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Roll No : 121

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Fischer black

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Fischer Black was born 11 Jan 1938 in Georgetown, Washington

DC, USA.

1959 Fischer Black earned his bachelor's degree in physics.

In 1964, he earned a PhD from Harvard University in appliedmathematics.

After graduating he worked at the consulting firm of Arthur D.Little

1972-75 Black was at the University of Chicago, Graduate School

of Business first as visiting professor and then as a full professor. He later left the University of Chicago to work at the MIT Sloan

School of Management. In 1984, he joined Goldman Sachs.

HISTORY

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In 1997, the Nobel Prize for Economics was

awarded jointly to Myron Scholes and to Robert C.

Merton (In the development of the valuation ofstock-options).

Memorial prize awarded in honor of Fischer Black

that rewards individual financial research.

Fischer black Awards

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Main Contribution in two models

Capital assets pricing modelOption pricing model / Black and schole

model.

Fischer black Model

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Systematic Risk : These are market risks that cannot

be diversified away. Interest rates, recessions and wars

are examples of systematic risks.Unsystematic Risk: Also known as "specific risk," this

risk is specific to individual stocks and can be

diversified away as the investor increases the number

of stocks in his or her portfolio.The Formula:

Capital assets pricing model

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What Is an Option:

contract between two parties in which one party has

the right but not the obligation to do something,usually to buy or sell some underlying asset .

Put options are contracts giving the option holder the

right to sell something.

call options conversely entitle the holder to buysomething.

The Black and Scholes Model

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Fischer's most impressive work is the Black-Scholes formula

which calculates the price of a call option.

It was originally developed in 1973 by two professors,Fischer Black and Myron Scholes.

They designed the model to calculate the price of a

European-style call option on non-dividend-paying stocks.

(Recall that a European option is one that can beexercised only on the expiration date, not before, asopposed to an American option, which can be executedanytime before the expiration date.)

The Black and Scholes Model

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The price that is paid for the assets when the option is exercise

called the exercise price or striking price.

Higher the price of the stock greater the value of the option. The strike price is the price at which the option can be exercised,

or the price at which you can buy the underlying stock.

If the price of the stock is above the strike price, the call optionis said to be in the money and option almost sure to be exercise.

If the price of the stock is the same as the strike price the calloption is said to be at the money.

If the price of the stock is below the strike price the call optionis said to be out of the money.

The Black and Scholes Model

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The Black and Scholes Model

The variable N(d1) is called the hedge ratio, or the delta, for the calloption. The hedge ratio tells how much the option price will changewhen the underlying stock price changes by some small amount.

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The stock pays no dividends during the option's life.

European exercise terms are used

European exercise terms dictate that the option canonly be exercised on the expiration date.

Markets are efficient

No commissions are charged

Interest rates remain constant and known

Assumptions of the Black and Scholes Model

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