scholarly journals BARRIER OPTION PRICING BY BRANCHING PROCESSES

2009 ◽  
Vol 12 (07) ◽  
pp. 1055-1073 ◽  
Author(s):  
GEORGI K. MITOV ◽  
SVETLOZAR T. RACHEV ◽  
YOUNG SHIN KIM ◽  
FRANK J. FABOZZI
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Analytical Formula ◽  
Model Parameters ◽  
Barrier Options ◽  
Call Option ◽  
Barrier Option ◽  
Market Prices ◽  
Underlying Asset ◽  
Barrier Option Pricing

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.

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.

Brownian Excursions and Parisian Barrier Options

1997 ◽  
Vol 29 (1) ◽  
pp. 165-184 ◽  
Author(s):  
Marc Chesney ◽  
Monique Jeanblanc-Picqué ◽  
Marc Yor
Keyword(s):  
Essential Role ◽  
Fixed Number ◽  
Time Interval ◽  
Barrier Options ◽  
Barrier Option ◽  
Underlying Asset

In this paper we study a new kind of option, called hereinafter a Parisian barrier option. This option is the following variant of the so-called barrier option: a down-and-out barrier option becomes worthless as soon as a barrier is reached, whereas a down-and-out Parisian barrier option is lost by the owner if the underlying asset reaches a prespecified level and remains constantly below this level for a time interval longer than a fixed number, called the window. Properties of durations of Brownian excursions play an essential role. We also study another kind of option, called here a cumulative Parisian option, which becomes worthless if the total time spent below a certain level is too long.

scholarly journals A Semigroup Expansion for Pricing Barrier Options

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Takashi Kato ◽  
Akihiko Takahashi ◽  
Toshihiro Yamada
Keyword(s):  
Expansion Method ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Parabolic Partial Differential Equations ◽  
Barrier Options ◽  
Barrier Option ◽  
Volatility Model ◽  
Barrier Option Pricing ◽  
Asymptotic Expansion Method ◽  
Expansion Scheme

This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develop a semigroup expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, we propose a concrete approximation formula under a stochastic volatility model and demonstrate its validity by some numerical experiments.

Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dimitar Atanasov ◽  
Vessela Stoimenova ◽  
Nikolay M. Yanev
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Data Availability ◽  
Model Parameters ◽  
Reproduction Rate ◽  
Direct Computation ◽  
Infection Dynamics ◽  
Secondary Infections ◽  
Proposed Model ◽  
The Mean

Abstract We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.

BARRIER OPTIONS PRICING WITH JOINT DISTRIBUTION OF GAUSSIAN PROCESS AND ITS MAXIMUM

2017 ◽  
Vol 20 (06) ◽  
pp. 1750042
Author(s):  
PINGJIN DENG ◽  
XIUFANG LI
Keyword(s):  
Gaussian Process ◽  
Joint Distribution ◽  
Options Pricing ◽  
Time Interval ◽  
Exotic Options ◽  
Barrier Options ◽  
Rate Process ◽  
Barrier Option ◽  
Explicit Formulas ◽  
Underlying Asset

Barrier options are one of the most popular exotic options. In this contribution, we propose a performance barrier option, which is a type of barrier option defined with the [Formula: see text]th period logarithm return rate process on an underlying asset over the time interval [Formula: see text], [Formula: see text]. We show that the price of this performance barrier option is determined by the joint distribution of a Slepian process and its maximum. Furthermore, we derive a tractable formula for this joint distribution and obtain explicit formulas for the up-out-call performance option and up-out-put performance option.

scholarly journals Semi-Analytical method for the pricing of barrier options in case of time-dependent parameters (with Matlab® codes)

2018 ◽  
Vol 9 (1) ◽  
pp. 42-67 ◽  
Author(s):  
C. Guardasoni
Keyword(s):  
Analytical Method ◽  
Boundary Integral ◽  
Time Dependent ◽  
Barrier Options ◽  
Barrier Option ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Interest Rate Volatility ◽  
Black Scholes ◽  
Barrier Option Pricing

Abstract A Semi-Analytical method for pricing of Barrier Options (SABO) is presented. The method is based on the foundations of Boundary Integral Methods which is recast here for the application to barrier option pricing in the Black-Scholes model with time-dependent interest rate, volatility and dividend yield. The validity of the numerical method is illustrated by several numerical examples and comparisons.

ANALYTICAL PATH-INTEGRAL PRICING OF DETERMINISTIC MOVING-BARRIER OPTIONS UNDER NON-GAUSSIAN DISTRIBUTIONS

2020 ◽  
Vol 23 (01) ◽  
pp. 2050005
Author(s):  
ANDRÉ CATALÃO ◽  
ROGÉRIO ROSENFELD
Keyword(s):  
Path Integral ◽  
First Passage Time ◽  
Passage Time ◽  
Barrier Options ◽  
Barrier Option ◽  
Entropy Model ◽  
Gaussian Distributions ◽  
Pricing Options ◽  
Barrier Option Pricing ◽  
Non Gaussian

In this work, we present an analytical model, based on the path-integral formalism of statistical mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possibly non-Gaussian distributions of the underlying object. We adapt to our problem a model originally proposed by De Simone et al. (2011) to describe the formation of galaxies in the universe, which uses cumulant expansions in terms of the Gaussian distribution, and we generalize it to take into account drift and cumulants of orders higher than three. From the probability density function, we obtain an analytical pricing model, not only for vanilla options (thus removing the need of volatility smile inherent to the Black & Scholes (1973) model), but also for fixed or deterministically moving barrier options. Market prices of vanilla options are used to calibrate the model, and barrier option pricing arising from the model is compared to the price resulted from the relative entropy model.

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 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.

scholarly journals PENENTUAN HARGA JUAL OPSI BARRIER TIPE EROPA DENGAN METODE ANTITHETIC VARIATE PADA SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (2) ◽  
pp. 71
Author(s):  
LUH HENA TERECIA WISMAWAN PUTRI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
Monte Carlo ◽  
Analytic Solution ◽  
Asset Price ◽  
Selling Price ◽  
Barrier Options ◽  
Option Prices ◽  
Barrier Option ◽  
Underlying Asset ◽  
Closing Price ◽  
Path Dependent

The purpose of this research is to compare the selling price of down and out barrier option when the prices are simulated by the Antithetic Variate Monte Carlo and the standar Monte Carlo. Barrier options are path dependent options and the payoff depend on whether the underlying asset price touched the barrier or not during the life of the option. In this research, we conducted simulations against the closing price of the shares of PT Adhi Karya using Standard Monte Carlo simulation and the Monte Carlo-Antithetic Variate simulation. After the simulation, we obtained that the option prices using Antithetic Variate produces a cheaper price than the standar one. We also found that the analytic solution has a smaller error on its confidence interval compare to the Monte Carlo Standar.

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