Option Valuation Using Asymptotic Expansion

Evo-SETI Entropy identifies with Molecular Clock

Multiscale Intensity Models for Single Name Credit Derivatives

On the investment–uncertainty relationship in a real option model with stochastic volatility

The aim of this paper is to investigate, in general terms, the effects of storm movement on the resulting flood peaks, and the underlying process controls. For this purpose, we utilize a broad theoretical framework that uses characteristic time and space scales associated with stationary rainstorms as well as moving rainstorms. For a stationary rainstorm the characteristic timescales that govern the peak response include two intrinsic timescales of a catchment and one extrinsic timescale of a rainstorm. On the other hand, for a moving rainstorm, two additional extrinsic scales are required, the storm travel time and storm size. The relationship between the peak response and the timescales appropriate for a stationary rainstorm can be extended in a straightforward manner to describe the peak response for a moving rainstorm. However, the interdependence between rainfall duration and storm travel time makes the behavior of the peak response for a moving rainstorm fundamentally different from that of a stationary rainstorm. We show that the relationship between peak response and characteristic timescales also depends on the relative size of the rainstorm with respect to catchment size. For moving rainstorms, we show that the augmentation of peak response arises from both the effect of overlaying the responses from subcatchments (resonance condition) and the effect of increased responses from subcatchments due to increased duration (interdependence), which results in maximum peak response when the moving rainstorm is slower than the channel flow velocity.

We analyzed spatial and temporal variograms of precipitation, runoff, and groundwater levels in Austria to examine whether characteristic scales exist and, if so, how big they are. In time, precipitation and runoff are stationary with characteristic scales on the order of a day and a month, respectively, while groundwater levels are nonstationary. In space, precipitation is almost fractal, so no characteristic scales exist. Runoff is nonstationary but not a fractal as it exhibits a break in the variograms. An analysis of the variograms of catchment precipitation indicates that this break is due to aggregation effects imposed by the catchment area. A spatial variogram of hypothetical point runoff back calculated from runoff variograms of three catchment size classes using aggregation statistics (regularization) is almost stationary and exhibits shorter characteristic space scales than catchment runoff. Groundwater levels are nonstationary in space, exhibiting shorter‐scale variability than precipitation and runoff, but are also not fractal as there is a break in the variogram. We suggest that the decrease of spatial characteristic scales from catchment precipitation to runoff and to groundwater is the result of a superposition of small‐scale variability of catchment and aquifer properties on the rainfall forcing. For comparison, TDR soil moisture data from a comprehensive Australian data set were examined. These data suggest that in time, soil moisture is close to stationary with characteristic scales of the order of 2 weeks while in space soil moisture is nonstationary and close to fractal over the extent sampled. Space‐time traces of characteristic scales fit well into a conceptual diagram of Blöschl and Sivapalan [1995]. The scaling exponents z in T ∼ Lz (where T is time and L is space) are of the order of 0.5 for precipitation, 0.8 for runoff from small catchments, 1.2 for runoff from large catchments, 0.8 for groundwater levels, and 0.5 for soil moisture.

The ability to price risks and devise optimal investment strategies in the presence of an uncertain random market is the cornerstone of modern finance theory. We first consider the simplest such problem of a so-called European call initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize the analysis to a large class of stochastic processes, such as ARCH, jump or Levy processes. We also address the case of correlated Gaussian processes, which is shown to be a good description of three different market indices (MATIF, CAC40, FTSE100). Our main result is the introduction of the concept of an optimal strategy in the sense of (functional) minimization of the risk with respect to the portfolio. If the risk may be made to vanish for particular continuous uncorrelated 'quasiGaussian' stochastic processes (including Black and Scholes model), this is no longer the case for more general stochastic processes. The value of the residual risk is obtained and suggests the concept of risk-corrected option prices. In the presence of very large deviations such as in Levy processes, new criteria for rational fixing of the option prices are discussed. We also apply our method to other types of options, `Asian', `American', and discuss new possibilities (`doubledecker'...). The inclusion of transaction costs leads to the appearance of a natural characteristic trading time scale.

By employing a randomisation procedure on the variance parameter of the standard geometric Brownian motion (GBM) model, we construct new families of analytically tractable asset pricing models. In particular, we develop two explicit families of processes that are respectively referred to as the randomised gamma (G) and randomised inverse gamma (IG) models, both characterised by a shape and scale parameter. Both models admit relatively simple closed-form analytical expressions for the transition density and the no-arbitrage prices of standard European-style options whose Black-Scholes implied volatilities exhibit symmetric smiles in the log-forward moneyness. Surprisingly, for integer-valued shape parameter and arbitrary positive real scale parameter, the analytical option pricing formulas involve only elementary functions and are even more straightforward than the standard (constant volatility) Black-Scholes (GBM) pricing formulas. Moreover, we show some interesting characteristics of the risk-neutral transition densities of the randomised G and IG models, both exhibiting fat tails. In fact, the randomised IG density only has finite moments of the order less than or equal to one. In contrast, the randomised G density has a finite first moment with finite higher moments depending on the time-to-maturity and its scale parameter. We show how the randomised G and IG models are efficiently and accurately calibrated to market equity option data, having pronounced implied volatility smiles across several strikes and maturities. We also calibrate the same option data to the wellknown SABR (Stochastic Alpha Beta Rho) model.

