December 1 2009 What are financial derivatives They are financial instruments whose value is derived from some other asset index event value or condition Those from which it is derived is known as an ID: 675684
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Slide1
Financial Derivatives
Daniel Thaler
December 1, 2009Slide2
What are financial derivatives?
They are financial instruments whose value is derived from some other asset, index, event, value, or condition.
Those from which it is
derived is known as an
underlying asset. Slide3
Conceptual Example
It’s Super Bowl XLII between the Giants and the Patriots and the Patriots are a 4-1 favorite. Your friend places a $1,000 bet on the Giants to win the game. How much would you pay your friend to have the option to purchase his bet? (Question 1)Slide4
Scenarios
Would you pay him more than $1,000 for this option at the start of the game?
No, you could make the bet yourself
The Giants are winning 3-0 at the end of the first quarter how would the price of the option change?
The price of the option would increase
The Patriots are winning 14-10 with 2:42 left in the game how would the price of the option change?
The price of the option would decrease
The Giants score a late touchdown to make it 17-14 with 0:35 left in the game would you pay him more than $1,000 for this option?
Yes, considering if the Giants win the payout is $4,000.Slide5
Background information
Rather than trade or exchange the underlying asset itself, derivative traders enter into an agreement to exchange cash or assets over time based on the underlying asset.
Derivates
are often highly levered, so a small change in the underlying asset can cause a large change in the value of the derivative.Slide6
More background
Derivatives can be used by investors to speculate and to make a profit if the value of the underlying moves the way they expect
Traders can use derivatives to hedge or mitigate risk in the underlying, by entering into a derivative contract whose value moves in the opposite direction to their underlying position and cancels part or all of it out. Slide7
Back to the Super Bowl
You are a Patriots fan and bet $4,000 on them to win the game (remember the odds are 1-4 so the payout is $1,000). It’s the end of the 3
rd
Quarter and the Patriots are only up 4pts. You want to hedge your risk so you find someone to sell you a $500 option on a $1,000 bet that the Giants win. Answer Question 2.Slide8
Hedging Solutions
How much will you win/lose if the Patriots win/lose?
Pats win, you
win $1,000 - $500 =
$500
Pats lose, you
lose $4,000 – $4,000 - $500 = -$
500
How much would have had to wager without options if you wanted to win $500
$2,000Slide9
Categories
The type of the underlying
Stocks, Bonds, Commodity
The market which they trade
Over-the-counter (OTC), Exchange-traded derivates (ETD)
The relationship between the underlying and the derivative
Options, Futures/Forwards, SwapsSlide10
Options
Contracts that give the owner the right, but not the obligation to buy or sell an asset
The strike price is the price at which the transaction would take place
The option must also have a maturity date
1 Options contract usually represents the right to buy 100 shares of the underlying securitySlide11
Types of Options Trades
Long Call
Long Put
Short Call (“Write a Call”)
Short Put (“Write a Put”)Slide12
Long Call
Buy the right to purchase the stock at the strike price.
Will only exercise if the stocks price is higher than the strike price plus the price paid for the option
Believe the price will INCREASE
For the same amount of money you can obtain a larger amount of options than sharesSlide13
Long CallSlide14
Long Put
Buy the right to sell the stock at the strike price
Will exercise only if the stock price plus the premium is below the strike
Believe the stock price will DECREASESlide15
Long PutSlide16
Write a Call
Selling a call option to a buyer and had the
obligation
to fulfill the contract at a strike price
Will profit only if the stock price remains below that of the strike price plus the premium
Potential loss is unlimited
Believe the stock price will DECREASESlide17
Write a CallSlide18
Write a put
An
obligation
to buy the stock from the put buyer at the strike price
Will profit if stock price plus the premium is above the strike price.
Loss is capped at the full value of the stock
Believe the stock price will INCREASESlide19
Write a putSlide20
Identifying options
Google’s stock price is $570 and Bill has bought 3 option contracts for $15($5 per contract) with a Strike Price of $580.
If the Stock price goes above $600 Bill will exercise the option, What has he bought?
He has a call option
How much will he make?
($600-$580)*300 – $15 = $5,985Slide21
Identifying options
Google’s stock price is $570 and Bill has written 3 option contracts for $9,000 ($3,000 per contract) with a Strike Price of $600.
If the Stock price goes down to $560 Bill will have to exercise the option, What has he written?
He has written a put
How much will he lose?
($560-$600)*300 + $9,000 = -$3,000Slide22
How Risky are Options?
They can expire worthless and they increase leverage
Example: Stock A is selling at 100 and its options are selling at $2.50 with a strike price of $120
You want to invest $1,000
So you can buy 10 shares of stock or….
