scholarly journals ESTIMASI NILAI IMPLIED VOLATILITY MENGGUNAKAN SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (3) ◽  
pp. 239
Author(s):  
MAKBUL MUFLIHUNALLAH ◽  
KOMANG DHARMAWAN ◽  
NI MADE ASIH
Keyword(s):  
Monte Carlo ◽  
Capital Market ◽  
Implied Volatility ◽  
Option Price ◽  
European Options ◽  
Price Variation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Alternative Investment ◽  
The Capital Market

Investing among investors is an exciting activity to gain profit in the financial world. The development of investment in the financial world affects the number of alternative investment instruments that can be offered to investors in the capital market. The management of instruments in finance depends on the accuracy of forecasting of variables for example volatility. Volatility is a statistic of the degree of price variation in one period to the next which is expressed by ?. Volatility values can be estimated using Implied Volatility. Implied Volatility is the volatility used in determining the price of European options obtained by equalizing the price of the theoretical options, the price obtained from the Black-Scholes model, with the option price in the market. In this research will discuss how to estimate Implied Volatility value using the option obtained from simulation with Monte Carlo.

scholarly journals The Black-Scholes Model Guideline For Options Course As Taught At Notre Dame University - Lebanon

2011 ◽  
Vol 4 (1) ◽  
Author(s):  
Viviane Y. Naimy
Keyword(s):  
Option Price ◽  
Stochastic Calculus ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Calculus I ◽  
Relationship Of ◽  
The Relationship

This paper presents the methodology used for Notre Dame University’s finance students to explain and explore the Black-Scholes model without going through the complexity of mathematics to model random movements or through stochastic calculus. I will name and develop the steps that I follow in order to allow students to properly use the Black-Scholes model and to understand the relationship of the model’s inputs to the option price while monitoring the risk via delta and gamma hedging.

The Financial Clouds Review

2012 ◽  
pp. 1062-1083 ◽  
Author(s):  
Victor Chang ◽  
Chung-Sheng Li ◽  
David De Roure ◽  
Gary Wills ◽  
Robert John Walters ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Monte Carlo ◽  
Least Square ◽  
Software As A Service ◽  
Special Technique ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Speed Accuracy ◽  
Financial Software ◽  
Business Framework

This paper demonstrates financial enterprise portability, which involves moving entire application services from desktops to clouds and between different clouds, and is transparent to users who can work as if on their familiar systems. To demonstrate portability, reviews for several financial models are studied, where Monte Carlo Methods (MCM) and Black Scholes Model (BSM) are chosen. A special technique in MCM, Least Square Methods, is used to reduce errors while performing accurate calculations. Simulations for MCM are performed on different types of Clouds. Benchmark and experimental results are presented for discussion. 3D Black Scholes are used to explain the impacts and added values for risk analysis. Implications for banking are also discussed, as well as ways to track risks in order to improve accuracy. A conceptual Cloud platform is used to explain the contributions in Financial Software as a Service (FSaaS) and the IBM Fined Grained Security Framework. This study demonstrates portability, speed, accuracy, and reliability of applications in the clouds, while demonstrating portability for FSaaS and the Cloud Computing Business Framework (CCBF).

The Financial Clouds Review

2013 ◽  
pp. 125-146
Author(s):  
Victor Chang ◽  
Chung-Sheng Li ◽  
David De Roure ◽  
Gary Wills ◽  
Robert John Walters ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Monte Carlo ◽  
Least Square ◽  
Software As A Service ◽  
Special Technique ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Speed Accuracy ◽  
Financial Software ◽  
Business Framework

This paper demonstrates financial enterprise portability, which involves moving entire application services from desktops to clouds and between different clouds, and is transparent to users who can work as if on their familiar systems. To demonstrate portability, reviews for several financial models are studied, where Monte Carlo Methods (MCM) and Black Scholes Model (BSM) are chosen. A special technique in MCM, Least Square Methods, is used to reduce errors while performing accurate calculations. Simulations for MCM are performed on different types of Clouds. Benchmark and experimental results are presented for discussion. 3D Black Scholes are used to explain the impacts and added values for risk analysis. Implications for banking are also discussed, as well as ways to track risks in order to improve accuracy. A conceptual Cloud platform is used to explain the contributions in Financial Software as a Service (FSaaS) and the IBM Fined Grained Security Framework. This study demonstrates portability, speed, accuracy, and reliability of applications in the clouds, while demonstrating portability for FSaaS and the Cloud Computing Business Framework (CCBF).

