Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms

Even if the correct modeling of default dependence is essential for the valuation of portfolio credit derivatives, for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equalpairwise correlationsfor all assets in the reference portfolio has become the standard market model. If this model were a re?ection of market opinion, there wouldn't be the implied correlation smilethatis observedinthe market. Thepurposeof thispaperistoderive a correlation structure from observed CDO tranche spreads. The correlation structure is chosen such that all tranche spreads of the traded CDO can be reproduced. This implied correlation structure can then be used to price o?-market tranches with the same underlying as the traded CDO. Using this approach we can significantly reduce the risk to misprice o?-market derivatives. Due to the complexity of the optimization problem we apply Evolutionary Algorithms. --

Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms

Even if the correct modeling of default dependence is essential for the valuation of portfolio credit derivatives, for the pricing of synthetic CDOs a one-factor Gaussian copula model with constant and equal pairwise correlations for all assets in the reference portfolio has become the standard market model. If this model were a reflection of market opinion, there wouldn't be the implied correlation smile that is observed in the market. The purpose of this paper is to derive a cor-relation structure from observed CDO tranche spreads. The correlation structure is chosen such that all tranche spreads of the traded CDO can be reproduced. This implied correlation structure can then be used to price off-market tranches with the same underlying as the traded CDO. Using this approach we can significantly reduce the risk to misprice off-market derivatives. Due to the complexity of the optimization problem we apply Evolutionary Algorithms

Evolutionary estimation of a Coupled Markov Chain credit risk model

There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions and thereby default probabilities of companies. As the likelihood of the model turns out to be a non-convex function of the parameters to be estimated, we apply heuristics to find the ML estimators. To this extent, we outline the model and its likelihood function, and present both a Particle Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm to maximize the likelihood function. Numerical results are shown which suggest a further application of evolutionary optimization techniques for credit risk management

Pricing American options with Mellin transforms

Mellin transforms in option pricing theory were introduced by Panini and Srivastav (2004). In this contribution, we generalize their results to European power options. We derive Black-Scholes-Merton-like valuation formulas for European power put options using Mellin transforms. Thereafter, we restrict our attention to plain vanilla options on dividend-paying stocks and derive the integral equations to determine the free boundary and the price of American put options using Mellin transforms. We recover a result found by Kim (1990) regarding the optimal exercise price of American put options at expiry and prove the equivalence of integral representations herein, the representation derived by Kim (1990), Jacka (1991), and by Carr et al. (1992). Finally, we extend the results obtained in Panini and Srivastav (2005) and show how the Mellin transform approach can be used to derive the valuation formula for perpetual American put options on dividend-paying stocks. --Mellin transform,Power option,American put option,Free boundary,Integral representation

Valuing options in Heston's stochastic volatility model: Another analytical approach

We are concerned with the valuation of European options in Heston's stochastic volatility model with correlation. Based on Mellin transforms we present new closed-form solutions for the price of European options and hedging parameters. In contrast to Fourier-based approaches where the transformation variable is usually the log-stock price at maturity, our framework focuses on transforming the current stock price. Our solution has the nice feature that similar to the approach of Carr and Madan (1999) it requires only a single integration. We make numerical tests to compare our results to Heston's solution based on Fourier inversion and investigate the accuracy of the derived pricing formulae. --Stochastic volatility,European option,Mellin transform

Insider trading in Germany: Do corporate insiders exploit inside information?

Our study analyzes a large sample of transactions carried out by corporate insiders reported to the German regulatory authority BaFin in the period July 1, 2002 to April 30, 2005 employing event study methodology. In particular, we focus on the question whether corporate insiders exploit inside information while trading in their company's stock. Therefore we use a distinct property of German law, i.e. company's obligation to reveal inside information through ad-hoc news disclosures, to link trading of insiders to their foreknowledge of important corporate news. We find strong evidence that insiders exploit inside information as they earn above average profits by front-running on subsequent news disclosures. Furthermore, looking at the type of insider, we find that members of the supervisory board (directors) and the group of other insiders (basically family members of senior managers and directors) profit substantially from exploiting inside information. In contrast, members of the executive board (senior managers) can be largely exculpated from exploiting inside information as they realize below average returns with their rare front-running transactions. --insider trading,inside information,§15a WpHG,German stock market,regulation of financial markets

Credibility theory and filter theory in discrete and continuous time

It is well known that credibility theory in discrete time is closely related to the discrete technique of Kalman filtering. In this paper we show the close relationship between credibility theory and filter theory in discrete and continuous time as well as between credibility theory in a discrete and continuous time setting. --

The proximity-concentration trade-off in a dynamic framework

This paper presents a dynamic framework which implements risk as a continuous variable into the proximity-concentration trade-of concept. Additionally firms have the possibility to postpone their investment decision which gives them the possibility to collect further information about the volatile variable over time. On the basis of the real option theory (Dixit and Pindyck, 1994) an investment plan under uncertainty is derived. In contrast to static models firms postpone their investment decision although positive returns can be achieved. For specific risk values the model predicts, in the presence of a foreign direct investment choice, the export strategy can be rejected although it is dominating the FDI project and although it is worthier than its option value. The results of the model undermine empirical findings which analyze the impact of continuous variables on export and FDI patterns. --export,FDI,uncertainty,real option approach

Creditor coordination with social learning and endogenous timing of credit decisions

In case of multiple source lending even solvent firms may be forced into bankruptcy due to uncoordinated credit withdrawals of their lenders. This paper analyzes whether a debtor firm can thwart such inefficient liquidations by offering creditors the option to delay their foreclosure decision rather than obliging them to simultaneous actions as suggested by Morris and Shin (2004). With this option, lenders can endogenously determine the timing of their credit decisions, trading of the informational benefit from waiting against the associated cost of delay. Our results state that the option to delay diminishes creditor coordination failure whenever the firm is expected to be in distress. --global games,creditor coordination failure,option to delay,social learning

Phase coexistence in a forecasting game

Individual choices are either based on personal experience or on information provided by peers. The latter case, causes individuals to conform to the majority in their neighborhood. Such herding behavior may be very efficient in aggregating disperse private information, thereby revealing the optimal choice. However if the majority relies on herding, this mechanism may dramatically fail to aggregate correctly the information, causing the majority adopting the wrong choice. We address these issues in a simple model of interacting agents who aim at giving a correct forecast of a public variable, either seeking private information or resorting to herding. As the fraction of herders increases, the model features a phase transition beyond which a state where most agents make the correct forecast coexists with one where most of them are wrong. Simple strategic considerations suggest that indeed such a system of agents self-organizes deep in the coexistence region. There, agents tend to agree much more among themselves than with what they aim at forecasting, as found in recent empirical studies