4 options contracts
In a week the price of the stock is now at 110 so your profit with just the stocks is 10*10 = 100 but lets say the value of the option went up to $4.50(very reasonable) your profit is $2 * 400 = 800Slide23
Option Strategies
Combine any of the four basic options trades (possibly with different exercise prices)
Can also use the two basic kinds of stock trades (long and short)
Used to engineer a particular risk profile to movements in the underlying security. Slide24
Option Strategies
Bull Call SpreadCombines a short call and a callSlide25
Option Strategies
Long StrangleCombines a call and a putSlide26
Other Option Strategies
Bullish Strategies
Bearish Strategies
Neutral Strategies
Bull Put Spread Bear Put Spread Short Straddle
Bull Call
Spread Bear Call Spread
Long Straddle
Covered Straddle Put Time Spread Short Combo
Call
Time Spread Ratio Put Spread Guts
Ratio Call Spread Condor Strangle
Long ButterflySlide27
ExcelSlide28
How are options priced?
Want to find a way to quantify the expected payoffs that would occur if the stock price goes up or goes down.
Also, it must incorporate the length for which the option is available Slide29
How are options priced?
Binomial Options Pricing Model
Uses a “discrete-time” model of the varying price over time of the underlying financial instrument
Black-Scholes Model
A continuous extension of the binomial modelSlide30
Binomial Model
Provides a general numerical model
Process is iterative
Each node represents a possible price at a particular point in timeSlide31
Binomial Model
Steps:
Price tree generation
Calculation of option value at each final node
Calculation of option value at each earlier node
The value at the first node is the price of the optionSlide32
Price Tree Generation
It assumed that at point in the tree the underlying instrument will move either up or down.
Let S = Current Price
Let S
u
= S * u = Price when stock moves up (u >1)Let S
d
= S * d = Price when stock moves down (0<d<1)Slide33
Price Tree Generation
To determine d and u we will use the volatility of the underlying asset which is
σ
u = e ^
σ
rad
(t)
d = e ^ -
σ
rad
(t) = 1/u
t is the time between periods measured in years
This ensure that the tree is recombining which accelerates the computation of the option priceSlide34
Price Tree Generation
Answer Question 5 part (a) Slide35
Value at Final Nodes
The final node is expiration, there if it is profitable to exercise the option you will if not you will let it expire.
For a call option For a put option
Max [ (K – S), 0 ] Max [ (S – K), 0 ]
K is the strike price, S is price of underlying assetSlide36
Value at Final Nodes
Answer Question 5 part (b)Slide37
Value of Option at earlier nodes
Use the value of the option at an intermediate node using the value of the option at the following nodes.
First: need to assign a probability to the price will increase by u or decrease by d (We will use 50/50 chance to keep it simple)Slide38
Value of Option at earlier nodes
The value of an option at an earlier node is then equal to the following:
Max [ (S – Strike), p × V
u
+ (1-p) ×
Vd
] × e
(- r × t)Slide39
Value of Option at earlier nodes
Answer question 5 part (c), calculate the value of the optionSlide40
ExcelSlide41
Black-Scholes Model
A continuous continuation of the binomial model
The binomial model assumes that movements in the price follow a binomial distribution; for many trials, this binomial distribution approaches the normal distribution assumed by Black-
Scholes
.Slide42
Black-Scholes Model
Developed by Fischer Black and Myron
Scholes
in a 1973 paper.
They received the 1997 Nobel Prize in economics for this and related work.Slide43
Black-Scholes Model
It assumes the underlying asset follows a geometric Brownian Motion and using partial differential equations to get the Black-
Scholes
PDE:Slide44
Black-Scholes Model
The value of a call option is found by solving the PDE and the result is
N(•) is the standard normal distribution
T - t is the time to maturity
S is the price of the underlying asset
K is the strike price
r is the risk free rate
σ is the standard deviation Slide45
ExcelSlide46
Futures/Forwards
Futures contract is a standardized contract to buy or sell a specified commodity at a certain date in the future for a certain price.
Forwards are similar to futures except that they are traded OTC and as such are more customizableSlide47
Futures
A futures contract gives the holder the obligation to make or take delivery under the terms of the contract
Differs from an options contract in that both parties must fulfill the contract at the settlement date. Slide48
Who Buys Them?
Speculators who seek to make a profit by predicting market moves.
Producers and consumers purchase futures contracts to guarantee a certain price. Slide49
Types of Futures
Crude Oil
Corn
Soybean
Sugar
WoolCottonCoffeeCocoa
Wheat
Lumber
Orange Juice
Silver
Gold
CopperSlide50
Trading PlacesSlide51
Trading Places Explanation
Standard contract size is 15,000 pounds
The Dukes got a fake report and think that FCOJ is going to be valuable and cause the price to rise
V
and W wait until the price gets to $1.42 per pound and then sell contracts that they don’t own. Slide52
Trading Places Explanation
When the real crop report is announced it is obvious that the crop will be good and prices begin to fall all the way down to 46.
Since V and W don’t own any FCOJ they start to buy back contracts at this price to cover the ones that were sold. Slide53
Trading Places Explanation
Just
some rough numbers:
($1.42 - $0.46) * 15,000pounds/contract
* 20,000 contracts =
= 288,000,000 Slide54
Conclusions
Derivatives can offer a way to:
Hedge portfolio risk
Lock in a specific price for a commodity
Provide investing leverage
Cheap form of speculating