scholarly journals Bond and Option Prices under Skew Vasicek Model with Transaction Cost

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hossein Samimi ◽  
Alireza Najafi
Keyword(s):  
Brownian Motion ◽  
Analytical Formula ◽  
Option Price ◽  
European Option ◽  
Skew Brownian Motion ◽  
Vasicek Model ◽  
European Option Pricing ◽  
The Interest Rate ◽  
Random Part ◽  
Coupon Bond

This paper studies the European option pricing on the zero-coupon bond in which the Skew Vasicek model uses to predict the interest rate amount. To do this, we apply the skew Brownian motion as the random part of the model and show that results of the model predictions are better than other types of the model. Besides, we obtain an analytical formula for pricing the zero-coupon bond and find the European option price by constructing a portfolio that contains the option and a share of the bond. Since the skew Brownian motion is not a martingale, thus we add transaction costs to the portfolio, where the time between trades follows the exponential distribution. Finally, some numerical results are presented to show the efficiency of the proposed model.

scholarly journals Pricing Option with Stochastic Interest Rates and Transaction Costs in Fractional Brownian Markets

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Lina Song ◽  
Kele Li
Keyword(s):  
Interest Rates ◽  
Transaction Costs ◽  
Estimation Methods ◽  
European Option ◽  
Stochastic Interest Rates ◽  
European Option Pricing ◽  
Stochastic Interest ◽  
Two Factors ◽  
Parameter Estimation Methods ◽  
Coupon Bond

This work deals with European option pricing problem in fractional Brownian markets. Two factors, stochastic interest rates and transaction costs, are taken into account. By the means of the hedging and replicating techniques, the new equations satisfied by zero-coupon bond and the nonlinear equation obeyed by European option are established in succession. Pricing formulas are derived by the variable substitution and the classical solution of the heat conduction equation. By the mathematical software and the parameter estimation methods, the results are reported and compared with the data from the financial market.

REPLICATION SCHEME FOR THE PRICING OF EUROPEAN OPTIONS

2021 ◽  
pp. 2150014
Author(s):  
HIDEHARU FUNAHASHI
Keyword(s):  
Diffusion Process ◽  
Density Function ◽  
Numerical Experiments ◽  
Analytical Formula ◽  
Option Price ◽  
Option Prices ◽  
European Options ◽  
European Option ◽  
Volatility Models ◽  
Replication Scheme

This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the option price of the target asset. By comparison with previous works and numerical experiments, we show that the accuracy of our approximation is high, and the calculation is fast enough for practical purposes; hence, it is suitable for calibration purposes.

scholarly journals PRICING BERMUDAN-TYPE CALL OPTION THROUGH BINOMIAL TREE METHOD

2018 ◽  
Vol 3 (01) ◽  
pp. 16
Author(s):  
Izma Fahria
Keyword(s):  
Option Price ◽  
American Option ◽  
Discrete Models ◽  
Series Data ◽  
Call Option ◽  
European Option ◽  
Binomial Tree ◽  
Early Exercise ◽  
European Option Pricing ◽  
Tree Method

<p class="Default"><em>Bermudan option is a type of option that has characteristics between American option and European option whose its value never exceeds the value of the American option and is never less than the European option. The objective of this research is to calculate Bermudan call option of John Keels Stock through the binomial tree method using statistics software of Matlab R2010a. </em><em>Assessment of Bermudan type option relates to discrete issues, in which the Bermudan type option has a certain number of times of early exercise specified in the option contract, where such times can only be made at some time prior to the option due date. Precise pricing for Bermudan type option can be obtained by discrete models such as the binomial tree method, a numerical method that is one of the most popular approaches for calculating option prices. This research uses time series data obtained from BNI Financial Update Corner, FEB UGM. The Bermudan call option price calculation will be compared with the calculation of European option pricing and American option price with underlying asset without dividend. The results show that the price of John Keels's Bermudan type call option using the binomial tree method yields the same value as American type call option and European type call option.</em><em></em></p><strong><em>Keywords:</em></strong><em> Bermudan Type Option, Binomial Tree Method, Matlab R2010a, Spss 20</em>

European Option Pricing under Fractional Stochastic Interest Rate Model

2010 ◽  
Vol 171-172 ◽  
pp. 787-790
Author(s):  
Wen Li Huang ◽  
Gui Mei Liu ◽  
Sheng Hong Li ◽  
An Wang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Stochastic Interest Rate ◽  
European Option ◽  
European Option Pricing ◽  
Stochastic Interest ◽  
Pde Method ◽  
And Control

Under the assumption of stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with fractional stochastic interest rate. By choosing suitable Hurst index, we can calibrate the pricing model, so that the price can be used as the actual price of option and control the risk management

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