scholarly journals An Analytic Valuation of a Deposit Insurance

MATEMATIKA ◽  
2018 ◽  
Vol 34 (3) ◽  
pp. 115-128 ◽  
Author(s):  
Endah RM Putri ◽  
Venansius R Tjahjono ◽  
Daryono B Utomo
Keyword(s):  
Deposit Insurance ◽  
Insurance Premium ◽  
Transform Method ◽  
Put Option ◽  
Black Scholes Model ◽  
Interest Rate Volatility ◽  
Asset Value ◽  
Black Scholes ◽  
Option Model ◽  
Insurance Model

A deposit insurance is a measure to protect bank’s depositors fully or partly from the risk of losses caused by the banks failure to pay its debts when due. If the bank does not meet the payment since the asset value of the bank is less than debt, the guarantor will do the payment and take over the bank’s assets. The role of the guarantor is considered as a deposit insurance. Similar mechanism of the insurance to the European put option model, motivates the use of a Black-Scholes model in the valuation. The deposit insurance model is solved using a Fourier transform method analytically. Numerical results based on the solution confirms the results obtained by previous research. Also, some behaviours of the deposit insurance premium due to interest rate, volatility, and deposit-to-asset value ratio are presented.

scholarly journals Can The IDX Be Hegded ? : Comparison of Black Scholes Option Model And Garch Option Model Using Long Strangle Strategy

2020 ◽  
Vol 20 (3) ◽  
pp. 252
Author(s):  
Riko Hendrawan ◽  
Gede Teguh Laksana ◽  
Wiwin Aminah
Keyword(s):  
Arima Model ◽  
Garch Model ◽  
Call Option ◽  
Average Percentage ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Model ◽  
The One ◽  
The Garch Model

The purpose of this research was to compare the accuracy of the Black Scholes option model and the GARCH option model on index options using IDX Composite (IHSG) data from 2009-2018 with the long strangle strategy. The Black Scholes volatility constructed by using historical volatility, while GARCH volatility constructed by using the ARIMA model and the best lag. The accuracy of options analyzed using the average percentage mean square error (AMSE) to find the best model. The results of this study showed that for the one month option, the GARCH model is more accurate for a call option with 0.26%, while the Black Scholes model is more accurate for a put option with 0.18%. For the two month option, the GARCH model is more accurate for a call option with 0.92%, while the Black Scholes model is more accurate for a put option with 0.26%. For the three month option, the Black Scholes model is more accurate for a call option and put option with 2.00% and 0.31%, respectively. The results of this study further sharpen the research conducted by Bhat and Arekar (2016)and Hendrawan(2010) Keywords : Black Scholes Options Model; GARCH Option Model; Long Strangle; ,Index Option.,

scholarly journals On Comparative Analysis for the Black-Scholes Model in the Generalized Fractional Derivatives Sense via Jafari Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Saima Rashid ◽  
Sobia Sultana ◽  
Rehana Ashraf ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Fractional Derivative ◽  
Adomian Decomposition Method ◽  
Capital Asset Pricing ◽  
Transform Method ◽  
Uniqueness Results ◽  
Black Scholes Model ◽  
Asset Pricing Models ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Generalized Fractional Derivatives

The Black-Scholes model is well known for determining the behavior of capital asset pricing models in the finance sector. The present article deals with the Black-Scholes model via the Caputo fractional derivative and Atangana-Baleanu fractional derivative operator in the Caputo sense, respectively. The Jafari transform is merged with the Adomian decomposition method and new iterative transform method. It is worth mentioning that the Jafari transform is the unification of several existing transforms. Besides that, the convergence and uniqueness results are carried out for the aforesaid model. In mathematical terms, the variety of equations and their solutions have been discovered and identified with various novel features of the projected model. To provide additional context for these ideas, numerous sorts of illustrations and tabulations are presented. The precision and efficacy of the proposed technique suggest its applicability for a variety of nonlinear evolutionary problems.

The Constant Elasticity of Variance Models: New Evidence from S&P 500 Index Options

2004 ◽  
Vol 07 (02) ◽  
pp. 173-190 ◽  
Author(s):  
C. F. Lee ◽  
Ta-Peng Wu ◽  
Ren-Raw Chen
Keyword(s):  
European Contract ◽  
Chi Square ◽  
Index Options ◽  
Market Prices ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Model ◽  
New Evidence

The seminal work by Cox (1975, 1996), MacBeth and Merville (1979, 1980) and Emanuel and Macbeth (1982) show that, both theoretically and empirically, the constant elasticity of variance option model (CEV) is superior to the Black–Scholes model in explaining market prices. In this paper, we extend the MacBeth and Merville (1979, 1980) research by using a European contract (S&P 500 index options). We find supportive evidence to the MacBeth and Merville results although our sample is not subject to American premium biases. Furthermore, we reduce the approximation errors by using the non-central chi-square probability functions proposed by Shroder (1989).

