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.

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.

Brownian Excursions and Parisian Barrier Options

1997 ◽  
Vol 29 (01) ◽  
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 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.

ON OPTIMAL SUPER-HEDGING AND SUB-HEDGING STRATEGIES

2013 ◽  
Vol 16 (06) ◽  
pp. 1350038 ◽  
Author(s):  
YUKIHIRO TSUZUKI
Keyword(s):  
Joint Distribution ◽  
Optimal Pricing ◽  
Exotic Options ◽  
Underlying Asset ◽  
Knock Out ◽  
Basket Options ◽  
Hedging Strategies ◽  
Pricing Bounds ◽  
Exchange Options ◽  
Underlying Processes

This paper proposes optimal super-hedging and sub-hedging strategies for a derivative on two underlying assets without any specification of the underlying processes. Moreover, the strategies are free from any model of the dependency between the underlying asset prices. We derive the optimal pricing bounds by finding a joint distribution under which the derivative price is equal to the hedging portfolio's value; the portfolio consists of liquid derivatives on each of the underlying assets. As examples, we obtain new super-hedging and sub-hedging strategies for several exotic options such as quanto options, exchange options, basket options, forward starting options, and knock-out 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 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 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.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

2021 ◽  
pp. 2150002
Author(s):  
Guimin Yang ◽  
Yuanguo Zhu
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Numerical Experiments ◽  
Critical Value ◽  
The Other ◽  
Options Pricing ◽  
Underlying Asset ◽  
Pricing Problems ◽  
Fractional Differential ◽  
The One

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

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