## 歡迎登陸 Real Options Valuation 網站

Black-Scholes Option Pricing Formula

In their 1973 paper, *The Pricing of Options and Corporate 歡迎登陸 Real Options Valuation 網站 Liabilities*, Fischer Black and Myron Scholes published an option valuation formula that today is known as the Black-Scholes model. It has become the standard method of pricing options.

The Black-Scholes formula calculates the price of a call option to be:

C = price of the call option |

S = price of the underlying stock |

X = option exercise price |

r = risk-free interest rate |

T = current time until expiration |

N() = area under the normal curve |

d_{1} = [ ln(S/X) + (r + σ 2 /2) T ] / σ T 1/2 |

d_{2} = d_{1} - σ T 1/2 |

Put-call parity requires that:

Then the price of a put option is:

**Assumptions**

The Black-Scholes model assumes that the option can be exercised only at expiration. It requires that both the risk-free rate and the volatility of the underlying stock price remain constant over the period of analysis. The model also assumes that the underlying stock does not pay dividends; adjustments can be made to correct for such distributions. For example, the present value of estimated dividends can be deducted from the stock price in the model.

**Warrant Pricing**

Warrants are call options issued by **歡迎登陸 Real Options Valuation 網站** a corporation. They tend to have longer durations than do exchange-traded call options. Warrants can be valued by the Black-Scholes model, but some modifications must be made to the parameters.歡迎登陸 Real Options Valuation 網站

When warrants are exercised, the company typically issues new shares at the exercise price to fill the order. The resulting increase in shares outstanding dilutes the share value. If there were ** n** shares outstanding, and

**warrants are exercised,**

*m***α**represents the percentage of the value of the firm that is represented by the warrants, where

When using the Black-Scholes model to value the warrants, it is worthwhile to use total amounts instead of per share amounts in order to better account for the dilution. The current share price ** S** becomes the enterprise value (less debt) to be acquired by the warrant holders. The exercise price is the total warrant exercise amount, adjusted for the fact that in paying cash to the firm to exercise the warrants, the warrant holders in effect are paying a portion of the cash,

**α**, to themselves.

The inputs to the Black-Scholes model for both option pricing and warrant pricing are outlined in the following table.

**Black-Scholes Parameters for Pricing Options and Warrants**

Input Parameter | Option Pricing | Warrant Pricing |

S | current share price | α V, where V is enterprise value minus debt. |

X | exercise price per share | total warrant exercise amount multiplied by (1 - α). |

T | current time to expiration | average T for warrants |

r | interest rate | interest rate |

σ | standard deviation of stock return | standard deviation for returns on enterprise value, including warrants |

**Recommended Reading**

The articles on this website are copyrighted material and may not be reproduced,

stored on a computer disk, republished on another website, or distributed in any

form without the prior express written permission of QuickMBA.com.

## real option valuation

Dear Sir, as well as I understood the value of option comprices intrinsic value and time value. The intrinsic value is difference between asset price and exercise price.

In the 歡迎登陸 Real Options Valuation 網站 technical article related real option valuation there was example with the following initial data:

Asset Value (Pa) = $90m

Exercise price (Pe) = $140m

Exercise date (t) = Four years

Risk free rate (r) = 5%

Volatility (s) = 40%

as the result of call option calculation 20.8

So, intrinsic value = 60, and the time value 20.8-60=-39.2

How it could be explained taking that option value is always 歡迎登陸 Real Options Valuation 網站 positive?

- Topics: 57
- Replies: 50063

The intrinsic value is the amount you would pay for an option if you could exercise it now.

On your figures, the intrinsic value is 歡迎登陸 Real Options Valuation 網站 zero. Nobody would pay 140 for something worth 90 :-).

(Had the asset value been 140 and the exercise price had been 90, then the intrinsic value would be 140 – 90 = 50. Obviously the value of the option would be completely different and not be 20.8.)

## Real Option Valuation 1.0

The Real Option Valuation model 歡迎登陸 Real Options Valuation 網站 encompasses a suite of option pricing tools to quantify the 歡迎登陸 Real Options Valuation 網站 embedded strategic value for a range of financial analysis and investment scenarios. Traditional discounted cash flow investment analysis will only **歡迎登陸 Real Options Valuation 網站** accept an investment if the returns on the project exceed the hurdle rate. While this is a worthwhile exercise, it fails to consider the myriad of strategic options that are associated with many investments. This model provides the ability to identify what options might exist in your proposal and the tools to estimate the quantification of them. The key features of this model include: Ease and flexibility of input, with embedded help prompts; Informative 'Quick Start' menu for choosing the correct tool for the situation; Modified Black Scholes models to value the options to delay, expand, or abandon investments; Automatic binomial 'tree' builder model to evaluate complex strategic options with multiple stages; Nash equilibrium Game Theory model to evaluate market entry strategies in a competitive environment; and Ability to predefine historical investment and/or industry risk profiles to utilize across models.

## 歡迎登陸 Real Options Valuation 網站

188.18.253.215 copy

198.41.242.30

53450

PJSC Rostelecom

The internet is a big network of connected devices, every device has a unique address where others can send information when they want to communicate. This unique identifier is your IP address and it is automatically assigned to you by your Internet Service Provider (ISP).

Width/height:

Width/height:

Preferred language: Russian

URL:

Headers:

User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_7_3) AppleWebKit/535.20 (KHTML, like Gecko) Chrome/19.0.1036.7 Safari/535.20

Currently most of internet traffic is served over IPv4, consisting in four series of numbers ranging from 0 to 255. There are "only" 4 billion IPv4 adresses, to avoid running out of available addresses IPv6 was developed, expanding the number to 340 trillion trillion trillion (2 128 ).