بسم الله الرحمن الرحیم

1. بسم الله الرحمن الرحیم

2. The SverigesRiksbank Prize in Economic Sciences in Memory of Alfred Nobel 1997 Fischer Black Myron S. Scholes Robert C. Merton Prize motivation:“For a new method to determine the value of derivatives"

3. Presented By AbdolmohammadKashian P.H.D Student of Economics, ISU, Tehran

6. Myron S. ScholesBorn: 1 July 1941, Timmins, ON, CanadaAffiliation at the time of the award: Long Term Capital Management, Greenwich, CT, USAPrize motivation: "for a new method to determine the value of derivatives"Field: financial economics

7. Education: McMaster University (1961) (liberal arts, majoring in Economics) University of Chicago (1964) finance and economics University of Chicago (1969) Financial Economics

8. Contribution: Developed a method of determining the value of derivatives, the Black-Scholes formula (together with Fischer Black, who died two years before the Prize award). This methodology paved the way for economic valuations in many areas. It also generated new financial instruments and facilitated more effective risk management in society. The work generated new financial instruments and has facilitated more effective risk management in society

9. Robert C. MertonBorn: 31 July 1944, New York, NY, USAAffiliation at the time of the award:Harvard University, Cambridge, MA, USAPrize motivation: "for a new method to determine the value of derivatives"Field: financial economics

10. Education B.S., Columbia University (Engineering Mathematics), 1966 M.S., California Institute of Technology (Applied Mathematics), 1967 Ph.D., Massachusetts Institute of Technology (Economics), 1970

11. Contribution: Had a direct influence on the development of the Black-Scholes formulaand generalized it in important ways. By devising another way of deriving the formula, he applied it to other financial instruments, such as mortgages and student loans. The work generated new financial instruments and has facilitated more effective risk management in society.

12. Fischer BlackBorn: January 11, 1938 – August 30, 1995Education: Harvard UniversityDied: August 30, 1995 (aged 57)New York, U.S.Field: financial economics

13. Risk management: Risk management is essential in a modern market economy. Financial markets enable firms and households to select an appropriate level of risk in their transactions, by redistributing risks towards other agents who are willing and able to assume them

14. The Instrument of Risk Management and its Valuation: Markets for options, futures and other so-called derivative securities - derivatives, for short - have a particular status. The valuation of these instrument is very important. Effective risk management requires that such instruments be correctly priced.

15. Fischer Black, Robert Merton and Myron Scholes made a pioneering contribution to economic sciences by developing a new method of determining the value of derivatives. Their innovative work in the early 1970s, which solved a longstanding problem in financial economics, has provided us with completely new ways of dealing with financial risk, both in theory and in practice. Their method has contributed substantially to the rapid growth of markets for derivatives in the last two decades. Fischer Black died in his early fifties in August 1995.

16. Black, Merton and Scholes´ contribution extends far beyond the pricing of derivatives, however. Whereas most existing options are financial, a number of economic contracts and decisions can also be viewed as options: an investment in buildings and machinery may provide opportunities (options) to expand into new markets in the future.

17. The history of option valuation Attempts to value options and other derivatives have a long history. One of the earliest endeavors to determine the value of stock options was made by Louis Bachelier in his Ph.D. thesis at the Sorbonne in 1900. The formula that he derived, however, was based on unrealistic assumptions, a zero interest rate, and a process that allowed for a negative share price.

18. Case Sprenkle, James Boness and Paul Samuelson improved on Bachelierís formula. They assumed that stock prices are log-normally distributed (which guarantees that share prices are positive) and allowed for a non-zero interest rate. They also assumed that investors are risk averse and demand a risk premium in addition to the risk-free interest rate. In 1964, Boness suggested a formula that came close to the Black-Scholes formula, but still relied on an unknown interest rate, …

19. The attempts at valuation before 1973 basically determined the expected value of a stock option at expiration and then discounted its value back to the time of evaluation. Such an approach requires taking a stance on which risk premium to use in the discounting.. But assigning a risk premium is not straightforward.

