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6. International Aspects of Derivative Securities Markets
The global OTC derivatives market is huge, and dwarfs the size of exchange traded contracts.
According to the BIS, at year-end 2013 there was $710.182 trillion worth of OTC contracts
outstanding compared to $62.14 trillion in exchange traded contracts. Interest rate contracts are
the predominate type. Securities in the U.S. markets and the euro and U.S. dollar are the most
common bases for derivatives.
Summary of Text Table
10-11 & 10-12
Amounts of OTC Global Derivative Securities
Outstanding (Bill $)
Contract Jun-08 Dec-13 % Growth
Total OTC $683,814 $632,579 -7%
Currency Contracts $62,983 $67,358 7%
Interest Rate Contracts $458,304 $489,703 7%
Equity Linked Contracts $10,177 $6,251 -39%
Amounts of Exchange Traded Global Derivative Securities (Bill $)
Futures Contracts $28,631.7 $26,012.7 -31%
Option Contracts $55,655.0 $33,796.2 -21%
Many of the amounts have declined since their 2008 levels due to the financial crisis. As of 2013
the decline was starting to reverse in many of the markets.
1.1.1.1 Appendix 10: Black-Scholes Option Pricing Model (available on Connect
or from your McGraw-Hill representative)
The Black-Scholes model is notoriously difficult to explain to students. The model is
C = SN(d1) - E(e-rfT)N(d2) Black-Scholes Model
d1 = {Ln(S0/E) + [(r+(²/2))]T}/(T)
(How far have to go + Normal Return)/ Standard Error
d2 = d1 - (T)
C = the call option’s price
S = the underlying asset price
E = Exercise price of the option
2 = Continuous annual variance of the underlying spot price
r = continuously compounded annual risk free rate
N(dx) = value of the cumulative normal density function for the value d1 or d2
respectively. In Excel N(dx) can be found using the Normsdist function.
Conceptually, d1 and d2 measure the probability that the option will wind up in the
money.
The assumptions of the model include:
Constant
Constant r
Lognormal probability distribution of asset prices
The spot asset has no cash flows prior to the option’s expiration, or early exercise is not
allowed.
Frictionless, perfect capital markets.
Suppose you have a European call option on a stock with 90 days to maturity. The continuously
compounded risk free interest rate is 5%. The stock price is $55 and the exercise price is $60.
The continuously compounded annual standard deviation of the stock’s returns is 48%. The
stock pays no dividends. The Black-Scholes Call Premium C0 can be found from the following:
194160
36590480
36590
2
480
5
60
55
1
2
.
/.
)/()
.
(%)
$
$
(Ln
d
N(d1) = 0.423027
432510365904801941602 .)/.(.d
N(d2) = 0332687
using the Normsdist function in excel to find N(dx)
C0 = ($55 x 0.423027) – [$60e-0.05(90/365) x 0.332687]= $3.55
The value of European put options may be found from:
P0 = -SN(-d1) + E(e-rfT)N(-d2) Black-Scholes Model
For the same example as above the Black-Scholes Put premium P0 may be found as:
P0 = -$55 x (1-0.423027) + $60 (e-0.05(90/365)(1-0.332687) = $7.81
Teaching Tip: European put options may also be valued via put call parity as follows:
P0 = C0 - S0 + (E e-rfT)
1.1.1.2 VI. Web Links
http://www.federalreserve.gov/ Website of the Board of Governors of the Federal Reserve
http://www.cmegroup.com/ Website of CME Group which includes CME, CBOT,
NYMEX and COMEX
http://www.cboe.com/ Chicago Board Option’s Exchange. The CBOE has a built
in downloadable tutorial on option trading.
http://www.eurexchange.com/ Eurex’s website, the electronic futures exchange located in
Chicago is a division of Eurex.
http://www.americanbanker.com The publication of the banker’s trade association.
http://www.cftc.gov/ Commodity Futures Trade Commission homepage.
http://www.sec.gov/ The Securities Exchange Commission
http://www.wsj.com/ Website of the Wall Street Journal Interactive edition. The
web version of the well known financial newspaper can be
personalized to meet your own needs. Instructors can also
receive via e-mail current events cases keyed to financial
market news complete with discussion questions.
http://www2.isda.org/ International Swap and Derivatives Association, the trade
association for the derivatives industry. Statistics on OTC
derivatives may now be found at www.bis.org, the Bank of
International Settlements.
http://www.fdic.gov/ The Federal Deposit Insurance Corporation’s website. New
regulations and current and historical banking statistics are
available on this site.
http://www.ft.com/ Financial Times, won two Espy awards for best new site
and best non U.S. news site. Coverage of global events and
markets.
1.1.1.2.1.1 VII. Student Learning Activities
1. Go the CBOE’s website and find the Option Calculator. Learn how to use the calculator to
find option prices. What are an option’s delta, gamma, theta, vega, and rho?
2. At the CBOE website play the Options Quest Online Game. You can choose any level of
difficulty. Write a two paragraph report on what you learned and indicate how well you did
in the game.
3. Go to the CME’s website and investigate margin requirements for different contracts and
answer the following:
a) Why are the margin requirements different for the T-bond contract and a stock
contract?
b) Why are the margin requirements different for the T-bond contract and a Eurodollar
contract?
4. Research the attempt by Herbert and Nelson Hunt to corner the silver market in 1980. What
does it mean to ‘corner the market?’ What was their goal and were they successful? Why or
why not?
5. There has been significant concern that oil price speculators unnecessarily drive up the price
of oil via futures market speculation. Indeed many news commentators have been unable to
cogently explain exactly who sets the price of oil in the first place. Some proposals that
come forth to limit speculation including vastly increasing margin requirements on oil futures
contracts.
a) Discuss the pros and cons of attempting to limit speculation in this way. Think about
the effects on both speculators and hedgers.
b) Do you agree that oil prices are ‘too high’? Is this due to speculation?
c) What could be done to reduce oil prices?
