Abstract
This paper presents a structural credit model with underlying stochastic volatility, a CIR process, combining the Black/Cox framework with the Heston Model. We allow to calibrate a Heston Model for a non-observable process as underlying of the Black/Cox Model. A closed-form solution for the price of a down-and-out call option on the assets with the debt as barrier and strike price is derived using the concept of optional sampling. Furthermore, estimators are derived with the Method of Moments for Hidden Markov Chains. As an application in Statistical Finance, the default probabilities of Merrill Lynch during the financial crisis are examined.
Highlights
In order to describe the performance of a company on a daily basis, we can often refer to quoted stock prices only
This paper presents a structural credit model with underlying stochastic volatility, a CIR process, combining the Black/Cox framework with the Heston Model
A closed-form solution for the price of a down-and-out call option on the assets with the debt as barrier and strike price is derived using the concept of optional sampling
Summary
In order to describe the performance of a company on a daily basis, we can often refer to quoted stock prices only. The value is modeled as the value of a down-and-out call option (DOC) with the assets as underlying and the value of the debt as both, knock-out barrier and strike price. Heston Model, which is used here to model the assets allows the company’s assets to have stochastic volatility This model is chosen for its suitability in the pricing of financial products as well as for its closed-form expression for higher conditional moments. This generalization is inspired by the work of Genon-Catalot et al, (2000) and allows for the calibration of the parameters of the asset process.
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