Three essays on bankruptcy risk

Abstract Market prices of corporate bond spreads and of credit default swap (CDS) rates do not match each other. In this paper, we argue that the liquidity premium, the cheapest-to-deliver (CTD) option and actual market segmentation explain the pricing differences. Using the European transaction data from Reuters and Bloomberg, we estimate the liquidity premium that is time- varying and firm-specific. We show that when time-dependent liquidity premiums are considered, corporate bond spreads and CDS rates behave in a much closer way than previous studies have shown. We find that high equity volatility drives pricing differences that can be explained by the CTD option.

Valuing equity-linked death benefits in jump diffusion models

The paper is motivated by the valuation problem of guaranteed minimum death benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. The stock price process is assumed to be the exponential of a Brownian motion plus an independent compound Poisson process whose upward and downward jumps are modeled by combinations (or mixtures) of exponential distributions. Results for exponential stopping of a Lévy process are used to derive a series of closed-form formulas for call, put, lookback, and barrier options, dynamic fund protection, and dynamic withdrawal benefit with guarantee. We also discuss how barrier options can be used to model lapses and surrenders.