Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes (BS) expression with volatility in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile

Calibration to American options: numerical investigation of the de-Americanization method.

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors

Gapless Assembly of Maize Chromosomes Using Long-Read Technologies

Creating gapless telomere-to-telomere assemblies of complex genomes is one of the ultimate challenges in genomics. We use two independent assemblies and an optical map-based merging pipeline to produce a maize genome (B73-Ab10) composed of 63 contigs and a contig N50 of 162 Mb. This genome includes gapless assemblies of chromosome 3 (236 Mb) and chromosome 9 (162 Mb), and 53 Mb of the Ab10 meiotic drive haplotype. The data also reveal the internal structure of seven centromeres and five heterochromatic knobs, showing that the major tandem repeat arrays (CentC, knob180, and TR-1) are discontinuous and frequently interspersed with retroelements

Static versus dynamic hedges: an empirical comparison for barrier options

Barrier options, Static hedging, Dynamic hedging, Local volatility model, Empirical hedging analysis, G13,

Local volatility dynamic models

Implied volatility surface, Local volatility surface, Market models, Arbitrage-free term structure dynamics, Heath–Jarrow–Morton theory, C61, 60H10, 91B24,