Transcript Document

Financial Information Management
Options
Stefano Grazioli
Critical Thinking
 Financial Engineering = Financial
analytics
 Lab Easy meter
Financial Information Management
Options
An introduction
(spans two lectures)
Risk
Managing Risk
Auditing
Disaster
planning
Risk Mitigation
Business
continuity
Insurance
Diversification
Hedging &
Options
Option
is a contract giving the buyer the right,
but not the obligation, to buy or sell an
underlying asset (for example a stock) at
a specific price on or before a specified
date
 Options are derivatives.
CBOE
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CBOE trades options on 3,300 securities.
More than 50,000 series listed.
1/4 of US option trading
Hybrid market: 97% total (68% volume) is electronic
Year 2013
Source: CBOE & OCC web site – 2013 - Table includes CBOE + C2 combined
Example Scenario
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You own 100,000 GOOGLE stocks.
@ $1,200 -> $120,000,000.
You are pretty happy.
But you are also worried. What if the price drops to $1,000?
You need some kind of insurance against that.
Somebody is willing to commit to buying your GOOGLE stock at $1,200 (if
you want), two years from now.
But she wants $10 per stock. Now.
You decide that it is a good deal. So, you buy 100,000 contracts that give
you the choice to sell your stock at the agreed price two years from now.
You have bought 100,000 put options.
Put Options
 A put option gives to its holder the right
to sell the underlying security at a given
price on or before a given date.
 "Insurance" analogy
Types of Traders
 Speculators
 Arbitrageurs
 Hedgers (us)
Financial Information Management
WINIT
What Is New
In Technology?
Another Scenario
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You are an executive at the Coca Cola Company.
You make $1,000,000 a year.
You are pretty happy.
The Board wants to make sure that you will do your best to keep the price of the
CocaCola stock up.
Rather than giving you a well-deserved raise, they offer to you a deal. They
promise that in three years they will give you the chance to buy 200,000 stocks at
$40.
Right now the stock is valued at $40.
If the company does well, the stock price could go as up as $50.
So you think: “In three years I could just get my 200,000 @ $40 and then
immediately sell them back to the market for $50....”
You conclude that an extra $2,000,000 in your pocket is a good thing.
You have been given 200,000 call options.
Call Options
 A call option gives to its holder the right
to buy the underlying security at a given
price on or by a given date
 "security deposit" analogy
Nomenclature
option price = premium
Call Option
can buy 1 IBM stock
@ $180.00
on 5 Mar 2014
underlier
IBM Stock
Price: $185.00
“spot” (i.e.,
market) price
strike
price
Put Option
can sell 1 IBM stock
@ $190.00
on 18 Apr 2014
expiration:
European vs. American
Nomenclature
IBM Stock
Spot Price: $185.00
Call Option
can buy 1 IBM stock
@ $180.00 today
In the
money
Call Option
can buy 1 IBM stock
@ $185.00 today
At the
money
Call Option
can buy 1 IBM stock
@ $190.00 today
Out of
the
money
Financial Information Management
Valuating Options
An introduction
Evaluating Options
 On expiration day, value is certain and
dependent on (= strike – spot)
 On any other day
value is not deterministic,
because of uncertainty
about the future.
Evaluating PUT Options
The current value of a Put Option depends on:
1) the current price of the underlier 2) the strike price +
3) the underlier volatility +
4) the time to expiration +
5) the risk-free interest rate Bought a put option on IBM for
$1
x = $200
IBM’s price is $205
Question:
what is the value
of the option
right now?
Put Option:
Can sell IBM for $200
a) IBM’s market price is
$190
b) IBM’s market price is
$210
PAST
NOW
EXPIRATION
Solving the Option Evaluation
Problem
The Black-Scholes Formulas
P = –S[N(–d1)] + Xe-rt[N(–d2)]
d1 = {ln(S/X) + (r + s 2/2)t}
st
d2 = d1 - st
P = value of a European put option,
S = current spot price,
X = option “strike” or “exercise” price,
t = time to option expiration (in years),
r = riskless rate of interest (per annum),
s = spot return volatility (per annum),
N(z) = probability that a standardized normal variable will be less than z. In Excel, this can be calculated using NORMSDIST(d).
Delta for a Call = N(d1) Delta for a Put = N(d1) -1
NORMSDIST(z)
N (z)
1.2
1
0.8
0.6
0.4
0.2
0
-3
-2
-1
0
z
d
1
2
3
Formulas
 Example:
S = $ 42, X = $40
t = 0.5
r = 0.10 (10% p.a.)
s = 0.2 (20% p.a.)
 Output:
d1 = 0.7693
d2 = 0.6278
N(d1) = 0.7791
N(d2) = 0.7349
C = $4.76 and P=$0.81
BS Assumptions
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Unlimited borrowing and lending at a constant risk-free
interest rate.
The stock price follows a geometric Brownian motion with
constant drift and volatility.
There are no transaction costs.
The stock does not pay a dividend.
All securities are perfectly divisible (i.e. it is possible to buy
any fraction of a share).
There are no restrictions on short selling.
The model treats only European-style options.
Black Scholes
was so much fun…
Let’s do it again!
Evaluating Call Options
The current value of a call Option depends on:
1) the current price of the underlier +
2) the strike price 3) the underlier volatility +
4) the time to expiration +
5) the risk-free interest rate +
Bought a call option for
$2.00, x=40
CocaCola’s price
is $40
Question:
what is the value
of the option
right now?
Call Option:
Can buy CocaCola
for $40
a) CocaCola’s price is $45
b) CocaCola’s price is $35
PAST
NOW
EXPIRATION
The Black-Scholes Formulas
C = S[N(d1)] – Xe-rt[N(d2)]
d1 = {ln(S/X) + (r + s 2/2)t}
st
d2 = d1 - st
C = value of a European call option
S = current spot price,
X = option “strike” or “exercise” price,
t = time to option expiration (in years),
r = riskless rate of interest (per annum),
s = spot return volatility (per annum),
N(z) = probability that a standardized normal variable will be less than d. In Excel, this can be calculated using NORMSDIST(z).
Delta for a Call = N(d1) Delta for a Put = N(d1) -1
Market Mechanics
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Market listed: bid & ask
Buyer & seller: holder & writer
Long & short positions
Blocks of 100 – NOT FOR THE TOURNAMENT
Option class: defined by the underlier and type
Option series: defined by an expiration date & strike
example: APPL May Call 290
Expiration: Sat after the 3rd Friday of the month
 America vs European (TOURNAMENT)
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Transaction costs: commissions on trading and exercising.