Citation Context

...ely. A similar result holds for the other maturities. Therefore, we argue that the power spectrum analysis for r(T, t) indicates a stochastic process with spectral components decreasing as S(f) ∼ f α =-=[12]-=-. The power spectrum for the increments (Figs.6 and 7 (Right)) is flat, typical of a white noise process. These results are also corroborated by a similar analysis performed on Eurodollars interest ra...

Citation Context

...ebruary 2008Fig. 1. LIBOR interest rates r(T,t) as a function of the current date t, for the maturities T=1, 3, 6 and 12 months and EURO currency (Left) and Pound Sterling currency (Right). recently =-=[6,7]-=-. In particular, the fat-tail property of the empirical distribution of price changes has been widely documented and is a crucial feature for monitoring the extreme risks and for accurately pricing in...

Citation Context

...ocess Lt, such that the expectation in the denominator is finite. In this case, it is possible to show that the discounted bond-price process is a martingale and that the martingale measure is unique =-=[19]-=-. Also, the European vanilla call option price on a bond maturing at time T can be obtained [18]. Along these lines, we believe, it is possible to develop a consistent option pricing theory taking int...

Citation Context

...d from several different perspectives. The classical theoretical approach models the term structure of interest rates using stochastic processes. Various models have been proposed and can be found in =-=[1,2,3]-=-. Although they provide analytical formulas for the pricing of interest rate derivatives, the implied deformations of the term structure have a Brownian motion component and are often rejected by empi...

Citation Context

...truncated Lévy distribution [16]. Wim Schoutens has recently published a book on Lévy processes in finance devoted to the extension of martingale methods to a large class of leptokurtic distributions =-=[17]-=-. The method can be described from a heuristic point of view. Let S(t) denote the stochastic process underlying a contingent claim C(S, t); thus, S(t) can be a price process, an interest rate process,...

Citation Context

...ebruary 2008Fig. 1. LIBOR interest rates r(T,t) as a function of the current date t, for the maturities T=1, 3, 6 and 12 months and EURO currency (Left) and Pound Sterling currency (Right). recently =-=[6,7]-=-. In particular, the fat-tail property of the empirical distribution of price changes has been widely documented and is a crucial feature for monitoring the extreme risks and for accurately pricing in...

Citation Context

...d from several different perspectives. The classical theoretical approach models the term structure of interest rates using stochastic processes. Various models have been proposed and can be found in =-=[1,2,3]-=-. Although they provide analytical formulas for the pricing of interest rate derivatives, the implied deformations of the term structure have a Brownian motion component and are often rejected by empi...

Citation Context

...component and are often rejected by empirical data (see [4]). The inadequacies of the Gaussian model for the description of financial time series has been reported since a long time ago by Mandelbrot =-=[5]-=-, but thanks to the availability of large sets of financial data, the interest on this point has risen ∗ Corresponding author: Tel: +39 0131 283854, fax: +39 0131 283841. Email address: scalas@cicladi...

Citation Context

...r forward LIBOR or forward swap rates while keeping interest rates stable [8]. To our knowledge, up to now, no universally accepted theory has been obtained for the description of interest rates data =-=[9]-=-. In this framework, we have empirically studied the probability density distribution of LIBOR, in order to characterize the stochastic behavior of the daily fluctuations. In Section 2, we present the...

Citation Context

...d from several different perspectives. The classical theoretical approach models the term structure of interest rates using stochastic processes. Various models have been proposed and can be found in =-=[1,2,3]-=-. Although they provide analytical formulas for the pricing of interest rate derivatives, the implied deformations of the term structure have a Brownian motion component and are often rejected by empi...

Citation Context

... reliable. As early as 1977, some years after the seminal paper of Black and Scholes, Parkinson generalized their approach to option pricing and explicitly took into account leptokurtic distributions =-=[15]-=-. More recently, Boyarchenko and Levendorskii have studied the problem of option pricing in the presence of a specific distribution which seems to fit well the empirical data in many instances: the tr...