scholarly journals Volatility Timing: Pricing Barrier Options on DAX XETRA Index

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 722
Author(s):  
Carlos Esparcia ◽  
Elena Ibañez ◽  
Francisco Jareño
Keyword(s):  
Option Pricing ◽  
Term Structure ◽  
Barrier Options ◽  
Barrier Option ◽  
Probability Term ◽  
Volatility Timing ◽  
The Right ◽  
The Impact ◽  
Complementary Study ◽  
Frequency Current

This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

scholarly journals Penentuan Harga Opsi Barrier Menggunakan Metode Trinomial Kamrad-Ritchken Dengan Volatilitas Model Garch

2019 ◽  
Vol 10 (1) ◽  
pp. 83-92
Author(s):  
S Sulastri ◽  
Lienda Novieyanti ◽  
Sukono Sukono
Keyword(s):  
Stock Price ◽  
Option Price ◽  
Barrier Options ◽  
Barrier Option ◽  
Market Conditions ◽  
Strike Price ◽  
Daily Data ◽  
Closing Price ◽  
The Right ◽  
Initial Price

Abstract. This study aims to minimize the violation of the assumptions of determining price options by taking into account the actual market conditions in order to obtain the right price that will provide high profits for investors. The method used to determine the option price in this study is the Kamrad Ritchken trinomial with volatility values that will be modeled first using GARCH. The data used in this study is daily data (5 working days per week) from the closing price of the stock price of PT. Bank Rakyat Indonesia, Tbk (BBRI. Based on the results of the research, the best model is GARCH (1,1). For the call up barrier option, increase the strike price with the initial price and barrier which causes the option price to call up the barrier "in" and "out" decreases, on the contrary to the put barrier option, an increase in strike price with the initial price and a barrier that causes the put barrier option price to both put up-in and put up-out. initial and barrier which still causes the call down barrier option price both in and out decreases, on the contrary in the put down barrier option, increasing strike price with the initial price and barrier which causes the put down barrier option price to increase in and out.Keywords: Barrier Options, Trinomial, Kamrad Ritchken, Volatility, GARCH  Abstrak. Penelitian ini bertujuan untuk meminimalkan pelanggaran asumsi-asumsi penentuan harga opsi dengan memperhatikan kondisi pasar yang sebenarnya sehingga diperoleh harga yang tepat yang akan memberikan keuntungan tinggi bagi investor. Metode yang digunakan untuk menentukan harga opsi dalam penelitian ini adalah trinomial Kamrad Ritchken dengan nilai volatilitas yang akan dimodelkan terlebih dahulu dengan menggunakan GARCH. Data yang digunakan dalam penelitian ini adalah data harian (5 hari kerja per minggu) dari harga penutupan harga saham PT. Bank Rakyat Indonesia, Tbk (BBRI). Berdasarkan hasil penelitian diperoleh model yang paling baik adalah GARCH (1,1). Untuk opsi call up barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi call up barrier baik "in" maupun "out" menurun, sebaliknya pada opsi put barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi put barrier baik put up-in maupun put up-out meningkat. Sedangkan untuk opsi call barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi call down barrier baik in maupun out menurun, sebaliknya pada opsi put down barrier, peningkatan strike price dengan harga awal dan barrier yang tetap menyebabkan harga opsi put down barrier baik in maupun out meningkat.Kata Kunci :  Opsi Barrier, Trinomial, Kamrad Ritchken, Volatilitas, GARCH

scholarly journals Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1271
Author(s):  
Marianito R. Rodrigo
Keyword(s):  
Mellin Transform ◽  
Jump Diffusion ◽  
Futures Contracts ◽  
Barrier Options ◽  
Barrier Option ◽  
Underlying Asset ◽  
Diffusion Dynamics ◽  
Path Dependent ◽  
The Right ◽  
Right To Buy

A barrier option is an exotic path-dependent option contract where the right to buy or sell is activated or extinguished when the underlying asset reaches a certain barrier price during the lifetime of the contract. In this article we use a Mellin transform approach to derive exact pricing formulas for barrier options with general payoffs and exponential barriers on underlying assets that have jump-diffusion dynamics. With the same approach we also price barrier options on underlying futures contracts.

