abstracts

• Herman Brodie, Cognitrend

Behavioral Finance: How to Model Investor Adaptation to Changing Levels of Wealth/Performance
Happiness resarchers know that despite improving conditions (lottery winners) or worsening conditions (accident victims) people tend to revert to baseline happiness levels after a certain time; they get used to it. Could adaptation explain why investors are able to hold onto stocks as they lose 95% and more?

• Dr Diana Diaz, Dresdner Bank

What drives Credit Risk in Emerging Markets? The Role of Country Fundamentals and Market Co-movements
This paper uses bond prices to investigate how the creditworthiness of Argentina, Brazil, Mexico and Venezuela is influenced by global, regional and country-specific factors. Each country’s distance-to-default is estimated monthly for 1994 to 2001, by fitting the structural model of Cathcart and El Jahel (2003) with a Kalman filter to Brady bonds. A small set of variables is able to explain up to 80% of the variance of the estimated distance-to-default for each country. Surprisingly, country-specific variables account for only about 8% of the explained variance; the largest part of the variance (45%) is explained by regional factors, which relate to joint stock-market returns, volatility and market sentiment; global conditions, related mainly to US stock-market returns, explain another 25% of the variance. Of the 20% variance which remains unexplained, more than half is due to another common (but unidentified) factor. The conclusion is that the creditworthiness of these four emerging markets is driven mainly by a common set of factors, which are related closely to stock-markets in the region and the US. This is joint work with Gordon Gemmill (Warwick Business School).
[paper], [slides]

• Dr Vitaly Dovgal, Capital Markets Trading GmbH, Frankfurt

Efficient computations for the local volatility model and consistent pricing of multiunderlying derivatives
After years of intensive development of derivative markets around the world, the local volatility approach turned out to be one of the most widely used pricing models despite of some serious arguments against it. In this talk the author would like to dispute again theoretical and practical issues around the local volatility approach and propose some original computational solutions providing efficient calibrating of the model for particular derivative markets. Within these solutions he will consider a new approach for pricing of such widespread multiunderlying derivatives as basket options or options on min/max of N assets, where N is not necessarily small. This approach allows to keep prices and risks of these options consistent with the individual assets volatility structures. As well it improves the speed and presicion of calculations as a result of reducing the Monte-Carlo part significantly if not sometimes completely.
[slides]

• Dr Hans-Peter Deutsch, d-fine

Portfolio Theory with a Drift
In this talk we introduce the Deutsch Ratio which is the correct market price of risk when drift effects are taken into account. This ratio (not the Sharpe Ratio) emerges naturally when excess returns (instead of returns) are considered throughout. We show by explicit construction that the Market Portfolio defining this capital market line is the same as in traditional Markowitz theory. Therefore, even when drift effects are taken into account there still exists the Market Portfolio everybody should invest (part of his/her money) in. Portfolio optimization is as stable and parameter-independent (w.r.t. holding period and confidence level) when maximizing the Deutsch Ratio as it is when maximizing the Sharpe Ratio, as long as holding period and confidence are chosen in a sensible way. Although the Market Portfolio is the same as the Markowitz Market Portfolio and therefore independent of holding period and confidence, any individual portfolio within the optimal strategy for a specific risk preference is different from the Markovitz portfolio.
[slides]

• Dr Götz Giese, Commerzbank

Bridging the gap between CreditRisk+ and Merton-style credit portfolio models
We discuss similarities and differences between Merton-style credit portfolio models and default-rate based approaches such as CreditRisk+. In particular, we present a generalised CreditRisk+ model (the multivariate Vasicek model), which employs distribution assumptions similar to those of Merton-style models. Special emphasis is put on the calculation of contributions to tail risk for individual obligors in this framework.
[slides]

• Dr Werner Koch, ComInvest

Consistent Return Estimates in the Asset Allocation Process - The Black-Litterman Approach
In asset management, the forecast of asset returns is essential within the investment process. In this context, the Black-Litterman approach (1992) yields consistent asset return forecasts as a wiighted combination of (strategic) market equilibrium returns and (tactical) subjective forecasts ("vies"). The Black-Litterman formalism allows to implement both absolute views (return levels) and relative views (outperforming vs. underperforming assets) for selected assets investigated under "core competence". For any particular view, individual confidence levels for the return estimates have to be specified. The formalism spreads this information consistently accross all assets in the portfolio. The BL-revised returns then serve as a consistent input for mean-variance portfolio optimization procedures, thus allowing for the implementation of additional constraints. It turns out that the BL-optimized portfolios overcome some well-known Markowitz insufficiencies as unrealistic sensitivity to input factors or extreme portfolio weights. The BL process will be introduced both from its theoretical background and its implementation in practice.
[slides]

