Lecture # 3
Stocktrak Investment Game
Dreivatives: Options etc
Relationship Spot Market & Option Market
Spot
Option
Spot
Share
Market
Share
Market
t=0
Call / Put
option
Market
t=n
Option market links spot market now with
the spot market future of the underlying value ( = share)
Forward contracts, futures and options

Forward contracts:
–

Futures:
–

An agreement to exchange currencies (or stocks etc) at
specified future date and at a specified price (forward rate)
An agreement to exchange currencies (or stocks etc) at
specified future date and at a specified price (forward rate).
Future contracts are normally traded on an exchange.
Options:
–
Gives the holder the right (but not the obligation) to buy (call
option) or to sell (put option) the underlying asset (e.g.
currencies, stocks etc) by a certain date (expiration or exercise
date or maturity) for a certain price (exercise or strike price)
Options
Long position (Net buy
position)
Short position (Net
sell position)
Call option
Buyer / Holder
Seller / Writer
Put option
Buyer / Holder
Seller / Writer
Pricing of options, the idea
C = S– X
C=
Price or value of an (european) call
(stock) option
S=
Price of asset underlying derivate (stock)
X=
Strike or exercise price of an option
Future market for Crude Oil
Future market for Crude Oil
Source: NYMEX 13/09/2006
Future market for Crude Oil
Month
Future
price
OCT
NOV
DEC
JAN
2006
2006
2006
2007
64.2
65.2
66.4
66.8
Source: NYMEX 13/09/2006
Future market for Crude Oil
Key Figures
1 Week
1 Month
3
Months
6
Months
1 Years
Performan
ce
23,40
0.00%
-76.85%
-67.27%
-42.82%
-5.24%
High
3.59
9.95
11.60
11.60
11.60
Low
2.35
0.01
0.01
0.01
0.01
Volatility
4,764.
03
5,393.03
3,090.40
2,161.58
1,806.46
European Call Option (Buyer)
Π
C = S -X
S
European Put Option (Buyer)
Π
P=X-S
S
Assumptions behind the Black-Scholes model







The stock prices follow a geometric Brownion motion
(Wiener process: S = λ*z +ρ*t) with λ and ρ being
constants (lognormal distribution)
The short selling of securities with full use of
proceeds is permitted
There are no transactions costs or taxes; all securities
are perfectly divisble
There are no dividends during the life of the derivate
There aer no riskless arbitrage opportunities
Security trading is continuous
The risk-free interest is constant and the same for all
maturities
Stuff to read!


Futures an Options Markets
–
JC Hull
–
Prentince Hall
–
ISBN 0137833172
Financial Management
–
EF Brigham cs
–
Dryden
–
ISBN9780030210297
Derivatives & Volatility
Option pricing
Black-Scholes (stock) option pricing formula (Call option)
C = S*N(d1) – X*e-r*(T-t)*N(d2)
C=
S=
X=
Price European call (stock) option
Price of asset underlying derivate (stock)
Strike or exercise price of an option
N(d1)
=Standardised normal distribution
N(d2)
=Standardised normal distribution
=
=
e=
r=
Standard deviation of the stock prices (volatility)
Mean of the stock prices
Base natural logarithmes: 2.718281828…
Risk-free interest rate (continuously compounded)