THE BINOMIAL INTERPOLATED LATTICE METHOD FOR STEP DOUBLE BARRIER OPTIONS

We consider the problem of pricing step double barrier options with binomial lattice methods. We introduce an algorithm, based on interpolation techniques, that is robust and efficient, that treats the "near barrier" problem for double barrier options and permits the valuation of step double barrier options with American features. We provide a complete convergence analysis of the proposed lattice algorithm in the European case.

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Quanto Pricing beyond Black–Scholes

Journal of Risk and Financial Management ◽

10.3390/jrfm14030136 ◽

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.

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CLOSED FORM FORMULAS FOR EXOTIC OPTIONS AND THEIR LIFETIME DISTRIBUTION

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024999000030 ◽

1999 ◽

Vol 02 (01) ◽

pp. 17-42 ◽

Cited By ~ 22

Author(s):

RAPHAËL DOUADY

Keyword(s):

Interest Rates ◽

Closed Form ◽

Term Structure ◽

Exit Time ◽

Exotic Options ◽

Barrier Options ◽

Double Barrier ◽

Knock Out ◽

The Mean ◽

Mirror Principle

We first recall the well-known expression of the price of barrier options, and compute double barrier options by the mean of the iterated mirror principle. The formula for double barriers provides an intraday volatility estimator from the information of high-low-close prices. Then we give explicit formulas for the probability distribution function and the expectation of the exit time of single and double barrier options. These formulas allow to price time independent and time dependent rebates. They are also helpful to hedge barrier and double barrier options, when taking into account variations of the term structure of interest rates and of volatility. We also compute the price of rebates of double knock-out options that depend on which barrier is hit first, and of the BOOST, an option which pays the time spent in a corridor. All these formulas are either in closed form or double infinite series which converge like e-α n2.

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Optimization of European Double-Barrier Options via Optimal Control of the Black-Scholes-Equation

Operations Research Proceedings 2001 ◽

10.1007/978-3-642-50282-8_21 ◽

2002 ◽

pp. 167-174 ◽

Cited By ~ 2

Author(s):

Michael H. Breitner ◽

Tobias Burmester

Keyword(s):

Optimal Control ◽

Barrier Options ◽

Double Barrier ◽

Black Scholes

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Pricing discretely-monitored double barrier options with small probabilities of execution

European Journal of Operational Research ◽

10.1016/j.ejor.2020.07.044 ◽

2021 ◽

Vol 290 (1) ◽

pp. 313-330 ◽

Cited By ~ 1

Author(s):

Vasileios E. Kontosakos ◽

Keegan Mendonca ◽

Athanasios A. Pantelous ◽

Konstantin M. Zuev

Keyword(s):

Barrier Options ◽

Double Barrier ◽

Small Probabilities

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Pricing Double Barrier Options by Combinatorial Approaches

Advances in Soft Computing - Soft Computing as Transdisciplinary Science and Technology ◽

10.1007/3-540-32391-0_116 ◽

2007 ◽

pp. 1131-1140

Author(s):

Tian-Shyr Dai ◽

Yuh-Dauh Lyuu

Keyword(s):

Barrier Options ◽

Double Barrier

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A lattice algorithm for pricing moving average barrier options

Journal of Economic Dynamics and Control ◽

10.1016/j.jedc.2009.10.008 ◽

2010 ◽

Vol 34 (3) ◽

pp. 542-554 ◽

Cited By ~ 15

Author(s):

Min Dai ◽

Peifan Li ◽

Jin E. Zhang

Keyword(s):

Moving Average ◽

Barrier Options ◽

Lattice Algorithm

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Efficient Lattice Method for Valuing of Options with Barrier in a Regime Switching Model

Discrete Dynamics in Nature and Society ◽

10.1155/2016/2474305 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Youngchul Han ◽

Geonwoo Kim

Keyword(s):

Regime Switching ◽

The Other ◽

Barrier Options ◽

Computational Results ◽

Lattice Method ◽

Regime Switching Model ◽

Switching Model ◽

Tree Methods ◽

Local Average ◽

Tree Method

We propose an efficient lattice method for valuation of options with barrier in a regime switching model. Specifically, we extend the trinomial tree method of Yuen and Yang (2010) by calculating the local average of prices near a node of the lattice. The proposed method reduces oscillations of the lattice method for pricing barrier options and improves the convergence speed. Finally, computational results for the valuation of options with barrier show that the proposed method with interpolation is more efficient than the other tree methods.

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