First-order calculus and option pricing

2014 ◽  
Vol 01 (01) ◽  
pp. 1450009 ◽  
Author(s):  
Peter Carr
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Option Pricing ◽  
Stochastic Calculus ◽  
Quadratic Variation ◽  
Modern Theory ◽  
Barrier Options ◽  
Barrier Option ◽  
First Order ◽  
Itô Calculus

The modern theory of option pricing rests on Itô calculus, which is a second-order calculus based on the quadratic variation of a stochastic process. One can instead develop a first-order stochastic calculus, which is based on the running minimum of a stochastic process, rather than its quadratic variation. We focus here on the analog of geometric Brownian motion (GBM) in this alternative stochastic calculus. The resulting stochastic process is a positive continuous martingale whose laws are easy to calculate. We show that this analog behaves locally like a GBM whenever its running minimum decreases, but behaves locally like an arithmetic Brownian motion otherwise. We provide closed form valuation formulas for vanilla and barrier options written on this process. We also develop a reflection principle for the process and use it to show how a barrier option on this process can be hedged by a static postion in vanilla options.

scholarly journals Investigation of the barrier options pricing models

2009 ◽  
Vol 50 ◽  
Author(s):  
Rita Palivonaitė ◽  
Eimutis Valakevičius
Keyword(s):  
Option Pricing ◽  
Adaptive Mesh ◽  
Options Pricing ◽  
Barrier Options ◽  
Barrier Option ◽  
Pricing Models ◽  
Black Scholes ◽  
Barrier Option Pricing ◽  
Critical Regions ◽  
Options Pricing Models

In the article three methods of barrier option pricing are analysed and compared: Black–Scholes, trinomial ant adaptive mesh algorithm. Investigation with Lithuanian firm’s stock showed, that to get better results it is offered to adapt higer resolution mesh on critical regions of trinomial tree.

scholarly journals Rating Migration and Bond Valuation: Towards Ahistorical Rating Migration Matrices and Default Probability Term Structures

2019 ◽  
Vol 5 (1) ◽  
pp. 12
Author(s):  
Brian Barnard
Keyword(s):  
Term Structure ◽  
Cash Flows ◽  
Default Probability ◽  
Reduced Form ◽  
Probability Of Default ◽  
Forward Rates ◽  
Bond Valuation ◽  
Term Structures ◽  
Probability Term ◽  
The Impact

The study examines rating migration, and default probability term structures obtained from rating migration matrices. It expands on the use of rating migration matrices with reduced form bond valuation models, by formally delineating the probability of default according to the likely rating paths of a bond, as implied by the rating migration matrix. Further, two alternatives are also considered. First, the cost of default is stipulated as the recovery of par according to the exit rating upon default. Also, in addition to stating the value of a bond in terms of expected cash flows, when considering the probability of default, the value of a bond is alternatively stated as the present value of all likely rating paths of the bond, discounted against the market risk-bearing bond forward rates of the different rating categories. The impact of term structure volatility and rating migration uncertainty on bond valuation is also considered.It is shown that the relationship between rating migration and default probability is complex, and the default probabilities of different rating categories are time-dependent and not isolated from each other. Also, rating migration resembles a delayed default process that influences default probabilities of subsequent intervals. The implications of a rating migration matrix may perhaps only be fully understood through simulation. This form one of the first points by which to evaluate rating migration matrices. The results of the valuation model show that historical rating migration matrices may not be optimal for pricing bonds ahistorically. A principal premise of the study is the dichotomy between historical values and ahistorical estimates, particularly with regards to rating migration. It is argued that historical estimates face two key shortcomings: they must be able to accurately forecast future rating migration and rating category intensities as a result, and they must specify a method to include rating migration uncertainty. An optimization model is delineated to extract ahistorical rating migration matrices from market prices. This too has implications that should be considered. In light of the above, reduced form models may have an advantage over structural models, in their ability to portray a far more sophisticated default process.

scholarly journals Pricing barrier options with discrete dividends

2017 ◽  
Vol 04 (04) ◽  
pp. 1750044
Author(s):  
D. Jason Gibson ◽  
Aaron Wingo
Keyword(s):  
Option Pricing ◽  
Analytic Approach ◽  
Barrier Options ◽  
Barrier Option ◽  
Discrete Dividends ◽  
And Performance ◽  
Barrier Option Pricing

The presence of discrete dividends complicates the derivation and form of pricing formulas even for vanilla options. Existing analytic, numerical, and theoretical approximations provide results of varying quality and performance. Here, we compare the analytic approach, developed and effective for European puts and calls, of Buryak and Guo with the formulas, designed in the context of barrier option pricing, of Dai and Chiu.