• Prof Christoph Kühn, Frankfurt MathFinance Institute (Goethe University)

Convertible bonds in jump-diffusion models
A convertible (callable) bond is a security that the holder can convert into a specified number of underlying shares. In addition, the issuer can recall the bond, paying some compensation, or force the holder to convert it immediately. We give explicit solutions to the corresponding stopping game in the context of a perpetual reduced form model with a Brownian motion part and exponentially distributed jumps. It turns out that the occurence of jumps leads to quite interesting optimal stopping strategies whose structure differs from the results for continuous models. Finally, we discuss a semiexplicite approximation of nonperpetual optimal stopping problems which is based on the randomization of the maturity date.
[slides], [paper], [extension]

• Prof Ludger Overbeck, Giessen University / Hypovereinsbank

Semi-analytics Techniques for CDO-modelling
Collateralized debt obligatons (CDOs) constitute an important subclass of asset backed securities. The evaluation of CDOs relies on mathematical modeling and on simulation as well as analytic and semi-analytic approaches, depending on the underlying asset pool and the cash flow structure of the transaction. In this paper we will present a semi-analytic approach where the granularity of the underlying portfolio is maintained, but the time-dependency is modeled by the upper Frechet-copula. In particular we investigate the accuracy of that approximation in concrete transactions
[slides]

• Prof Eckhard Platen, Sydney University of Technology

On the Role of the Growth Optimal Portfolio in Finance
The paper discusses various roles that the growth optimal portfolio (GOP) plays in finance. For the case of a continuous market we show how the GOP can be interpreted as a fundamental building block in financial market modeling, portfolio optimization, contingent claim pricing and risk measurement. On the basis of a portfolio selection theorem, optimal portfolios are derived. These allocate funds into the GOP and the savings account. A risk aversion coefficient is introduced, controlling the amount invested in the savings account, which allows to characterize portfolio strategies that maximize expected utilities. Natural conditions are formulated under which the GOP appears as the market portfolio. A derivation of the intertemporal capital asset pricing model is given without relying on Markovianity, equilibrium arguments or utility functions. Fair contingent claim pricing, with the GOP as numeraire portfolio, is shown to generalize risk neutral and actuarial pricing. Finally, the GOP is described in various ways as the best performing portfolio.
[paper], [slides]

• Dr Matthias Reimer, Postbank

What is the recipe for a successful derivative product?
We analyze a variety of financial instruments which we have observed in the markets during the past years, and draw the connection between derivative modelling and the management of derivative products. We then examine various business models to explain why some products succeed and others don’t.
[slides]

• Prof Wolfgang Schmidt, HfB - Business School of Finance and Management

Interest Rate Convexity and the Volatility Smile
Pricing the convexity effect in irregular interest rate derivatives such as e.g. Libor-in-arrears or CMS one often ignores the volatility smile which is quite pronounced in the interest rate options market. This note solves the problem of convexity by replicating the irregular interest flow or option with liquidly traded options with different strikes thereby taking into account the volatility smile. This idea is known among practitioners for pricing CMS caps. We approach the problem on a more general scale and apply the result to various examples.
[slides]

• Dr John Schoenmakers, Weierstrass Institute, Berlin

Iterative construction of the optimal Bermudan stopping time
We present a new iterative procedure for solving the discrete optimal stopping problem. The method produces monotonically increasing approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many steps. Then, by duality, the method induces a convergent sequence of upper bounds as well. Contrary to backward dynamic programming, the presented iterative procedure allows to calculate approximative solutions with only a few nestings of conditionals expectations and is, therefore, tailor-made for a plain Monte-Carlo implementation. The power of the procedure is demonstrated for high dimensional Bermudan products, in particular, for Bermudan swaptions in a full factor Libor market model.
[slides], [LiborBookFlyer]

• Milind Sharma, Deutsche Bank, New York

Alternative Risk-Adjusted Performance Measures for Alternative Investments
We highlight the inadequacies of traditional RAPMs (Risk-Adjusted Performance Measures) when applied to hedge funds. It surveys risk and risk-adjusted measures currently in use and discusses their pros and cons. Their inability to deal with higher moment risks and asymmetric distributions is noted along with evidence of non-normality in individual as well hedge fund index data. This issue is particularly germane because attractive mean-variance profiles are often coupled with undesirable exposure to skewness and kurtosis. Hence the necessity for a measure which incorporates investor preferences qua risk aversion and adjusts for iceberg risks lurking in the higher moments.

