A note on intraday option pricing

Compound renewal processes can be used as an approximate phenomenological model of tick-by-tick price fluctuations. An exact and explicit general formula is derived for the martingale price of a European call option written on a compound renewal process. The option price is obtained using the direct method of indicator functions. The applicability of this result is discussed

A note on intraday option pricing

Compound renewal processes can be used as an approximate phenomenological model of tick-by-tick price fluctuations. An exact and explicit general formula is derived for the martingale price of a European call option written on a compound renewal process. The option price is obtained using the direct method of indicator functions. The applicability of this result is discussed

A parsimonious model for intraday European option pricing

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools.Comment: Submitted to Economics E-Journal: http://www.economics-ejournal.org/economics/discussionpapers/2012-1

The near-extreme density of intraday log-returns

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of "near-extremes" -- the distance between a record and the maximal value -- can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations

Spectral densities of Wishart-Levy free stable random matrices: Analytical results and Monte Carlo validation

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively the derivation of an analytical expression for the spectra of covariance matrices approximated by free Levy stable random variables and validate it by Monte Carlo simulation.Comment: 10 pages, 1 figure, submitted to Eur. Phys. J.

Stochastic integration for uncoupled continuous-time random walks

Continuous-time random walks are pure-jump processes with several applications in physics, but also in insurance, finance and economics. Based on heuristic considerations, a definition is given for the stochastic integral driven by continuous-time random walks. The martingale properties of the integral are investigated. Finally, it is shown how the definition can be used to easily compute the stochastic integral by means of Monte Carlo simulations.Continuous-time random walks; models of tick-by-tick financial data; stochastic integration

Heart transplantation without informed consent: discussion of a case

OBJECTIVE: To discuss informed consent to heart transplantation in the case of an intensive care unit (ICU) patient: relatives' informed consent was refused by the patient himself whose cognitive ability appeared to be reasonable for the purpose. SETTING: ICU of a university teaching hospital. PATIENT: A 62-year-old man who underwent myocardial revascularization had in the immediate post-operative hemodynamic instability, continuous serious arrhythmias, ventilatory support, fentanyl infusion. Heart transplantation could be the only chance for his survival. INVENTION: Heart transplantation. RESULTS: Despite patient's refusal, we decided to hold the relative's consent as valid, and transplantation was accordingly performed, to the subsequent satisfaction of the patient. CONCLUSIONS: Our decision was based on two beliefs: (1) the severity of the patient's clinical condition may have impaired his cognitive abilities; (2) the very same conditions may mask impairment and certainly make reliable assessment of cognition and judgment impossible. This being so, the preservation of life assumes priority

Stochastic integration for uncoupled continuous-time random walks

Continuous-time random walks are pure-jump processes with several applications in physics, but also in insurance, finance and economics. Based on heuristic considerations, a definition is given for the stochastic integral driven by continuous-time random walks. The martingale properties of the integral are investigated. Finally, it is shown how the definition can be used to easily compute the stochastic integral by means of Monte Carlo simulations