Reduktionsmodelle zur Kreditderivatebewertung

Sequential Warrant Exercise in Large Trader Economies

It is well known that the sequential (premature) exercise of American-type warrants "may" be advantageous for large warrantholders, even in the absence of regular dividends, because using exercise proceeds to expand the firm's scale increases the riskiness of an equity share. We present sufficient conditions for the non-optimality of sequential exercise implying that for realistic interest rate levels even large warrantholders are better off not to exercise long before maturity. This result, however, does not justify in general the simplifying restriction that warrants or convertible securities are valued as if exercised as a block.

Robust Recovery Risk Hedging: Only the First Moment Matters

Credit derivatives are subject to at least two sources of risk: the default time and the recovery payment. This paper examines the impact of modeling the recovery payment on hedging strategies in a reduced-form model as well as a structural model. We show that all hedging approaches based on a quadratic criterion do only depend on the expected recovery payment at default and not the whole shape of the recovery payment distribution if the underlying hedging instrument (say, a defaultable zero coupon bond) jumps to or reaches a pre-specified value when the credit event occurs. This justifies assuming a \emph{certain} recovery rate conditional on default time and interest rate level. Hence, th…

A Reduced-Form Model for Warrant Valuation

This paper studies warrant valuation using a reduced-form model. Analogous to the credit risk literature, structural models require complete information about the asset value process and the firm’s liabilities. In contrast, reduced-form models require only information about the firm’s stock price process. We introduce a reduced-form model where the warrant holder is a price taker, and we relate our model to structural models appearing in the literature.

Jump-diffusion models of German stock returns

This paper discusses the statistical properties of jump-diffusion processes and reports on parameter estimates for the DAX stock index and 48 German stocks with traded options. It is found that a Poisson-type jump-diffusion process can explain the high levels of kurtosis and skewness of observed return distributions of German stocks. Furthermore, we demonstrate that the return dynamics of the DAX include a statistically significant jump component except for a few sample subperiods. This finding is seen to be inconsistent with asset pricing models assuming that the jump component of the stock's return is unsystematic and diversifiable in the market portfolio.

Warrant Exercise and Bond Conversion in Large Trader Economies

It is well known that the sequential (premature) exercise of American-type warrants may be advantageous for large warrantholders, even in the absence of regular dividends, because using exercise proceeds to repurchase stock or to expand the firm's scale increases the riskiness of an equity share. We present an upper bound on this advantage and show that this advantage is negligible for a realistic parameter setting. This result, however, does not justify in general the simplifying restriction that warrants or convertible securities are valued as if exercised as a block. It turns out that the option to exercise only a fraction of the outstanding convertibles at the maturity date (partial exe…

Optimal control of option portfolios and applications

We present an expected utility maximisation framework for optimally controlling a portfolio of options. By combining the replication approach to option pricing with ideas of the martingale approach to (stock) portfolio optimisation we arrive at an explicit solution of the option portfolio problem. Its characteristics are illustrated by some specific examples. As an application, we calculate an optimal option and consumption strategy for an investor who is obliged to hold a stock position until the time horizon.

Continuous-time portfolio optimization under terminal wealth constraints

Typically portfolio analysis is based on the expected utility or the mean-variance approach. Although the expected utility approach is the more general one, practitioners still appreciate the mean-variance approach. We give a common framework including both types of selection criteria as special cases by considering portfolio problems with terminal wealth constraints. Moreover, we propose a solution method for such constrained problems.

Impact of Stock Price Jumps on Option Values

Many empirical papers document the fact that the distribution of stock returns exhibits fatter tails than would be expected from a normal distribution. This might explain some of the pricing biases of the Black/Scholes model, which is] based on a normal return distribution. Given this result, alternative option pricing models should be based on one of the following three classes of return models: (1) a stationary process, such as a paretian stable or a student’s t-distribution, (2) a mixture of stationary distributions, such as two normal distributions with different means or variances, or a mixture of a diflusion and a pure jump process, or (3) a distribution such as a normal distribution …

Local Expected Shortfall-Hedging

This paper proposes a self-financing trading strategy that minimizes the expected shortfall locally when hedging a European contingent claim. A positive shortfall occurs if the hedger is not willing to follow a perfect hedging or a superhedging strategy. In contrast to the classical variance criterion, the expected shortfall criterion depends only on undesirable outcomes where the terminal value of the written option exceeds the terminal value of the hedge portfolio. Searching a strategy which minimizes the expected shortfall is equivalent to the iterative solution of linear programs whose number increases exponentially with respect to the number of trading dates. Therefore, we partition th…