On the Numerical Solution of Black-Scholes Equation - Article Example


Extract of sample
On the Numerical Solution of Black-Scholes Equation

An option is a financial instrument that gives an individual the right to buy or sell an asset, at some time in the future. Options are traded on a number of exchanges throughout the world, the first of which was the Chicago Board Options Exchange (CBOE), which started in 1971.The price V(S,t) of the derivative or the option depends on the price of the underlying S and time t. V(S,t) satisfies the Black Scholes partial differential equation. (1) Where r is the interest free interst rate and ? is the volatility of the underlying. The right to buy the underlying in the future for an agreed upon price , called the Exercise price(E) ,with in a date called the expiry date, is called a Call Option.. Similarly the right to sell the underlying for the Exercise price before the expiry date is the Put Opttion.The time to expiry is the expiry time denoted by T. The pay-off equations for the options gives the boundary conditions for the Black-Scholes equation.The variable t can take values between 0 and T while S can take values from 0 to ? . ...
Download paper


Numerical Solution of Black-Scholes equation. 1 Introduction Black-Scholes model is used to describe behaviour of derivative instruments like call and put option. The model yields a partial differential equation called the Black-scholes equation which can reduced to the form of the famous heat equation…
Author : garmstrong
Download 1

Related Essays

Risk Management: Principles and Applications
If the market price for the asset is greater than the strike price, it will be worth while for the holder to use the option. In this instance the option writer is forced to trade the asset to the option owner. The price at which a call is traded is called premium. In the case of calls, a higher stock price means that other things being equal; the option is more likely to be in the money on maturity. Therefore, a higher S is associated with a higher premium (Hull, 1997). Conversely, the higher the exercise price K, the lower is the premium. A higher exercise price makes it less likely that the...
10 pages (2510 words) Assignment
Option Pricing Theory
An option provides the buyer the right to buy or sale the quantity of goods he or she wants at a fixed price known as the strike price. Since the process of buying an option is optional, the holder can choose not to buy or sale the assets. There are two options these are; right to buy and right to sale. Options can come in several varieties like; a put option, gives the seller an underlying price to sale an option (Bostock, 2004). A call option gives its holder the right to buy an option on its set price; these options depend on when the option is offered. Therefore, the paper aims at giving a...
8 pages (2008 words) Essay
The accounting equation and it's componants
The accounting equation and it's componants ...
3 pages (753 words) Essay
Understand & explain the Accounting Equation and its components
Understand & explain the Accounting Equation and its components ...
3 pages (753 words) Essay
The Black Model for Interest Rate Derivatives
Over the last two and half decades, finance has experienced tremendous and exciting developments especially with reference to derivatives markets. One of the reasons explaining the idea of tremendous and exciting developments within financial sector is the fact that both hedger and speculators within financial markets find it attractive to trade derivate specifically assets rather than trading on the assets themselves (Gupta and Subrahmanyam. 2005). Development of derivatives is considered as one of the most successful upcoming within capital markets (Brigo and Mercurio 2001). Within...
6 pages (1506 words) Essay
Ff options can only be priced because they can be replicated, why do we need them?
Although derivatives are technically conspicuous reason being they can undergo replication using basic financial instruments, they are still the tools that provide those who participate in the market to full of risk to manage the particular risks. Nature of options dynamic replication Dynamic hedging of options is never conducted even with the market makers(Lussier & PareI, 2004). In nature, options are hard to deal with due to the technicality of the language used to describe the tools. The difference between dynamic and static hedging is small since hedging is only realized on minor...
4 pages (1004 words) Assignment
Debate the thoeries of Accounting for stock options
Fair value model, lattice model and finally minimum value method which is based upon the someone’s willingness to purchase a call option on a share of stock at the current fair value of the stock with the right to postpone payment of the exercise until the end of the options period, ignoring the volatility of the underlying stock in valuation calculation. This has necessitated the emergence of alternative incentive methods to premium cash thus employee stock options. Any stock option with exercise price higher than the price of the underlying stocks at the exercise date are exchanged for new...
8 pages (2008 words) Research Paper
Got a tricky question? Receive an answer from students like you! Try us!