical measures within a Merton framework using binomial trees, enhancing credit risk modeling and stress testing capabilities.

Findings

Constructed implied probability surfaces from market data

Calibrated asset volatility using implied volatility surfaces

Mapped risk-neutral to physical measures for credit risk analysis

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.