A path-independent approach to integrated variance under the CEV model

In this paper, a closed form path-independent approximation of the fair variance strike for a variance swap under the constant elasticity of variance (CEV) model is obtained by applying the small disturbance asymptotic expansion. The realized variance is sampled continuously in a risk-neutral market environment. With the application of a Brownian bridge, we derive a theorem for the conditionally expected product of a Brownian motion at two different times for arbitrary powers. This theorem enables us to provide a conditional Monte-Carlo scheme for simulating the fair variance strike. Compared with results in the recent literature, the method outlined in our paper leads to a simplified approach for pricing variance swaps. The method may also be applied to other more sophisticated volatility derivatives. An empirical comparison of this model with the Heston model and a conditional Monte Carlo scheme is also presented using option data on the S&P 500

Pricing Extendible Options Using the Fast Fourier Transform

This paper applies the fast Fourier transform (FFT) approach, within the Black-Scholes framework, to the valuation of options whose time to maturity can be extended to a future date (extendible options). We determine the valuation of the extendible options as sums of expectations of indicator functions, leading to a semianalytic expression for the value of the options over a range of strikes. Compared to Monte Carlo simulation, numerical examples demonstrate that the FFT is both computationally more efficient and higher in accuracy.</jats:p

Event prediction within directional change framework using a CNN-LSTM model

Financial forecasting has always been an intriguing research area in the field of finance. The widely accepted approach to forecast financial data is to perform predictions using time series data. In time series analysis, sampling the financial data with a predefined frequency (e.g. hourly, daily) leads to an uneven and discontinued data flow. Directional Change is a newly proposed approach that replaces physical time within the financial data and establishes an event-driven framework. With the emergence of the machine and deep learning-based methods, researchers have utilised them in financial time series. These techniques have shown to outperform conventional approaches. This paper aims to employ the CNN-LSTM model to investigate its predictive competence within the Directional Change (DC) framework to predict DC event prices. To obtain this objective, we first create the tick bars/candles of the GBPUSD, EURUSD, USDCHF, and USDCAD tick prices from January to August 2019. Then, the DC-based summaries of the selected tick bar/candle for each currency pair will be generated and fed to the CNN-LSTM model. The CNN-LSTM network architecture incorporates the robustness of Convolutional Neural Network (CNN) in feature extraction and Long Short-Term Memory (LSTM) in predicting sequential data. The results suggest that the performance of the CNN-LSTM model improves significantly within the DC framework

Lie symmetry analysis of a fractional Black-Scholes equation

In 2000, Walter Wyss looked into the fractional version of the Black-Scholes equation for the first time. He gave a solution of the fractional Black-Scholes equation by using the Greens function [14]. In this paper, Lie symmetry analysis of a time fractional Black-Scholes equation with Riemann-Liouville derivative is performed. The operators admitted are obtained and finally an example of the invariant solution of the equation is discussed

Highly Efficient Shannon Wavelet-based Pricing of Power Options under the Double Exponential Jump Framework with Stochastic Jump Intensity and Volatility

We propose a highly efficient and accurate valuation method for exotic-style options based on the novel Shannon wavelet inverse Fourier technique (SWIFT). Specifically, we derive an efficient pricing methods for power options under a more realistic double exponential jump model with stochastic volatility and jump intensity. Inclusion of such innovations may accommodate for the various stylised facts observed in the prices of financial assets, and admits a more realistic pricing framework as a result. Following the derivation of our SWIFT pricing method for power options, we perform extensive numerical experiments to analyse both the method's accuracy and efficiency. In addition, we investigate the sensitivities in the resulting prices, as well as the inherent errors, to changes in the underlying market conditions. Our numerical results demonstrate that the SWIFT method is not only more efficient when benchmarked to its close competitors, such as the Fourier- cosine (COS) and the widely-acclaimed fast-Fourier transform (FFT) methods, but it is also robust across a range of different market conditions exhibiting exponential error convergence

Transnasal endoscopy: no gagging no panic!

BACKGROUND: Transnasal endoscopy (TNE) is performed with an ultrathin scope via the nasal passages and is increasingly used. This review covers the technical characteristics, tolerability, safety and acceptability of TNE and also diagnostic accuracy, use as a screening tool and therapeutic applications. It includes practical advice from an ear, nose, throat (ENT) specialist to optimise TNE practice, identify ENT pathology and manage complications. METHODS: A Medline search was performed using the terms “transnasal”, “ultrathin”, “small calibre”, “endoscopy”, “EGD” to identify relevant literature. RESULTS: There is increasing evidence that TNE is better tolerated than standard endoscopy as measured using visual analogue scales, and the main area of discomfort is nasal during insertion of the TN endoscope, which seems remediable with adequate topical anaesthesia. The diagnostic yield has been found to be similar for detection of Barrett's oesophagus, gastric cancer and GORD-associated diseases. There are some potential issues regarding the accuracy of TNE in detecting small early gastric malignant lesions, especially those in the proximal stomach. TNE is feasible and safe in a primary care population and is ideal for screening for upper gastrointestinal pathology. It has an advantage as a diagnostic tool in the elderly and those with multiple comorbidities due to fewer adverse effects on the cardiovascular system. It has significant advantages for therapeutic procedures, especially negotiating upper oesophageal strictures and insertion of nasoenteric feeding tubes. CONCLUSIONS: TNE is well tolerated and a valuable diagnostic tool. Further evidence is required to establish its accuracy for the diagnosis of early and small gastric malignancies. There is an emerging role for TNE in therapeutic endoscopy, which needs further study

