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 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 A Numerical Method for Pricing Discrete Double Barrier Option by Lagrange Interpolation on Jacobi Nodes

2021 ◽  
Author(s):  
Amirhossein Sobhani ◽  
mariyan milev
Keyword(s):  
Numerical Method ◽  
Lagrange Interpolation ◽  
Integral Formula ◽  
Operational Matrix ◽  
Barrier Option ◽  
Double Barrier ◽  
Knock Out ◽  
Black Scholes Model ◽  
Important Benefit ◽  
Black Scholes

In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. With regard to the well-known Black-Scholes model, the price of an option in each monitoring date could be calculated by computing a recursive integral formula that is based on the heat equation solution. We have approximated these recursive solutions with the aid of Lagrange interpolation on Jacobi polynomial nodes. After that, an operational matrix, that makes our computation significantly fast, has been derived. In some theorems, the convergence of the presented method has been shown and the rate of convergence has been derived. The most important benefit of this method is that its complexity is very low and does not depend on the number of monitoring dates. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.

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