SIMPLIFIED OPTION PRICING TECHNIQUES

2019 ◽  
Vol 14 (01) ◽  
pp. 1950003 ◽  
Author(s):  
MOAWIA ALGHALITH ◽  
CHRISTOS FLOROS ◽  
THOMAS POUFINAS
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Asset Price ◽  
Alternative Methods ◽  
Strike Price ◽  
Put Options ◽  
Simplifying Assumptions ◽  
Risk Free Rate ◽  
Increasing Function ◽  
Free Rate

In this paper we provide alternative methods for pricing European and American call and put options. Our contribution lies in the simplification attempted in the models developed. Such simplification is feasible due to our observation that the value of the option can be derived as a function of the underlying stock price, strike price and time to maturity. This route is supported by the fact that both the risk-free rate and the volatility of the stock are captured by the move of the underlying stock price. Moreover, looking at the properties of the Brownian motion, widely used to map the move of the stock price, we realize that volatility is well depicted by time. Last but not the least, the value of an option is an increasing function of both time and volatility. We find simplified option pricing formulas depending on the underlying asset (price and strike price) and the time to maturity only. We test our formulas against the S&P 500 index options; the advantage of the approach is that less simplifying assumptions are needed and much simpler methods are produced. We provide alternative formulas for pricing European- and American-type options.

scholarly journals Valuing Coca-Cola And PepsiCo Options Using The Black-Scholes Option Pricing Model And Data Downloads From The Internet

2012 ◽  
Vol 8 (6) ◽  
pp. 559-564
Author(s):  
John C. Gardner ◽  
Carl B. McGowan Jr
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Risk Free Rate ◽  
Daily Returns ◽  
Free Rate

In this paper, we demonstrate how to collect the data and compute the actual value of Black-Scholes Option Pricing Model call option prices for Coca-Cola and PepsiCo.The data for the current stock price and option price are taken from Yahoo Finance and the daily returns variance is computed from daily prices.The time to maturity is computed as the number of days remaining for the stock option.The risk-free rate is obtained from the U.S. Treasury website.

scholarly journals OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS

2004 ◽  
Vol 07 (07) ◽  
pp. 901-907
Author(s):  
ERIK EKSTRÖM ◽  
JOHAN TYSK
Keyword(s):  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Strike Price ◽  
Call Options ◽  
Alternative Approach ◽  
Black Scholes ◽  
Market Practice ◽  
The Difference ◽  
Risk Free Rate

There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.

scholarly journals Good Volatility, Bad Volatility, and Option Pricing

2018 ◽  
Vol 54 (2) ◽  
pp. 695-727 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Asset Price ◽  
Jump Diffusion ◽  
Quadratic Variation ◽  
Pricing Model ◽  
Economic Gain ◽  
Underlying Asset ◽  
Model Free ◽  
Option Pricing Model

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

Solutions for Sustainable Banking and Enhancing Banking Competitiveness – Vietinbank Case in Vietnam

2021 ◽  
Vol 11 (2) ◽  
pp. 327-334
Author(s):  
Nguyen Van Dat ◽  
Dinh Tran Ngoc Huy
Keyword(s):  
Stock Price ◽  
Industry 4.0 ◽  
Financial Accounting ◽  
Gdp Growth ◽  
Financial Risks ◽  
Management Implications ◽  
Sustainability Strategies ◽  
Lending Rate ◽  
Risk Free Rate ◽  
Free Rate

During and after China-USA commerce ward, financial accounting transparency will become hot issues as it will help to attract more FDIs capitals flows into the country and stock market. Financial accounting transparency policy will prove enough data for firms and esp., banks in evaluating business risks and financial risks. For economic development during industry 4.0, enhancing banking sustainability in emerging markets such as Vietnam is becoming necessary. The results show us that CPI, GDP growth and risk free rate (Rf) has higher effects on beta CAPM and stock price of Vietinbank (CTG). Risk free rate and lending rate have positive correlation with these 2 variables. Then, this study can enable to propose management implications and risk management to enhance banking sustainability strategies.

scholarly journals A Green′s function for a convertible bond using the Vasicek model

2002 ◽  
Vol 2 (5) ◽  
pp. 219-232 ◽  
Author(s):  
R. Mallier ◽  
A. S. Deakin
Keyword(s):  
Random Walk ◽  
Laplace Transform ◽  
Stock Price ◽  
Mellin Transform ◽  
Convertible Bond ◽  
Vasicek Model ◽  
Function Solution ◽  
Risk Free Rate ◽  
Free Rate

We consider a convertible security where the underlying stock price obeys a lognormal random walk and the risk-free rate is given by the Vasicek model. Using a Laplace transform in time and a Mellin transform in the stock price, we derive a Green′s function solution for the value of the convertible bond.