The Expected Utility framework of Von Neumann–Morgenstern is introduced as the foundation for the proposed RAPM. AIRAP (Alternative Investments Risk Adjusted Performance) is the implied equivalent return that the risk-averse investor desires with certainty in exchange for the uncertain return from holding risky assets. Key benefits to the hedge fund community of using AIRAP is that it captures the full distribution, penalizes appropriately for volatility and leverage, is customizable by risk aversion, works with negative mean returns and eschews convergence requirements of series expansions. The general solution is based on non-parametric fits in addition to a closed form special case. A modified Sharpe Ratio formulation is also provided. AIRAP is contrasted with Sharpe, Treynor and Jensen rankings of the HFR universe of hedge funds to show significant divergence. A framework for generating peer percentile rankings by incorporating stressed scenarios or regime-switching models is proposed.

The results have implications for manager selection to the extent that better RAPMs facilitate better discernment. In terms of the portfolio construction of fund of hedge funds, transcending the mean-variance framework should help mitigate the bias in optimal style weights towards illiquidity and short volatility. Finally, AIRAP can also shed light on the degree of leverage optimal for a given track record and level of risk-aversion.



A.I.R.A.P. - Alternative Views on Alternative Investments

We investigate issues of risk-adjusted performance, value added and leverage for hedge funds. It applies AIRAP (Alternative Investments Risk Adjusted Performance), which is the power utility implied certain return that a risk-averse investor would trade off for holding risky assets, to hedge fund indices and individual hedge fund data. Inferences are made about the value added by hedge funds and the difference between directional and non-directional strategies. Evidence of non-normality, higher moment risks and the trade-off between mean-variance profile vis-à-vis skewness and kurtosis is noted across style categories. Further, survivorship bias is estimated across style categories in the first four moments.
[slides]
• Jurgen Tistaert, ING SWE Brussels

A Perfect Calibration! Now What?
We show that several advanced equity option models incorporating stochastic volatility can be calibrated very nicely to a realistic option surface. More specifically, we focus on the Heston stochastic volatility model (with and without jumps in the stock price process), the Barndorff-Nielsen-Shepard model and Lévy models with stochastic time. All these models are capable of accurately describing the marginal distribution of stock prices and indices and hence lead to almost identical European vanilla option prices. As such, we can hardly discriminate between the different processes on the basis of their smile-conform pricing characteristics. We therefore are tempted applying them to a range of exotics. However, due to the different structure in path-behavior between these models, the resulting exotics prices can vary significantly. It motivates a further study on how to model the fine stochastic behavior of assets over time. This is joint work with Wim Schoutens (K.U. Leuven, Belgium), Erwin Simons (ING SWE Brussels).
[paper], [slides], [extension]

• Prof Robert G Tompkins, HfB - Business School of Finance and Management

Volatile Days and Jumping Nights
Most empirical studies of financial market returns only consider prices when the markets are open. While considerable research has examined the return process when markets are closed, this has been restricted to comparisons of means and variances. Little research has considered the higher moments or the shape of the distributions of the returns.

In this research, we decompose returns estimated on the usual close-to-close basis into the returns from the close to the open and the open to the close. We consider a wide range of stock markets in this study and examine the distributional properties of the alternative returns periods.

We find that for all markets, overnight returns are higher, the variance is lower and display significant non-zero skewness and excess kurtosis. During the trading day, returns are consistent with stochastic volatility with Gaussian increments. Extensive statistical testing confirms that for most markets, the average return is statistically significantly higher overnight and that the variance is significantly lower. Hypothesis tests of higher moments confirm that these also are statistically significantly different between overnight and trading periods.

The implications of these results are considered with the most likely reason for this effect is that trading day returns are driven by stochastic volatility and overnight returns by jumps. Given that returns are higher overnight suggests that risk premia are more likely associated with jumps than stochastic volatility.
[slides]

• Dr Thomas Weber, Weber und Partner

Efficient Calibration for Libor Market Models - Alternative strategies and implementation issues
During the talk we compare and test alternative methods for calibrating LIBOR Market Models and give arguments for choices we made while developing a calibration applications.
[slides]

• Prof Uwe Wystup, HfB - Business School of Finance and Management

On the Cost of Delayed Fixing Announcements and its Impact on FX Exotic Options


In Foreign Exchange Markets vanilla and barrier options are traded frequently. The market standard is a cutoff time of 10 am in New York for the strike of vanillas and a knock-out event based on a continuously observed barrier. However, many clients, particularly from Italy, prefer the cutoff and knock-out event to be based on the fixing published by the European Central Bank on the Reuters Page ECB37. These barrier options are called discretely observed barrier options. While these options can be priced in several models by various techniques, the ECB source of the fixing causes two problems. First of all, it is not tradable, and secondly it is published with a delay of about 15 - 20 minutes. We examine here the effect of these problems on the hedge of these options and consequently suggest a cost based on the additional uncertainty encountered. This is joint work with Christoph Becker (Trier University/MathFinance AG)
[paper], [slides]

www.mathfinance.de Last modified: March 2005