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.

PRICING OPTIONS UNDER STOCHASTIC INTEREST RATE AND THE FRASCA–FARINA PROCESS: A SIMPLE, EXPLICIT FORMULA

2021 ◽  
pp. 2150003
Author(s):  
MOAWIA ALGHALITH
Keyword(s):  
Interest Rate ◽  
Simple Formula ◽  
Stochastic Interest Rate ◽  
European Options ◽  
Pricing Options ◽  
Black Scholes Model ◽  
Stochastic Interest ◽  
Black Scholes ◽  
Practical Complexity ◽  
Theoretical Limitation

Assuming a stochastic interest rate, we introduce a simple formula for pricing European options. In doing so, we provide a complete closed-form formula that does not require any numerical/computational methods. Furthermore, the model and formula are far simpler than the previous models/formulas. Our formula is as simple as the classical Black–Scholes pricing formula. Moreover, it removes the theoretical limitation of the original Black–Scholes model without any added practical complexity.

Discounted optimal stopping problems for the maximum process

2000 ◽  
Vol 37 (4) ◽  
pp. 972-983 ◽  
Author(s):  
Jesper Lund Pedersen
Keyword(s):  
Optimal Stopping ◽  
Infinite Horizon ◽  
Stopping Times ◽  
Value Functions ◽  
Black Scholes Model ◽  
Lookback Options ◽  
Black Scholes ◽  
Maximum Process ◽  
Optimal Stopping Problems ◽  
Optimal Stopping Times

The maximality principle [6] is shown to be valid in some examples of discounted optimal stopping problems for the maximum process. In each of these examples explicit formulas for the value functions are derived and the optimal stopping times are displayed. In particular, in the framework of the Black-Scholes model, the fair prices of two lookback options with infinite horizon are calculated. The main aim of the paper is to show that in each considered example the optimal stopping boundary satisfies the maximality principle and that the value function can be determined explicitly.

Discounted optimal stopping problems for the maximum process

2000 ◽  
Vol 37 (04) ◽  
pp. 972-983 ◽  
Author(s):  
Jesper Lund Pedersen
Keyword(s):  
Optimal Stopping ◽  
Infinite Horizon ◽  
Stopping Times ◽  
Value Functions ◽  
Black Scholes Model ◽  
Lookback Options ◽  
Black Scholes ◽  
Maximum Process ◽  
Optimal Stopping Problems ◽  
Optimal Stopping Times

The maximality principle [6] is shown to be valid in some examples of discounted optimal stopping problems for the maximum process. In each of these examples explicit formulas for the value functions are derived and the optimal stopping times are displayed. In particular, in the framework of the Black-Scholes model, the fair prices of two lookback options with infinite horizon are calculated. The main aim of the paper is to show that in each considered example the optimal stopping boundary satisfies the maximality principle and that the value function can be determined explicitly.

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