Emotional Reactivity to Visual Content as Revealed by ERP Component Clustering

2015 ◽  
Vol 29 (4) ◽  
pp. 135-146 ◽  
Author(s):  
Miroslaw Wyczesany ◽  
Szczepan J. Grzybowski ◽  
Jan Kaiser
Keyword(s):  
Emotional Reactivity ◽  
Brain Activity ◽  
Affective State ◽  
Occipital Lobe ◽  
Stimulus Onset ◽  
Emotional States ◽  
Neural Basis ◽  
Temporoparietal Junction ◽  
The Right ◽  
The Impact

Abstract. In the study, the neural basis of emotional reactivity was investigated. Reactivity was operationalized as the impact of emotional pictures on the self-reported ongoing affective state. It was used to divide the subjects into high- and low-responders groups. Independent sources of brain activity were identified, localized with the DIPFIT method, and clustered across subjects to analyse the visual evoked potentials to affective pictures. Four of the identified clusters revealed effects of reactivity. The earliest two started about 120 ms from the stimulus onset and were located in the occipital lobe and the right temporoparietal junction. Another two with a latency of 200 ms were found in the orbitofrontal and the right dorsolateral cortices. Additionally, differences in pre-stimulus alpha level over the visual cortex were observed between the groups. The attentional modulation of perceptual processes is proposed as an early source of emotional reactivity, which forms an automatic mechanism of affective control. The role of top-down processes in affective appraisal and, finally, the experience of ongoing emotional states is also discussed.

The Impact of Internal Work Environment on the Retention of Healthcare Providers at Turaif General Hospital

2019 ◽  
Vol 10 (12) ◽  
pp. 1183-1199
Author(s):  
Mohammed Alrouili ◽  
Keyword(s):  
Work Environment ◽  
General Hospital ◽  
Professional Growth ◽  
Healthcare Providers ◽  
Entire Study ◽  
Internal Work ◽  
Research Findings ◽  
Study Population ◽  
The Right ◽  
The Impact

This study attempted to identify the impact of internal work environment on the retention of healthcare providers at Turaif General Hospital in the Kingdom of Saudi Arabia. In particular, the study aimed to identify the dimensions of work circumstances, compensation, and relationship with colleagues, professional growth, and the level of healthcare providers’ retention. In order to achieve the study goals, the researcher used the descriptive analytical approach. The researcher used the questionnaire as the study tool. The study population comprised all the healthcare providers at Turaif General Hospital. Questionnaires were distributed to the entire study sample that consisted of 220 individuals. The number of questionnaires valid for study was 183 questionnaires. The research findings were as follows: the participants’ estimate of the work circumstances dimension was high (3.64), the participants’ estimate of the compensation dimension was moderate (3.32), the participants’ estimate of the relationship with colleagues dimension was high (3.62), the participants’ estimate of the professional growth dimension was weak (2.39), and the participants’ estimate of healthcare providers’ retention level was intermediate (2.75). Accordingly, the researcher’s major recommendations are: the need to create the right atmosphere for personnel in hospitals, the interest of the hospital to provide the appropriate conditions for the staff in terms of the physical and moral aspects for building the work adjustment in the staff, and conducting training courses and educational lectures for personnel in hospitals on how to cope with the work pressures.

The Right to Housing: Challenges Associated with the ‘Waiting List System’ Ekurhuleni Metropolitan Municipality V Various Occupiers, Eden Park Extension 5 2014 3 SA 23 (SCA)

2017 ◽  
Vol 30 (1) ◽  
pp. 112-121
Author(s):  
Shamier Ebrahim
Keyword(s):  
Supreme Court ◽  
Waiting Lists ◽  
The State ◽  
Waiting List ◽  
Allocation Process ◽  
The Supreme Court ◽  
The Right ◽  
The Impact ◽  
Court Of Appeal

The right to adequate housing is a constitutional imperative which is contained in section 26 of the Constitution. The state is tasked with the progressive realisation of this right. The allocation of housing has been plagued with challenges which impact negatively on the allocation process. This note analyses Ekurhuleni Metropolitan Municipality v Various Occupiers, Eden Park Extension 51 which dealt with a situation where one of the main reasons provided by the Supreme Court of Appeal for refusing the eviction order was because the appellants subjected the unlawful occupiers to defective waiting lists and failed to engage with the community regarding the compilation of the lists and the criteria used to identify beneficiaries. This case brings to the fore the importance of a coherent (reasonable) waiting list in eviction proceedings. This note further analyses the impact of the waiting list system in eviction proceedings and makes recommendations regarding what would constitute a coherent (reasonable) waiting list for the purpose of section 26(2) of the Constitution.

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