Liver and muscle glycogen oxidation and performance with dose variation of glucose-fructose ingestion during prolonged (3 h) exercise

Purpose This study investigated the effect of small manipulations in carbohydrate (CHO) dose on exogenous and endogenous (liver and muscle) fuel selection during exercise. Method Eleven trained males cycled in a double-blind randomised order on 4 occasions at 60% V˙O2max for 3 h, followed by a 30-min time-trial whilst ingesting either 80 g h−1 or 90 g h−1 or 100 g h−1 13C-glucose-13C-fructose [2:1] or placebo. CHO doses met, were marginally lower, or above previously reported intestinal saturation for glucose–fructose (90 g h−1). Indirect calorimetry and stable mass isotope [13C] techniques were utilised to determine fuel use. Result Time-trial performance was 86.5 to 93%, ‘likely, probable’ improved with 90 g h−1 compared 80 and 100 g h−1. Exogenous CHO oxidation in the final hour was 9.8–10.0% higher with 100 g h−1 compared with 80 and 90 g h−1 (ES = 0.64–0.70, 95% CI 9.6, 1.4 to 17.7 and 8.2, 2.1 to 18.6). However, increasing CHO dose (100 g h−1) increased muscle glycogen use (101.6 ± 16.6 g, ES = 0.60, 16.1, 0.9 to 31.4) and its relative contribution to energy expenditure (5.6 ± 8.4%, ES = 0.72, 5.6, 1.5 to 9.8 g) compared with 90 g h−1. Absolute and relative muscle glycogen oxidation between 80 and 90 g h−1 were similar (ES = 0.23 and 0.38) though a small absolute (85.4 ± 29.3 g, 6.2, − 23.5 to 11.1) and relative (34.9 ± 9.1 g, − 3.5, − 9.6 to 2.6) reduction was seen in 90 g h−1 compared with 100 g h−1. Liver glycogen oxidation was not significantly different between conditions (ES < 0.42). Total fat oxidation during the 3-h ride was similar in CHO conditions (ES < 0.28) but suppressed compared with placebo (ES = 1.05–1.51). Conclusion ‘Overdosing’ intestinal transport for glucose–fructose appears to increase muscle glycogen reliance and negatively impact subsequent TT performance

Glucose and fructose hydrogel enhances running performance, exogenous carbohydrate oxidation, and gastrointestinal tolerance

Purpose Beneficial effects of carbohydrate (CHO) ingestion on exogenous CHO oxidation and endurance performance require a well-functioning gastrointestinal (GI) tract. However, GI complaints are common during endurance running. This study investigated the effect of a CHO solution-containing sodium alginate and pectin (hydrogel) on endurance running performance, exogenous and endogenous CHO oxidation, and GI symptoms. Methods Eleven trained male runners, using a randomized, double-blind design, completed three 120-min steady-state runs at 68% V˙O2max, followed by a 5-km time-trial. Participants ingested 90 g·h−1 of 2:1 glucose–fructose (13C enriched) as a CHO hydrogel, a standard CHO solution (nonhydrogel), or a CHO-free placebo during the 120 min. Fat oxidation, total and exogenous CHO oxidation, plasma glucose oxidation, and endogenous glucose oxidation from liver and muscle glycogen were calculated using indirect calorimetry and isotope ratio mass spectrometry. GI symptoms were recorded throughout the trial. Results Time-trial performance was 7.6% and 5.6% faster after hydrogel ([min:s] 19:29 ± 2:24, P < 0.001) and nonhydrogel (19:54 ± 2:23, P = 0.002), respectively, versus placebo (21:05 ± 2:34). Time-trial performance after hydrogel was 2.1% faster (P = 0.033) than nonhydrogel. Absolute and relative exogenous CHO oxidation was greater with hydrogel (68.6 ± 10.8 g, 31.9% ± 2.7%; P = 0.01) versus nonhydrogel (63.4 ± 8.1 g, 29.3% ± 2.0%; P = 0.003). Absolute and relative endogenous CHO oxidation was lower in both CHO conditions compared with placebo (P < 0.001), with no difference between CHO conditions. Absolute and relative liver glucose oxidation and muscle glycogen oxidation were not different between CHO conditions. Total GI symptoms were not different between hydrogel and placebo, but GI symptoms were higher in nonhydrogel compared with placebo and hydrogel (P < 0.001). Conclusion The ingestion of glucose and fructose in hydrogel form during running benefited endurance performance, exogenous CHO oxidation, and GI symptoms compared with a standard CHO solution

BMQ

BMQ: Boston Medical Quarterly was published from 1950-1966 by the Boston University School of Medicine and the Massachusetts Memorial Hospitals