Barrier Options Under Negative Rates in Black-Scholes

2014 ◽  
Author(s):  
Fabien Le Floc'h ◽  
Alexander Prrll
Keyword(s):  
Barrier Options ◽  
Black Scholes

scholarly journals Quanto Pricing beyond Black–Scholes

2021 ◽  
Vol 14 (3) ◽  
pp. 136
Author(s):  
Holger Fink ◽  
Stefan Mittnik
Keyword(s):  
Option Pricing ◽  
Goodness Of Fit ◽  
Calibration Procedure ◽  
Barrier Options ◽  
Pricing Models ◽  
Modeling Framework ◽  
Double Barrier ◽  
Parameter Stability ◽  
Comprehensive Data ◽  
Black Scholes

Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.

scholarly journals Pricing Exotic Options Using Some Lattice Procedures

2021 ◽  
Vol 41 (1) ◽  
pp. 26-40
Author(s):  
Sadia Anjum Jumana ◽  
ABM Shahadat Hossain
Keyword(s):  
Stock Price ◽  
Lattice Models ◽  
Exotic Options ◽  
Barrier Options ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Binomial Tree Model ◽  
Trinomial Tree Model

In this work, we discuss some very simple and extremely efficient lattice models, namely, Binomial tree model (BTM) and Trinomial tree model (TTM) for valuing some types of exotic barrier options in details. For both these models, we consider the concept of random walks in the simulation of the path which is followed by the underlying stock price. Our main objective is to estimate the value of barrier options by using BTM and TTM for different time steps and compare these with the exact values obtained by the benchmark Black-Scholes model (BSM). Moreover, we analyze the convergence of these lattice models for these exotic options. All the results have been shown numerically as well as graphically. GANITJ. Bangladesh Math. Soc.41.1 (2021) 26-40

scholarly journals DIGITAL DOUBLE BARRIER OPTIONS: SEVERAL BARRIER PERIODS AND STRUCTURE FLOORS

2013 ◽  
Vol 16 (08) ◽  
pp. 1350044 ◽  
Author(s):  
SÜHAN ALTAY ◽  
STEFAN GERHOLD ◽  
RAINER HAIDINGER ◽  
KARIN HIRHAGER
Keyword(s):  
Arbitrary Number ◽  
Barrier Options ◽  
Time Intervals ◽  
Double Barrier ◽  
Black Scholes Model ◽  
Black Scholes

We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black–Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose individual coupons are digital double barrier options. This value can also be approximated by the price of a corridor put.

scholarly journals Use of radial basis functions for meshless numerical solutions applied to financial engineering barrier options

2009 ◽  
Vol 29 (2) ◽  
pp. 419-437 ◽  
Author(s):  
Gisele Tessari Santos ◽  
Maurício Cardoso de Souza ◽  
Mauri Fortes
Keyword(s):  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Analytical Solutions ◽  
Financial Engineering ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Barrier Options ◽  
Black Scholes ◽  
Non Linear ◽  
Radial Basis

A large number of financial engineering problems involve non-linear equations with non-linear or time-dependent boundary conditions. Despite available analytical solutions, many classical and modified forms of the well-known Black-Scholes (BS) equation require fast and accurate numerical solutions. This work introduces the radial basis function (RBF) method as applied to the solution of the BS equation with non-linear boundary conditions, related to path-dependent barrier options. Furthermore, the diffusional method for solving advective-diffusive equations is explored as to its effectiveness to solve BS equations. Cubic and Thin-Plate Spline (TPS) radial basis functions were employed and evaluated as to their effectiveness to solve barrier option problems. The numerical results, when compared against analytical solutions, allow affirming that the RBF method is very accurate and easy to be implemented. When the RBF method is applied, the diffusional method leads to the same results as those obtained from the classical formulation of Black-Scholes equation.

PRICING TWO-ASSET BARRIER OPTIONS UNDER STOCHASTIC CORRELATION VIA PERTURBATION

2015 ◽  
Vol 18 (03) ◽  
pp. 1550018 ◽  
Author(s):  
MARCOS ESCOBAR ◽  
BARBARA GÖTZ ◽  
DANIELA NEYKOVA ◽  
RUDI ZAGST
Keyword(s):  
Perturbation Theory ◽  
Stochastic Volatility ◽  
Correlation Structure ◽  
Barrier Options ◽  
Correlation Effects ◽  
Stochastic Correlation ◽  
Black Scholes ◽  
Leading Term ◽  
Path Dependent ◽  
Correction Terms

The correlation structure is crucial when pricing multi-asset products, in particular barrier options. In this work, we price two-asset path-dependent derivatives by means of perturbation theory in the context of a bi-dimensional asset model with stochastic correlation and volatilities. To our best knowledge, this is the first attempt at pricing barriers with stochastic correlation. It turns out that the leading term of the approximation corresponds to a constant covariance Black–Scholes type price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

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