A Closed-Form Expansion Approach for Pricing Discretely Monitored Variance Swaps - Online Supplementary Material

2015 ◽  
Author(s):  
Chenxu Li ◽  
Xiaocheng Li
Keyword(s):  
Closed Form ◽  
Variance Swaps ◽  
Online Supplementary Material ◽  
Supplementary Material

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

A NOVEL ANALYTICAL APPROACH FOR PRICING DISCRETELY SAMPLED GAMMA SWAPS IN THE HESTON MODEL

2016 ◽  
Vol 57 (3) ◽  
pp. 244-268
Author(s):  
SANAE RUJIVAN
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Analytical Approach ◽  
Solution Procedure ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Variance Swaps ◽  
Closed Form Solutions ◽  
Volatility Model ◽  
Closed Form Formula

The main purpose of this paper is to present a novel analytical approach for pricing discretely sampled gamma swaps, defined in terms of weighted variance swaps of the underlying asset, based on Heston’s two-factor stochastic volatility model. The closed-form formula obtained in this paper is in a much simpler form than those proposed in the literature, which substantially reduces the computational burden and can be implemented efficiently. The solution procedure presented in this paper can be adopted to derive closed-form solutions for pricing various types of weighted variance swaps, such as self-quantoed variance and entropy swaps. Most interestingly, we discuss the validity of the current solutions in the parameter space, and provide market practitioners with some remarks for trading these types of weighted variance swaps.

Cement plug technique for the management of disc-associated cervical spondylopathy in 52 Dobermann Pinscher dogs

2016 ◽  
Vol 29 (03) ◽  
pp. 195-201 ◽  
Author(s):  
Jonathan Pink ◽  
Toby Gemmill ◽  
Malcolm McKee
Keyword(s):  
Bone Cement ◽  
Vertebral Body ◽  
Cervical Disc ◽  
Adjacent Segment ◽  
Variable Degree ◽  
Cervical Spondylopathy ◽  
Online Supplementary Material ◽  
Supplementary Material ◽  
Neurologically Normal ◽  
Cement Plug

SummaryObjectives: To report the radiographic and clinical outcome of an intervertebral bone cement plug technique for the management of disc-associated cervical spondylopathy in Dobermann Pinscher dogs.Methods: Retrospective study of 52 Dobermann Pinscher dogs.Results: A variable degree of cement plug subsidence with loss of vertebral distraction was evident in all dogs (n = 40) that were radiographed >6 weeks postoperatively. In no case was there definitive evidence of vertebral body fusion. Eight dogs had a sudden deterioration in neurological status, cervical hyperaesthesia, or both between three days and 12 weeks following surgery that was considered to be implant-associated; six of these dogs were euthanatized. Following surgery, 43/52 dogs were considered to be neurologically normal or to have improved, however, nine of 43 subsequently deteriorated due to adjacent segment disease. At the long-term follow-up, 34 dogs were considered to be neurologically normal or to have improved. Twenty-nine dogs were dead by the end of the study period.Clinical significance: Intervertebral bone cement plug surgery results in an initial improvement in clinical signs in the majority of Dobermann Pinschers with disc-associated cervical spondylopathy. However, it fails to maintain vertebral distraction or achieve vertebral body fusion, and is associated with acute implant complications, additional cervical disc protrusions or mortality in a significant proportion of cases.Online Supplementary Material: Please note that online supplementary material for this paper is available at: http://dx.doi.org/10.3415/VCOT-15-09-0160.

Modeling Caries Experience: Advantages of the Use of the Hurdle Model

2016 ◽  
Vol 50 (6) ◽  
pp. 517-526 ◽  
Author(s):  
Hedwig Hofstetter ◽  
Elise Dusseldorp ◽  
Achim Zeileis ◽  
Annemarie A. Schuller
Keyword(s):  
Linear Models ◽  
Skewed Distribution ◽  
Caries Experience ◽  
Hurdle Model ◽  
Special Focus ◽  
Online Supplementary Material ◽  
Dmf Index ◽  
Supplementary Material ◽  
Hurdle Regression ◽  
Zero Counts

In dental epidemiology, the decayed (D), missing (M), and filled (F) teeth or surfaces index (DFM index) is a frequently used measure. The DMF index is characterized by a strongly positive skewed distribution with a large stack of zero counts for those individuals without caries experience. Therefore, standard generalized linear models often lead to a poor fit. The hurdle regression model is a highly suitable class to model a DMF index, but its use is subordinated. We aim to overcome the gap between the suitability of the hurdle model to fit DMF indices and the frequency of its use in caries research. A theoretical introduction to the hurdle model is provided, and an extensive comparison with the zero-inflated model is given. Using an illustrative data example, both types of models are compared, with a special focus on interpretation of their parameters. Accompanying R code and example data are provided as online supplementary material.

scholarly journals Language Learning Difficulties Reported by Beginner-Level Learners of Arabic Using Online Tools

2020 ◽  
Vol 11 ◽  
pp. 19-35
Author(s):  
Mahmoud Amer
Keyword(s):  
Language Learning ◽  
Learning Difficulties ◽  
Online Supplementary Material ◽  
Vocabulary Recall ◽  
Online Tools ◽  
Supplementary Material ◽  
Weekly Journal ◽  
Journal Entries

This study examined how two classes used online supplementary material to learn Arabic and the difficulties they reported in the process of their learning. The two classes have a total of 33 students who completed the course. The data from their weekly journal entries and log information from the site where the material was housed are used to describe the extent and the ways in which students used the material and issues they faced learning Arabic. Results show that students in both classes spent roughly 265 hours practicing Arabic with an average of 8 hours per student throughout the semester and that vocabulary recall and pronunciation were key struggles in their learning. Furthermore, this paper discusses some of the themes that emerged of students’ journal entries about their learning Arabic. Further implications are provided and discussed.

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