scholarly journals VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS

2020 ◽  
Vol 4 (5) ◽  
pp. 1-5
Author(s):  
Akash Singh ◽  
Ravi Gor Gor ◽  
Rinku Patel
Keyword(s):  
Quadrature Method ◽  
European Option ◽  
Brownian Motion Process ◽  
Asset Pricing Model ◽  
Pricing Options ◽  
Put Option ◽  
Variance Gamma Process ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Dynamic Asset Pricing

Dynamic asset pricing model uses the Geometric Brownian Motion process. The Black-Scholes model known as standard model to price European option based on the assumption that underlying asset prices dynamic follows that log returns of asset is normally distributed. In this paper, we introduce a new stochastic process called levy process for pricing options. In this paper, we use the quadrature method to solve a numerical example for pricing options in the Indian context. The illustrations used in this paper for pricing the European style option.  We also try to develop the pricing formula for European put option by using put-call parity and check its relevancy on actual market data and observe some underlying phenomenon.

scholarly journals Interval Pricing Study of Deposit Insurance in China

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Sulin Wu ◽  
Shenggang Yang ◽  
Yifan Wu ◽  
Sangzhi Zhu
Keyword(s):  
Option Pricing ◽  
Deposit Insurance ◽  
Hunan Province ◽  
Pricing Model ◽  
European Option ◽  
Intuitionistic Fuzzy Numbers ◽  
European Option Pricing ◽  
Asset Value ◽  
Black Scholes ◽  
Option Pricing Model

This paper first proposes a European option pricing method for deposit insurance based on triangular intuitionistic fuzzy numbers. In the proposed method, we take into account the randomness and fuzziness of bank asset value simultaneously, and hence, the method can adequately reflect the high uncertainty of bank asset value. This method fuzzifies the value of bank asset, resubmits it into the original deposit insurance option pricing model as a fuzzy random variable, and then gives an analytic formula of deposit insurance rates using a risk-neutral method. After this, we have also conducted a numerical analysis. In specific, we have obtained the premium interval and presented the static analysis of key parameters. Finally, seven small- and middle-sized banks in Hunan Province in China are used as examples to validate the proposed interval pricing model. The Black-Scholes option pricing model and Yoshida’s triangular fuzzy model are also employed for comparison. The research results show that the interval rates obtained from the proposed European option pricing method for deposit insurance can better reflect the uncertainty of bank asset evaluation than the fixed rates obtained from the Black-Scholes option pricing model. Moreover, the model proposed in this paper is also superior to Yoshida’s model in practice.

scholarly journals Application of the Laplace Homotopy Perturbation Method to the Black–Scholes Model Based on a European Put Option with Two Assets

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 310 ◽  
Author(s):  
Din Prathumwan ◽  
Kamonchat Trachoo
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Explicit Solution ◽  
Homotopy Perturbation Method ◽  
Approximation Methods ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes

In this paper, the Laplace homotopy perturbation method (LHPM) is applied to obtain the approximate solution of Black–Scholes partial differential equations for a European put option with two assets. Different from all other approximation methods, LHPM provides a simple way to get the explicit solution which is represented in the form of a Mellin–Ross function. The numerical examples represent that the solution from the proposed method is easy and effective.

The Probability of Default and Its Design of Experiment

2020 ◽  
pp. 203-234
Author(s):  
Amir Ahmad dar ◽  
N. Anuradha
Keyword(s):  
Structural Model ◽  
Market Value ◽  
Threshold Value ◽  
Probability Of Default ◽  
Black Scholes Model ◽  
Five Factors ◽  
Asset Value ◽  
Black Scholes ◽  
Critical Model ◽  
Debt Holders

The Merton Model is the critical model for financial economics to measure the default of a firm. It was the first structural model because it uses the market value of the firm for estimating the default of the firm. The firm will be in default only when the values of the firm goes down to a threshold value (the debt of the firm), and if it occurs, the owner will put the firm to the debt holders. The effects of parameters-asset value V, firms debt D, interest rate r, the volatility σ, and period T on the probability of default was investigated. To estimate the probability of default of a firm, the Black Scholes Model for European call options is used. The aim is to determine which parameter effects more or less on the probability of default. The experiment is based on the orthogonal array L27 in which the five factors (parameters) are varied at three levels. The Taguchi L27 orthogonal method, ANOM, and ANOVA are used to examine the effect of these parameters on the probability of default. It also provides the best combination where the probability of default is minimum.

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.

Numerical Simulation of Black-Scholes Model by Finite Difference Method

2014 ◽  
Vol 513-517 ◽  
pp. 4090-4093
Author(s):  
Le Le Dong ◽  
Lian Xue ◽  
Lei Wei Lin ◽  
Tuo Chen ◽  
Ming Hui Wu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Empirical Studies ◽  
Financial Derivatives ◽  
Image Simulation ◽  
Pricing Model ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes

Option is the typical representative of financial derivatives, and this paper is focused on the valuation problem of Option. Based on the Black-Scholes Pricing model which had far-reaching influence on the pricing of financial derivatives, researched its theoretical basis and derivation process, and then get the numerical solution via finite difference method and image simulation. And it also includes the part of empirical studies. In research, ZTR and HQ is chosen and analyzed, in order to get the pricing of European put option.

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