We propose an efficient method for the construction of an arbitrage-free call option price function from observed call price quotes. The no-arbitrage theory of option pricing places various shape constraints on the option price function. For each available maturity on a given trading day, the proposed method estimates an option price function of strike price using a Bernstein polynomial basis. Using the properties of this basis, we transform the constrained functional regression problem to the least-squares problem of finite dimension and derive the sufficiency conditions of no-arbitrage pricing to a set of linear constraints. The resultant linearly constrained least square minimization problem can easily be solved using an efficient quadratic programming algorithm. The proposed method is easy to use and constructs a smooth call price function which is arbitrage-free in the entire domain of the strike price with any finite number of observed call price quotes. We empirically test the proposed method on S&P 500 option price data and compare the results with the cubic spline smoothing method to see the applicability.

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This paper deals with the studies of asymptotic normality and strong consistency of conditional U-statistics for dependent processes (including conditional mixing) under some regularity conditions. The novelty of the paper is that it unifies non parametric regression theory of stochastic processes (Bosq {1996)) with the theory of conditional U-statistics introduced by Stute (1991, 1994) and Liero (1991).

Background: COVID-19 associated pulmonary aspergillosis (CAPA) is an emerging complication among patients with COVID-19 but hasn’t been well studied in cancer patients. This study, we try to find out important aspects associated with CAPA among cancer patients with regards to clinico-epidemiological factors. Methods: In this retrospective observational study, we included 198 consecutive patients COVID-19 between April 2020 and February 2021. CAPA cases were classified according to CAPA-European Confederation of Medical Mycology criteria (2020 ECMM/ISHAM consensus criteria). Results: The overall incidence of CAPA was found to be 10.1% in our study population. The incidence among hematological malignancies was 11.25% and solid tumors was 10%. In-hospital mortality was significantly high among patients with CAPA as compared to that among without CAPA (40% versus 16.85%; p<0.012695). Significant number of patients with CAPA had received chemotherapy in last 3 months before diagnosis of COVID-19 (50% versus 28.09%, p=0.043222) and had evidence of culture positive bacterial infection (30% versus 5.62; p=0.000888). Significantly more patients having CAPA were on steroids, required oxygen and/or ventilator support as compared to those without CAPA. Conclusions: CAPA is a significant cause of mortality and length of hospital stay (16 versus 7 days; p=0.00001) among cancer patients with COVID-19. Cancer patients with COVID-19 were at increased risk of CAPA as compared to non-cancer patients.