Taking the retailerpsilas default in supply chain for example, in this paper, using the theory of credit default swap, the writer intends to make a research on the shift of default risk in supply chain. On the condition of insured interest rate and recovery rate, a supposition is made that the default rate of supply chain depends on the doubly stochastic Poisson default process, and then a model of credit default swap is established, and a simple pricing model of standard credit default swap and long-term credit default swap are discussed.

We present data from high-resolution numerical simulations of the Navier–Stokes-α and the Leray-α models for two-dimensional turbulence. It was shown previously (Lunasin et al 2007 J. Turbul. 8 30) that for wavenumbers k such that kα ≫ 1, the energy spectrum of the smoothed velocity field for the two-dimensional Navier–Stokes-α (NS-α) model scales as k−7. This result is in agreement with the scaling deduced by dimensional analysis of the flux of the conserved enstrophy using its characteristic time scale. We therefore hypothesize that the spectral scaling of any α-model in the sub-α spatial scales must depend only on the characteristic time scale and dynamics of the dominant cascading quantity in that regime of scales. The data presented here, from simulations of the two-dimensional Leray-α model, confirm our hypothesis. We show that for kα ≫ 1, the energy spectrum for the two-dimensional Leray-α scales as k−5, as expected by the characteristic time scale for the flux of the conserved enstrophy of the Leray-α model. These results lead to our conclusion that the dominant directly cascading quantity of the model equations must determine the scaling of the energy spectrum.

Glycolysis in saccharomyces cerevisiae: Algorithmic exploration of robustness and origin of oscillations

Extended Black and Scholes model under bankruptcy risk

Silicon wafers oxidized and stripped by reactive plasma etching were implanted with 5 keV B, 1×1013/cm2. The transient enhanced diffusion of B, usually observed in samples which receive such implants over characteristic time scales, is strongly retarded in these plasma etched samples upon annealing at 800, 900, or 1000 °C, as measured by secondary ions mass spectrometry. These results suggest that the defects generated by the plasma etching procedure in the near surface region, represent an efficient sink against the flow of interstitials which cause the transient enhanced diffusion. A slow release of interstitials from this trapping immobile background occurs with characteristic time scales which are, however, a factor of 30–60 times higher than the usual lifetimes of transient diffusion. This release is characterized by an activation energy of 2.4 eV. These data are reported and their implication on shallow junction formation are discussed.

Postseismic gravity changes after the 2011 Tohoku earthquake (Mw9.0) were investigated using the data from superconducting gravimeters (SGs) at Mizusawa, Japan. The data in the period from 2014 to 2021 were used in the analysis. The SG data were first corrected for instrumental drift using the results of absolute gravity measurements. Then, correction for the hydrological effect was applied based on physical modeling of soil moisture. Finally, the effect of vertical displacement of the station (free-air effect) was corrected using GNSS data. After these corrections, residual gravity indicated a long-term increase, with its rate gradually decreasing with time. This fact suggests that viscoelastic relaxation after the earthquake played an important role in producing the long-term gravity changes. Fitting a decaying exponential function of time to the residual series yielded 89.4 ± 4.4 µGal (1 µGal = 10–8 ms–2) as the total gravity change and 635 ± 17 days as the characteristic time scale. In addition to the ground-based observations, the data from satellite gravity missions GRACE/GRACE-FO were analyzed to retrieve gravity changes at Mizusawa. Similar analysis of the satellite-based data yielded 15.2 ± 1.6 µGal as the total gravity change and 3444 ± 599 days as the characteristic time scale. The difference in the estimates of the total gravity change, of a factor of about 6, from the ground-based and the satellite-based observations may be attributed to the limited spatial resolution in the latter method. The difference in the estimates of the time scale, of a factor of about 1/5, may originate from the difference in the depth where the two kinds of gravimetry are mainly sensitive. Referring to recent theoretical studies on postseismic deformations after the 2011 Tohoku earthquake, our results can be interpreted consistently by assuming the existence of a layer of viscoelastic materials with viscosity 2times {10}^{18} text{Pa s} underneath the Tohoku area of Japan.Graphical

Derivation of the Camassa–Holm equations for elastic waves

This paper studies the portfolio optimization of mean-variance utility with state-dependent risk aversion, where the stock asset is driven by a stochastic process. The sub-game perfect Nash equilibrium strategies and the extended Hamilton-Jacobi-Bellman equations have been used to derive the system of non-linear partial differential equations. From the economic point of view, we demonstrate the numerical evaluation of the suggested solution for a special case where the risk aversion rate is proportional to the wealth value. Our results show that the asset driven by the stochastic volatility process is more general and reasonable than the process with a constant volatility.