Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.Comment: 46 pages, 7 figures, accepted for publication in Journal of Banking & Financ

Risk aggregation, dependence structure and diversification benefit

Insurance and reinsurance live and die from the diversification benefits or lack of it in their risk portfolio. The new solvency regulations allow companies to include them in their computation of risk-based capital (RBC). The question is how to really evaluate those benefits. To compute the total risk of a portfolio, it is important to establish the rules for aggregating the various risks that compose it. This can only be done through modelling of their dependence. It is a well known fact among traders in financial markets that "diversification works the worst when one needs it the most''. In other words, in times of crisis the dependence between risks increases. Experience has shown that very large loss events almost always affect multiple lines of business simultaneously. September 11, 2001, is an example of such an event: when the claims originated simultaneously from lines of business which are usually uncorrelated, such as property and life, at the same time that the assets of the company were depreciated due to the crisis on the stock markets. In this paper, we explore various methods of modelling dependence and their influence on diversification benefits. We show that the latter strongly depend on the chosen method and that rank correlation grossly overestimates diversification. This has consequences on the RBC for the whole portfolio, which is smaller than it should be when correctly accounting for tail correlation. However, the problem remains to calibrate the dependence for extreme events, which are rare by definition. We analyze and propose possible ways to get out of this dilemma and come up with reasonable estimates.Risk-Based Capital, Hierarchical Copula, Dependence, Calibration

Bootstrapping the economy -- a non-parametric method of generating consistent future scenarios

The fortune and the risk of a business venture depends on the future course of the economy. There is a strong demand for economic forecasts and scenarios that can be applied to planning and modeling. While there is an ongoing debate on modeling economic scenarios, the bootstrapping (or resampling) approach presented here has several advantages. As a non-parametric method, it directly relies on past market behaviors rather than debatable assumptions on models and parameters. Simultaneous dependencies between economic variables are automatically captured. Some aspects of the bootstrapping method require additional modeling: choice and ransformation of the economic variables, arbitrage-free consistency, heavy tails of distributions, serial dependence, trends and mean reversion. Results of a complete economic scenario generator are presented, tested and discussed.economic scenario generator (ESG); asset-liability management (ALM); bootstrapping; resampling; simulation; Monte-Carlo simulation; non-parametric model; yield curve model

Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.Scaling exponents; Time series analysis; Multi-fractals

From Default Probabilities To Credit Spreads: Credit Risk Models Do Explain Market Prices

Credit risk models like Moody’s KMV are now well established in the market and give bond managers reliable estimates of default probabilities for individual firms. Until now it has been hard to relate those probabilities to the actual credit spreads observed on the market for corporate bonds. Inspired by the existence of scaling laws in financial markets by Dacorogna et al. (2001) and Di Matteo et al. (2005) deviating from the Gaussian behavior, we develop a model that quantitatively links those default probabilities to credit spreads (market prices). The main input quantities to this study are merely industry yield data of different times to maturity and expected default frequencies (EDFs) of Moody’s KMV. The empirical results of this paper clearly indicate that the model can be used to calculate approximate credit spreads (market prices) from EDFs, independent of the time to maturity and the industry sector under consideration. Moreover, the model is effective in an out-of-sample setting, it produces consistent results on the European bond market where data are scarce and can be adequately used to approximate credit spreads on the corporate level.

Equalization Reserves for Natural Catastrophes and Shareholder Value: a Simulation Study

This paper investigates the effects on the company value for shareholders of keeping equalization reserves for catastrophic risk in an insurance company. We perform an extensive simulation study to compare the performance of the company with and without equalization reserves for several standard profitability measures. Equalization reserves turn out to be beneficial for shareholders in terms of the resulting expected Sharpe ratio and also with respect to the value of the call option on assets at some reasonably large maturity time. Moreover, the expected total discounted tax payments are not smaller when using equalization reserves. The results are robust with respect to model parameters such as interest rate, time horizon, cost of raising capital and business cycle dynamics

The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market

We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with larger numbers of opportunities with shorter mean durations occurring during more liquid hours. We demonstrate further that the number of arbitrage opportunities has decreased in recent years, implying a corresponding increase in pricing efficiency. Using trading simulations, we show that a trader would need to beat other market participants to an unfeasibly large proportion of arbitrage prices to profit from triangular arbitrage over a prolonged period of time. Our results suggest that the foreign exchange market is internally self-consistent and provide a limited verification of market efficiency

Is the gamma risk of options insurable?

In this article we analyze the risk associated with hedging written call options. We introduce a way to isolate the gamma risk from other risk types and present its loss distribution, which has heavy tails. Moving to an insurance point of view, we define a loss ratio that we find to be well behaved with a slightly negative correlation to traditional lines of insurance business, offering diversification opportunities. The tails of the loss distribution are shown to be much fatter than those of the underlying stock returns. We also show that badly estimated volatility, in the Black-Scholes model, leads to considerably biased values for the replicating portfolio. Operational risk is defined as caused by imperfect delta hedging and is found to be limited in today's markets where the autocorrelation of stock returns is small.Option; Insurance; Risk

Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode

We investigate the emergence of a structure in the correlation matrix of assets' returns as the time-horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. Result crucially depends on whether the data is restricted to the ``internal'' dynamics of the market, where the ``center of mass'' motion (the market mode) is removed or not. If the market mode is not removed, we find that the structure emerges, as the time-horizon increases, from splitting a single large cluster. In NYSE we find that when the market mode is removed, the structure of correlation at the daily scale is already well defined at the 5 minutes time-horizon, and this structure accounts for 80 % of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.Comment: 12 pages, 17 figure