Exchange rate and interest rate polarization

Exchange Rate and Interest Rate Polarization. - The relationship between the polarization phenomenon in foreign exhange markets and a similar regu-larity in interest rate differentials is considered. In the case of perfect substitutability and of perfect foresight, both polarizations would be perfectly complementary. Risk premia and forecast errors, however, might induce some degree of substitutability between the two concepts. Throughout almost the entire EMS experience, in France and Italy both phenomena appear to be equivalent. At the end of the 80s, however, interest rate polarization has surged at the expense of exchange rate polarization. In fact, a bias in estimates was found to explain this recent behaviour.     

Pricing and Hedging Credit Derivatives with Copulas

In this paper, we apply a copula function pricing technique to the evaluation of credit derivatives, namely a vulnerable default put option and a credit switch. Also in this case, copulas enable one to separate the specification of marginal default probabilities from their dependence structure. Their use is based here on no–arbitrage arguments, which provide pricing bounds and easy–to–implement super–replication strategies.
At a second stage, we specify the copula function to be a mixture one. In this case, we obtain closed form prices and hedges, which we calibrate on real market data. For the sake of comparison, we add a Clayton calibration.
(J.E.L: G11, G12).     

THE DEPENDENCE STRUCTURE OF RUNNING MAXIMA AND MINIMA: RESULTS AND OPTION PRICING APPLICATIONS

We provide general results for the dependence structure of running maxima (minima) of sets of variables in a model based on (i) Markov dynamics; (ii) no Granger causality; (iii) cross-section dependence. At the time series level, we derive recursive formulas for running minima and maxima. These formulas enable to use a "bootstrapping" technique to recursively recover the pricing kernels of barrier options from those of the corresponding European options. We also show that the dependence formulas for running maxima (minima) are completely defined from the copula function representing dependence among levels at the terminal date. The result is applied to multivariate discrete barrier digital products. Barrier Altiplanos are simply priced by (i) bootstrapping the price of univariate barrier products; (ii) evaluating a European Altiplano with these values.     

Fuzzy Value-at-risk: Accounting for Market Liquidity

In this paper we present a value-at-risk measure which accounts for market liquidity. We show that taking into account market liquidity implies a decoupling of valuation of long and short positions. We present a pricing model, named fuzzy measure model, that yields different values for positions of different sign and that can be usefully exploited to account for liquidity risk. This methodology is well-suited to price options when the distribution of the underlying asset is not known precisely, as in the case of implied options in corporate claims or real options. As an example, we apply our pricing technique to an option based model of value-at-risk, in line with the Merton and Perold approach, and we recover different value-at-risk figures for long and short positions.
(J.E.L.: C00, D81, G12).     

Value-at-risk Trade-off and Capital Allocation with Copulas

This paper uses copula functions to evaluate tail probabilities and market risk trade-offs at a given confidence level, dropping the joint normality assumption on returns. Copulas enable one to represent distribution functions separating the marginal distributions from the association structure. We present an application to two stock market indices: for each market we recover the marginal probability distribution. We then calibrate copula functions and recover the joint distribution. The estimated copulas directly give the joint probabilities of extreme losses. Their level curves measure the trade-off between losses over different desks. This trade-off can be exploited for capital allocation and is shown to depend on fat tails.
(J.E.L.: C14, G19, G29).     

Stress testing techniques and value-at-risk measures: A unified approach

We investigate a methodology to set up consistent scenarios for stress testing analysis in financial risk control and management. The method, based on the Black and Litterman bayesian approach to portfolio optimization, enables to mix historic and implied or private information, accounting for the co-movement among the markets. By tuning the mean values chosen for the scenarios and the degree of precision attached to them we are able to devise a whole range of mean loss and maximum probable loss, or Value-at-Risk measures. In particular, by setting a very precise scenario the mean and maximum probable loss converge toward similar values, while for very imprecise scenarios the mean loss figure is found to converge to zero, and the maximum probable loss collapses to the standard Value-at-Risk figure computed using historical information. As for options, we show that tuning the precision of the scenarios allows for the effects of changes in volatility on the option value, under each different scenarios. Finally, for more complex positions, such as those involving credit risk exposures, or more generally exposures to different markets, we suggest a tree methodology to report the scenarios and to pinpoint the key sources of risk.