Tag Archive | "stock price"

Binary Options: Black-Scholes Valuation of Binary Options

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In the Black-Scholes model, we can find the price of the option by the formulas below. In these, stock price is denoted by S, strike price is denoted by K, time to maturity is denoted by T , dividend rate is denoted by q, risk-free interest rate is denoted by r and volatility is denoted by σ . the cumulative distribution function of the normal distribution is denoted by Φ,

 \Phi(x) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^x e^{-\frac{1}{2} z^2} dz.

and,

 d_1 = \frac{\ln\frac{S}{K} + (r-q+\sigma^{2}/2)T}{\sigma\sqrt{T}},\,d_2 = d_1-\sigma\sqrt{T}. \,
Black-Scholes Valuation

Cash-or-nothing call

If the spot is above the strike at maturity then this pays out one unit of cash. Now its value is given by,

 C = e^{-rT}\Phi(d_2). \,

Cash-or-nothing put

If the spot is below the strike at maturity then this pays out one unit of cash. Now its value is given by,

 P = e^{-rT}\Phi(-d_2). \,

Asset-or-nothing call

If the spot is above the strike at maturity then this pays out one unit of asset. Now its value is given by,

 C = Se^{-qT}\Phi(d_1). \,

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Warrant: Pricing of Warrants

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There are various methods (models) of evaluation that are available in order to value warrants theoretically, in these models the Black-Scholes evaluation model is also included. However, it is important for the investors to have some understanding about the various influences on warrant prices.

warrant price

Components of Market Value of Warrant

We can divide the market value of a warrant into two components:

  • Intrinsic value
  • Time value

Intrinsic Value

Intrinsic value is simply the difference between the exercise (strike) price and the underlying stock price. Warrants are also known as in-the-money or out-of-the-money, but that depends on where the current asset price is in relation to the warrant’s exercise price.

intrinsic value2

Thus, for example, for call warrants, the warrant has no intrinsic value (only time value – to be explained shortly), if the stock price is below the strike price. The warrant has intrinsic value and is said to be in-the-money if the stock price is above the strike.

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Warrant: Introduction to Warrant

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In finance, warrant is a name given to a security that entitles the holder to buy stock of the company that issued it at a specified price, usually this price is higher than the stock price at time of issue.

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Frequently Warrants are  attached as a sweetener to bonds or preferred stock, by which the issuer is allowed to pay lower interest rates or dividends. Also in order to enhance the yield of the bond they can be used, and they make bonds more attractive to potential buyers. Moreover warrants can also be used in private equity deals. Frequently, these warrants are detachable, and they can be sold independently of the bond or stock.

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Employee Stock Option: Employee Stock Options In USA

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In this article I will discuss the USA GAAP, Types of Employee Stock Options and Taxation of employee stock options in the USA.

USA GAAP

According to US generally accepted accounting principles that took effect before June 2005, stock options that are granted to employees did not need to be recognized as an expense on the income statement when granted, although in the notes the cost was disclosed to the financial statements. By this a potentially large form of employee compensation is allowed to not show up as an expense in the current year, and therefore, currently it overstate income. It has been asserted by many assert that over-reporting of income by such methods as this by American corporations had been one of the factors that contributed in the Stock Market Downturn of 2002.

GAAP

In the US, employee stock options have to be expensed under US GAAP. Each company must initiate expensing stock options from the first reporting period of a fiscal year that began after June 15, 2005. As for most companies the fiscal years are the calendars, for most companies by this it means beginning with the first quarter of 2006.

As a result of this, companies by which the expensing options have not been voluntarily started will only see an income statement effect in fiscal year 2006. After the effective date, companies will be allowed, but they are not required, to restate prior-period results.

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What do you understand by Strike Price?

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In options, a key variable in a derivatives contract between two parties is known as the strike price, or exercise price. Where the delivery of the underlying instrument is required by the contract, the trade will be at the strike price, regardless of the spot price (market price) of the underlying instrument at that time.

strike price

Definition of Strike Price 

The strike price is the fixed price at which the owner of an option is able to purchase the underlying security or commodity, in the case of a call, or sell, it in the case of a put. When the option is exercised it is that price  at which the stock will be bought or sold.

Usually the strike price is referred to as the exercise price.

For instance, an IBM May 50 Call has a strike/exercise price of $50 a share. When the option is exercised 100 shares of IBM stock for $50 a share will be bought (Call option) by the owner of the option.

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