THE INTERSECTION BETWEEN EUROPEAN PUT PRICE AND ITS PAYOFF FUNCTION

2013 ◽  
Vol 16 (04) ◽  
pp. 1350022
Author(s):  
JIN E. ZHANG ◽  
SHOUJUN HUANG ◽  
TIECHENG LI
Keyword(s):  
Asymptotic Expansion ◽  
Singular Point ◽  
Stock Price ◽  
American Option ◽  
Payoff Function ◽  
Expiration Date ◽  
Dividend Yield ◽  
Risk Free Rate ◽  
Free Rate

In this paper, we study the intersection between the price of a European put and its payoff function. We derive asymptotic expansion formulas for the intersection near expiration date for three different cases of risk-free rate r and dividend yield q, i.e. r > q, r = q, and r < q. The comparison with those of the critical stock price of an American option enhances our understanding on the convergence of the asymptotic expansion near a singular point.

Better Risk Management of Banks and Sustainability - A Case Study in Vietnam

2021 ◽  
Vol 11 (2) ◽  
pp. 481-490
Author(s):  
Nguyen Thi Hang ◽  
Dinh Tran Ngoc Huy ◽  
Le Thu Ha ◽  
Do Hong Nhung
Keyword(s):  
Risk Management ◽  
Stock Price ◽  
Industry 4.0 ◽  
Quantitative Methods ◽  
Management Strategies ◽  
Industrial Manufacturing ◽  
Rapid Economic Growth ◽  
Risk Free Rate ◽  
Free Rate

Modern advanced bank risk management is a current and hot issue for all Vietnam banks, during the context of industry 4.0. Because of rapid economic growth under impacts of China-US commerce war and effects from Covid 19, as welll as industry 4.0, enhancing roles of banks in Vietnam economic development is becoming necessary. This paper also refers to new perspectives on corporate governance issues that can be applied into bank management. This study mainly use combination of quantitative methods and qualitative methods including synthesis, inductive and explanatory methods for a special case of big listed bank in Vietnam, Eximbank. The results show us that better management of bank need to forecast effects from GDP growth, Industrial manufacturing (IM) and Risk free rate (Rf) on both beta and stock price of Eximbank (EIB), in this case we found out there is positive relationship. Then, we can suggest suitable plans for risk management to enhance the bank roles and sustainable management strategies.

scholarly journals Dynamic Asset Pricing with Interactions between Short-Sale and Borrowing Constraints

2021 ◽  
Author(s):  
Lei Shi ◽  
Yajun Xiao
Keyword(s):  
Stock Price ◽  
Borrowing Constraints ◽  
Joint Effect ◽  
Short Sale Constraints ◽  
Short Sale ◽  
Borrowing Constraint ◽  
Risk Free Rate ◽  
Dynamic Asset Pricing ◽  
Free Rate ◽  
Two Equilibria

Abstract This paper studies the joint effect of borrowing and short-sale constraints under heterogeneous beliefs and risk aversions. Although the constraints never simultaneously bind in equilibrium, interesting economics emerge in the anticipatory effects of potentially future binding constraints. In particular, the risk-free rate and Sharpe ratio experience endogenous jumps at a critical state, where two equilibria coexist. Moreover, a short-sale ban can lead to a lower stock price and higher volatility depending on the relative tightness between the constraints, and tightening the borrowing constraint during a short-sale ban can also make returns more volatile.

scholarly journals Numerical Solution of Heston-Hull-White Three-Dimensional PDE with a High Order FD Scheme

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 704 ◽  
Author(s):  
Malik Zaka Ullah
Keyword(s):  
Asset Price ◽  
Method Of Lines ◽  
Three Dimensional ◽  
High Order ◽  
Stochastic Nature ◽  
Numerical Tests ◽  
Pricing Options ◽  
Uniform Grids ◽  
Risk Free Rate ◽  
Free Rate

A new numerical method for tackling the three-dimensional Heston–Hull–White partial differential equation (PDE) is proposed. This PDE has an application in pricing options when not only the asset price and the volatility but also the risk-free rate of interest are coming from stochastic nature. To solve this time-dependent three-dimensional PDE as efficiently as possible, high order adaptive finite difference (FD) methods are applied for the application of method of lines. It is derived that the new estimates have fourth order of convergence on non-uniform grids. In addition, it is proved that the overall procedure is conditionally time-stable. The results are upheld via several numerical tests.

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