Transcript Robert C. Merton Born: 31 July 1944, New York, NY, USA

‫بسم هللا الرحمن‬
‫الرحیم‬
The Sveriges Riksbank 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"
Presented By Abdolmohammad Kashian
P.H.D Student of Economics, ISU, Tehran
Myron S. Scholes
Born: 1 July 1941, Timmins, ON, Canada
Affiliation at the time of the award: Long Term
Capital Management, Greenwich, CT, USA
Prize motivation: "for a new method to
determine the value of derivatives"
Field: financial economics
Education:
McMaster University (1961) (liberal arts,
majoring in Economics)
University of Chicago (1964) finance and
economics
University
Economics
of
Chicago
(1969)
Financial
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
Robert C. Merton
Born: 31 July 1944, New York, NY, USA
Affiliation at the time of the award: Harvard
University, Cambridge, MA, USA
Prize motivation: "for a new method to determine
the value of derivatives"
Field: financial economics
Education
B.S., Columbia University
Mathematics), 1966
M.S., California Institute of
(Applied Mathematics), 1967
(Engineering
Technology
Ph.D., Massachusetts Institute of Technology
(Economics), 1970
Contribution:
Had a direct influence on the development
of the Black-Scholes formula and 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.
Fischer Black
Born: January 11, 1938 – August 30, 1995
Education: Harvard University
Died:
August 30, 1995 (aged 57)
New York, U.S.
Field: financial economics
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
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.
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.
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.
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.
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 , …
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
straightforward.
𝐹𝑉
𝑃𝑉 =
(1 + 𝑟)𝑛
is
not
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))
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.
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.
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 riskfree 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 riskfree rate, at each point in time, implies a partial
differential equation, the solution of which is
the Black-Scholes formula for a call option:
𝐶 = 𝑆𝑁 𝑑 − 𝐿𝑒
−𝑟𝑡
𝑁(𝑑 − 𝜎 𝑡)
where the variable d is defined by:
𝑆
𝜎2
𝑙𝑛 + 𝑟 +
𝑡
𝐿
2
𝑑=
𝜎 𝑡
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
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))
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.
Pricing of derivatives
The laureates initiated the rapid
evolution of option pricing that has
taken place during the past two
decades.
Corporate liabilities
Black, Merton and Scholes realized already in
1973 that a share can be interpreted as an
option on the whole firm
‫و اخر دعوانا ان‬
‫ه‬
‫الحمد ّلل رب‬
‫العالمین‬
The Options Are Two Kinds:
Vanilla
options
Exotic
options
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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
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We sort options in two main groups, the vanilla options
described above and exotic options which are more complex
derivatives constructed on standard vanilla options. Barrier
option are part of exotic options but they are not the only
ones. We can invent every kind of exotic options and there
exists plenty of them, usually traded over-the-counter.
However the most common ones are:
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 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.
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 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 Americand Europe).
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