The Binomial Model, Bachelier’s Model and the Black-Scholes Model

2007 ◽  
pp. 140-152
Keyword(s):  
Binomial Model ◽  
Black Scholes Model ◽  
Black Scholes

scholarly journals CONVERGENCE OF EUROPEAN LOOKBACK OPTIONS WITH FLOATING STRIKE IN THE BINOMIAL MODEL

2014 ◽  
Vol 17 (04) ◽  
pp. 1450025 ◽  
Author(s):  
FABIEN HEUWELYCKX
Keyword(s):  
Interest Rate ◽  
Binomial Model ◽  
Black Scholes Model ◽  
Lookback Options ◽  
Lookback Option ◽  
Black Scholes ◽  
Double Sum

In this paper, we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox–Ross–Rubinstein to its evaluation with the Black–Scholes model. We do the same for its delta. We confirm that these convergences are of order [Formula: see text]. For this, we use the binomial model of Cheuk–Vorst which allows us to write the price of the option using a double sum. Based on an improvement of a lemma of Lin–Palmer, we are able to give the precise value of the term in [Formula: see text] in the expansion of the error; we also obtain the value of the term in 1/n if the risk free interest rate is nonzero. This modelization will also allow us to determine the first term in the expansion of the delta.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

scholarly journals Comparison: Binomial model and Black Scholes model

2018 ◽  
Vol 2 (1) ◽  
pp. 715-730
Author(s):  
Amir Ahmad Dar ◽  
◽  
N. Anuradha ◽  
Keyword(s):  
Binomial Model ◽  
Black Scholes Model ◽  
Black Scholes

scholarly journals Comparison: Binomial model and Black Scholes model

2018 ◽  
Vol 2 (1) ◽  
pp. 230-245 ◽  
Author(s):  
Amir Ahmad Dar ◽  
◽  
N. Anuradha ◽  
Keyword(s):  
Binomial Model ◽  
Black Scholes Model ◽  
Black Scholes

VALUATION AND OPTIMAL EXERCISE TIME FOR THE BANXICO PUT OPTION

2003 ◽  
Vol 06 (03) ◽  
pp. 257-275
Author(s):  
BEGOÑNA FERNÁNDEZ FERNÁNDEZ ◽  
PATRICIA SAAVEDRA BARRERA
Keyword(s):  
Central Bank ◽  
Additional Condition ◽  
Optimal Time ◽  
Binomial Model ◽  
Exercise Time ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Exotic Option ◽  
The Right

Since 1996, the Central Bank of México issues a put option in order to buy American Dollars as a way of increasing its international reserves. This is an exotic option that gives the right to the Mexican banks to sell this currency to the Central Bank at the price of the day before the date of exercise. The option has a maturity of one month and can be exercised on any day during this period, subject to an additional condition that depends on the average price of the Dollar during the previous 20 days. In this work we study the valuation and the optimal time of exercise of this option under the Binomial and the Black–Scholes Models. The optimal time of exercise is found for the Binomial model and a rule of exercise is proposed for the Black–Scholes Model. Numerical results are included to illustrate the performance of this rule of exercise.

An analytical approximation formula for the pricing of credit default swaps with regime switching

2021 ◽  
Vol 63 ◽  
pp. 143-162
Author(s):  
Xin-Jiang He ◽  
Sha Lin
Keyword(s):  
Regime Switching ◽  
Credit Default Swap ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Current Time ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Credit Default

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments. doi:10.1017/S1446181121000274

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