20. The Black-Scholes formula This years laureates resolved these problems by recognizing that it is not necessary to use any risk premium when valuing an option. This does not mean that the risk premium disappears, but that it is already incorporated in the stock price. In 1973 Fischer Black and Myron S. Scholes published the famous option pricing formula that now bears their name (Black and Scholes (1973)). They worked in close cooperation with Robert C. Merton, who, that same year, published an article which also included the formula and various extensions (Merton (1973))

21. The idea behind the new method developed by Black, Merton and Scholes can be explained in the following simplified way: European call option (gives the right to buy a certain share at a strike price of $100 in three months). The value of this call option depends on the current share price; the higher the share price today the greater the probability that it will exceed $100 in three months, in which case it will pay to exercise the option.

22. A formula for option valuation should thus determine exactly how the value of the option depends on the current share price. How much the value of the option is altered by a change in the current share price is called the "delta" of the option.

23. As the share price is altered over time and as the time to maturity draws nearer, the delta of the option changes. In order to maintain a risk-free stock-option portfolio, the investor has to change its composition. Black, Merton and Scholes assumed that such trading can take place continuously without any transaction costs (transaction costs were later introduced by others). The condition that the return on a risk-free stock-option portfolio yields the risk-free rate, at each point in time, implies a partial differential equation, the solution of which is the Black-Scholes formula for a call option:

24. where the variable d is defined by:

25. According to this formula, the value of the call option C , is given by the difference between the expected share price - the first term on the right-hand side - and the expected cost - the second term - if the option is exercised

26. The option pricing formula is named after Black and Scholes because they were the first to derive it. Black and Scholes originally based their result on the capital asset pricing model (CAPM, for which Sharpe was awarded the 1990 Prize). While working on their 1973 paper, they were strongly influenced by Merton. Black describes this in an article (Black (1989))

27. Scientific importance The option-pricing formula was the solution of a more than seventy-year old problem. As such, this is, of course, an important scientific achievement. The main importance of Black, Merton and Scholes´ contribution, however, refers to the theoretical and practical significance of their method of analysis. It has been highly influential in solving many economic problems. The scientific importance extends to both the pricing of derivative securities and to valuation in other areas.

28. Pricing of derivatives The laureates initiated the rapid evolution of option pricing that has taken place during the past two decades.

29. Corporate liabilities Black, Merton and Scholes realized already in 1973 that a share can be interpreted as an option on the whole firm

30. و اخر دعوانا ان الحمد للّه رب العالمین

31. The Options Are Two Kinds: • Vanilla options • Exotic options

32. Vanilla options Vanilla are the basic options also known as European and American. European options can be exercised only at maturity date where American options can be exercised at anytime up to the maturity date. Although European options are easier to analyze, mostly American options are traded on the real market

33. Exotic options We sort options in two main groups, the vanilla options described above andexotic options which are more complex derivatives constructed on standardvanilla options. Barrier option are part of exotic options but they are notthe only ones. We can invent every kind of exotic options and there existsplenty of them, usually traded over-the-counter. However the most commonones are:

34. Exotic Options • Barrier are normal puts and calls except that they disappear or appear if the underlying asset price cross a given level. • Asian have a pay out not determined by the underlying price at maturity but by the average underlying price over some pre-set period of time. • Lookback is a path dependent option where the option owner has the right to buy (sell) the underlying instrument at its lowest (highest) price over some preceding period. • Forward start option is an option whose strike price is determined in the future.

35. Exotic Options • Basket option is an option on the weighted average of several underlying's. • Digital/Binary option pays a fixed amount, or nothing at all, depending on the price of the underlying instrument at maturity. • Bermudan options is an option where the buyer has the right to exercise at a set (always discretely spaced) number of times. This is intermediate between a European option which allows exercise at a single time, namely expiry date, and an American option which allows exercise at any time (the name is a pun: Bermuda is between AmericandEurope).