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.

D espite the continuously increasing importance of the asset class private equity 1 there is still only a limited understanding of the main factors inf luencing the returns of private equity investments. Representative data for empirical research is fairly hard to procure, and therefore, only few studies have attempted to shed more light on this interesting topic. 2 Given the widely held expectation that private equity returns should experience only moderate gains or may even decline in the future, 3 there is an increasing necessity to thoroughly grasp the determinants of private equity fund performance.To this end, this article extends the existing literature in several ways. First, this research investigates the inf luence on private equity fund performance of numerous endogenous and exogenous factors that have barely been considered by other studies so far. 4 Endogenous factors, that is, information already provided by the database for each fund, include the region, the industry sector, and the financing stage (venture capital/buyout) of each deal as well as the vintage year and the general partner (GP) of each fund. Exogenous factors, that is, information drawn from other sources, include the performance of the public market, interest rates, and GDP growth. With the exact timing and value of the cash f lows of the private equity investments being available, we were able to match these exogenous factors with the information in our private equity fund database and thus are able to draw interesting conclusions.Second, the results presented in this article contribute further evidence of empirically already observed yet contended concepts: The relevance of a GP's experience for and the impact of economic growth on private equity fund performance, the money-chasing-deals phenomenon, and the risk-related behavior of successful GPs are substantiated with a data sample that has not been investigated with regard to these issues so far. 5 Third, possible determinants of a private equity fund's performance that are discussed in theory yet still have been largely disregarded by empirical studies are analyzed in this article. Thus, we shed light on the inf luence of interest rates both in the U.S. and Europe as well as the effect of diversification across portfolio companies, financing stages, regions, and target industries on a private equity fund's performance.Fourth, we are able to develop regression models that account for up to 64% of the variation in private equity returns (adjusted R 2 s), which is-given the subject scrutinized-a notably high value. Finally, to our best knowledge, this article is the first to employ a Markov transition and a linear regression analysis with regard to the same data sample. By doing so, we make the conclusions to be drawn from these two methods

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This paper analyzes an intensity-based approach for equity modeling. We use the Cox-Ingersoll-Ross (CIR) process to describe the intensity of the firm's default process. The intensity is purposely linked to the assets of the firm and consequently is also used to explain the equity. We examine two different approaches to link assets and intensity and derive closed-form expressions for the firms' equity under both models. We use the Kalman filter to estimate the parameters of the unobservable intensity process. We demonstrate our approach using historical equity time series data from Merrill Lynch.