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Mr. Noureddine Krichene

available in closed form. It is defined as ϕ ( u , t ) = ∫ 0 ∞ e iuS t p ( S T | S t ) dS T , u is the transform variable. Option Value in the Fourier Space: knowledge of the CF enables to compute option prices in the Fourier space according to two alternative methods. The first method, proposed by Heston (1993) , relies on a numerical inversion of the CF. However, noting the singularity of Heston’s formula at u = 0, Carr and Madan (1999) proposed, instead, a numerical inversion of the Fourier transform of the option value. More specifically, Define The

Mr. Fabio Scacciavillani

heuristic argument should help to clarify frequency domain analysis. The presentation here will be synthetic, as the reader can find an exhaustive treatment of spectral methods in many textbooks, e.g., in Priestley (1981) . The spectral density function (or spectrum) of a covariance stationary stochastic process is defined as the Fourier transform of its serial correlation function. In general, a transform “maps” a function from its natural functional space to another, while preserving certain characteristics. A transform is useful if it simplifies certain operations

Mr. Fabio Scacciavillani
Mr. Fabio Scacciavillani
This paper contains an empirical analysis of currency substitution in Turkey: a simple relationship between the share of foreign currency holdings in M2X on one side and movements in the exchange rate or inflation on the other is derived from a two-stage portfolio choice model. This relationship is estimated by band spectrum regression which allows to remove from the data the short-term cyclical components. The results show that the relationship between currency substitution depends mainly on long-term movements in the exchange rate, while the effect of inflation on currency substitution is not statistically significant.
Mr. Noureddine Krichene
Mr. Noureddine Krichene
Crude oil prices have been on a run-up spree in recent years. Their dynamics were characterized by high volatility, high intensity jumps, and strong upward drift, indicating that oil markets were constantly out-of-equilibrium. An explanation of the oil price process in terms of the underlying fundamentals of oil markets and world economy was provided, viewing pressure on oil prices mainly as a result of rigid crude oil supply and an expanding world demand for crude oil. A change in the oil price process parameters would require a change in the underlying fundamentals. Market expectations, extracted from call and put option prices, anticipated no change, in the short term, in the underlying fundamentals. Markets expected oil prices to remain volatile and jumpy, and with higher probabilities, to rise, rather than fall, above the expected mean.
Mr. Noureddine Krichene
One approach to oil markets is to treat oil as an asset, besides its role as a commodity. Speculative and nonspeculative activity by investors in the derivatives markets could be responsible for a sizable increase in oil prices. This paper recognizes both the consumption and investment aspects of crude oil and proposes Levy processes for modeling uncertainty and options pricing. Calibration to crude oil futures' options shows high volatility of oil futures prices, fat-tailed, and right-skewed market expectations, implying a higher probability mass on crude oil prices remaining above the futures' level. These findings support the view that demand for futures contracts by investors could lead to excessively high price volatility.
Mr. Renzo G Avesani

simply given by G λ ( z ) = ∏ n = 1 N G λ , n ( z ) = ∏ n = 1 N [ ( 1 − p n ) + p n ⋅ z ν n ] . This product of the individual loss PGF is a simple convolution that can be computed using the fast Fourier transform (FFT). From the convolution theorem, G λ ( z ) = I F F T ( ∏ n = 1 N { F F T [ G λ , n ( z ) ] } ) ≡ G λ , B ( z ) , where IFFT is the inverse fast Fourier transform. This algorithm can be efficiently implemented as long as the portfolio does not contain more than a few thousand obligors. 5 This is about as far as the model can be

Mr. Noureddine Krichene
Following record low interest rates and fast depreciating U.S. dollar, crude oil prices became under rising pressure and seemed boundless. Oil price process parameters changed drastically in 2003M5-2007M10 toward consistently rising prices. Short-term forecasting would imply persistence of observed trends, as market fundamentals and underlying monetary policies were supportive of these trends. Market expectations derived from option prices anticipated further surge in oil prices and allowed significant probability for right tail events. Given explosive trends in other commodities prices, depreciating currencies, and weakening financial conditions, recent trends in oil prices might not persist further without triggering world economic recession, regressive oil supply, as oil producers became wary about inflation. Restoring stable oil markets, through restraining monetary policy, is essential for durable growth and price stability.