Arbitrage Pricing

2019 ◽  
pp. 95-118
Author(s):  
Tomas Björk
Keyword(s):  
Continuous Time ◽  
Implied Volatility ◽  
Futures Contracts ◽  
Martingale Measures ◽  
Bank Account ◽  
No Arbitrage ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Financial Derivative ◽  
Delta Hedging

The chapter starts with a detailed discussion of the bank account in discrete and continuous time. The Black–Scholes model is then introduced, and using the principle of no arbitrage we study the problem of pricing an arbitrary financial derivative within this model. Using the classical delta hedging approach we derive the Black–Scholes PDE for the pricing problem and using Feynman–Kač we also derive the corresponding risk neutral valuation formula and discuss the connection to martingale measures. Some concrete examples are studied in detail and the Black–Scholes formula is derived. We also discuss forward and futures contracts, and we derive the Black-76 futures option formula. We finally discuss the concepts and roles of historic and implied volatility.

AN APPROPRIATE APPROACH TO PRICING EUROPEAN-STYLE OPTIONS WITH THE ADOMIAN DECOMPOSITION METHOD

2018 ◽  
Vol 59 (3) ◽  
pp. 349-369
Author(s):  
ZIWIE KE ◽  
JOANNA GOARD ◽  
SONG-PING ZHU
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
European Options ◽  
Black Scholes Model ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Digital Options ◽  
Continuous Estimation

We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black–Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black–Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results.

scholarly journals PREFERENCES, LÉVY JUMPS AND OPTION PRICING

2007 ◽  
Vol 03 (01) ◽  
pp. 0750001 ◽  
Author(s):  
CHENGHU MA
Keyword(s):  
Option Pricing ◽  
Contingent Claims ◽  
Economic Variable ◽  
European Options ◽  
Jump Risk ◽  
Representative Agent ◽  
Potential Explanation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Lévy Jumps

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black–Scholes, Naik–Lee, Cox–Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black–Scholes model is explored.

scholarly journals A Note on Numerical Solution of a Linear Black-Scholes Model

2014 ◽  
Vol 33 ◽  
pp. 103-115 ◽  
Author(s):  
Md. Kazi Salah Uddin ◽  
Mostak Ahmed ◽  
Samir Kumar Bhowmilk
Keyword(s):  
Time Integration ◽  
Weighted Average ◽  
Financial Mathematics ◽  
European Options ◽  
Average Scheme ◽  
Put Options ◽  
Weighted Average Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Solution Methods

Black-Scholes equation is a well known partial differential equation in financial mathematics. In this article we discuss about some solution methods for the Black Scholes model with the European options (Call and Put) analytically as well as numerically. We study a weighted average method using different weights for numerical approximations. In fact, we approximate the model using a finite difference scheme in space first followed by a weighted average scheme for the time integration. Then we present the numerical results for the European Call and Put options. Finally, we investigate some linear algebra solvers to compare the superiority of the solvers. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 103-115 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17664

A Simple Model for Option Pricing with Jumping Stochastic Volatility

1998 ◽  
Vol 01 (04) ◽  
pp. 487-505 ◽  
Author(s):  
Stefano Herzel
Keyword(s):  
Implied Volatility ◽  
Market Price ◽  
Volatility Risk ◽  
Simple Modification ◽  
Closed Form Solutions ◽  
Black Scholes Model ◽  
A Value ◽  
Black Scholes ◽  
Delta Hedging ◽  
Actual Price

This paper proposes a simple modification of the Black–Scholes model by assuming that the volatility of the stock may jump at a random time τ from a value σa to a value σb. It shows that, if the market price of volatility risk is unknown, but constant, all contingent claims can be valued from the actual price C0, of some arbitrarily chosen "basis" option. Closed form solutions for the prices of European options as well as explicit formulas for vega and delta hedging are given. All such solutions only depend on σa, σb and C0. The prices generated by the model produce a "smile"-shaped curve of the implied volatility.

scholarly journals Pricing Basket Options by Polynomial Approximations

2021 ◽  
Author(s):  
Pablo Olivares ◽  
Alexander Alvarez
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Closed Form ◽  
Computational Effort ◽  
Basket Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Power Moments ◽  
Exponential Power ◽  
Closed Form Approximation

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

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