Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees
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| Format: | Preprint |
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2025
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| _version_ | 1866916794268123136 |
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| author | Gnawali, Jagdish Shirvani, Abootaleb Rachev, Svetlozar T. |
| author_facet | Gnawali, Jagdish Shirvani, Abootaleb Rachev, Svetlozar T. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_12694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees Gnawali, Jagdish Shirvani, Abootaleb Rachev, Svetlozar T. Risk Management Computational Finance 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. |
| title | Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees |
| topic | Risk Management Computational Finance |
| url | https://arxiv.org/abs/2506.12694 |