Option Pricing

1
Option Pricing

• Uses
• Types
• Call Options
• Put Options
• Graphical representations
• Warrants and Convertibles
• Determining the value of the options
• Black-Scholes model
• Strategies for risk management

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What are the Uses of Options?

• 1.
• 2.
• 3.

3
What is a Call Option?

• Say you own 100 shares of IBM, which in January
  1998 sold for 53.50 per share. You can give (or
  sell) to some one the right to buy the 100 shares
  for 2 per share at any time during the next 6
  months for 55 per share.
• 1.
• 2.
• 3.
• 4.
• 5.
• If the price at the end of six months is 60 per
  share, then what is the worth of your option?

4
What is a Put Option?

• If you expect IBM stocks to fall in the next six
  months, you can buy the right to sell within the
  next six months for 2 a share at 50 per share.
• 1.
• What is your benefit if prices fall to 45 per
  share?

5
Graphical Representation

• Note that the only loss a trader of options incur
  is limited to the premium and it is known.
• The loss to the writer can be substantial. This
  indicate why options are risk transfer the tools
  from traders to writers.

6
What is a Warrants?

• Definition
• Infomatic example in 1983. They offered 20
  warrants for each 1,000 bond for 22 per share
  for the year 2003. The stocks were selling at 20
  at the time.
• They are long term call options that can make
  securities attractive to a broader range of
  investors.

7
What are Convertibles?

• Definition
• They offers a company the chance to sell debt and
  in a sense sell common stocks for prices higher
  than prevailing prices.
• Conversion price
• Pc Par value of bond given up/shares received
• Shares received Conversion ratio (CR)

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How can we determining the value of an option
1. Using a risk-free portfolio?

• Suppose your boss ask you to determine the
  premium of a one year option of your agribusiness
  firm with an exercise price of 35 and now
  selling for 40 a share. You realize that the
  low and high this stock has sold in the past are
  30 and 50. To determine the premium there are
  4 steps you should follow
• (1)
• Stock Price Option value
• Low 30 0 or
  worthless
• High 50 (50-35) 15
• Range 20 15

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Steps Cont..

• (2)
• Stock Price Value of 0.75 share
  Option value
• Low 30 22.5
  0 or worthless
• High 50 37.5
  (50-35) 15
• Range 20 15
  15

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Steps Cont..

• (3)
• Stock Price Value of 0.75 call effect value
  of P
• Low 30 22.5
  0 22.5
• High 50 37.5
  - 15 22.5
• Note You have created a risk-free portfolio by
  writing a call on that stock.

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Steps Cont..

• (4) ____________________________ In a year for
  sure the value of your portfolio will be 22.5,
  but what is the call premium? If risk-free today
  is 8 then discounted value of your portfolio
  today 22.5/1.08 20.83
• Since your hedge was with 0.75 share or 0.7540
  30, you must be able to sell the call for
  30-20.839.17 in order to break even.
• 9.17 is the equilibrium price if competition
  exist in the options market

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2. Using Black-Scholes model (B-S)

• It uses the basis risk-free portfolio but more
  applicable to the real world because it allows
  for a range of ending stock prices.
• A risk-free investment position is created by
  buying shares of a stock and simultaneously
  selling call options on that stock, so that gains
  on the stock will exactly offset losses on the
  option, and vice versa.
• How can you sell options as a speculator?

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Assumptions of the B-S Model

• 1.
• 2.
• 3.
• 4.

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Assumptions Continue

• 5.
• 6.
• 7.

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The B-S Model

• Used to value a call option
• V PN(d1) - Xe-ktN(d2)
• d1 (In(P/X) Krf (?2/2)t)/ ?t1/2
• d2 d1 - ?t1/2
• Where
• V
• P
• N(d1)
• Thus, N(d1) and N(d2) represent areas under a
  standard normal distribution function.

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Model Continue

• X
• e
• Krf
• t
• In(P/X)
• ?2

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The IBM Example

• V ?
• P 40
• N(d1) N(d1) ?
• X 35
• e 2.7183
• Krf 8
• t 1 year
• In(P/X) IN(40/35)
• ?2 0.32.

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3. Using the Put-Call Parity Strategy
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Strategies for risk management

• Outline
• Some Concepts and Theories
• Black-Scholes Pricing Model
• Fundamental Analysis
• Technical Analysis
• Management Strategies
• Basic Strategies for Forward-Pricing with Options
  
• Price Floors
• Price Ceilings
• Advanced Strategies for Forward-Pricing with
  Options
• Conservative Strategies
• Target pricing
• Target pricing plus moving averages
• Trend line pricing

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Outline Cont..

• Intermediate Hedging Strategies
• Moving averages
• Combination of fundamental and technical
  analysis
• Sophisticated Hedging Strategies
• Using regression to forecast prices
• Selling puts and buying calls

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Fundamental Analysis

• What is fundamental analysis?
• Graphical Illustration.

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Fundamental Analysis Cont..

• How does it relate to price risk management?
• Issues that arise when determining equilibrium
  price

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Fundamental Analysis Cont..

• The equilibrium price is the single price that
  would balance _____________________________. But
  the levels of supply and demand for a future time
  period are never know with certainty. The price
  discovered in future markets will reflect that
  uncertainty and will trace out some distribution
  over time as new information on supply and demand
  enters the market and prices adjust to reflect
  the change in the information.
• Supply side uncertainty include ______________,
  ___________________, etc
• Demand side uncertainty include ____________,
  ___________________, etc.

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Fundamental Analysis Cont..

• What are the different approaches used in
  fundamental analysis to determine price trends?
• 1 _______________ What are some seasons that are
  important?
• 2. ________________ What will the price range be
  if Price 2.79-0.0139(ES) and R2 0.347, N23,
  and standard deviation 0.6
• 3._______________________ Monitors short run
  changes in prices . Very simple but powerful
  tool to establish price range changes from year
  to year or quarter to quarter.
• Given beef elasticity of demand -0.67 and it is
  projected that demand will change from 6.642
  billion in 1999 to 6.450 billion in the year
  2000, what will be the price change?

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Technical Analysis

• Technical Analysis is anonymous to
  ______________________. It is used to ______ the
  __________________ within that price range.
• Graphical Representation
• How do we determine whether upward trends will
  persist with technical analysis?

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Management Strategies

• Basic Strategies for Forward-Pricing with Options
  
• 1
• Example Assume hog producers buy a 60 put
  option with a premium of 1.5/cwt, with October
  futures selling at 62.75/cwt. If basics are
  equals to zero, what is the forward price floor?
  What is the net payment and the worth of a floor
  strategy if cash and futures are trading at
  54/cwt? Present this results graphically?

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Management Strategies Cont..

• 2.
• Example Assume a cattle feeder buys a 2.8 call
  option with a premium of 0.25/bu and the
  underlining February futures contract is trading
  at 2.8/bu. If expected basis is 0.2/bu, what is
  the futures price ceiling. What is the net
  price? If the future price is trading for 3.55
  what is the value of this ceiling strategy.
  Present these results graphically?

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Advanced Strategies for Forward-Pricing with
Options

• 1.
• A. ______________ serve to evaluate economic
  variability with cash contracts price. The
  method used is incremental pricing until the
  target is reached.
• Price can be sealed-up once ____________________.
  
• Elevators keep a ____________ of each producer
  and their desired prices. If futures markets
  trade up, the cash contract offered by elevators
  will trade-up directly.
• Disadvantage

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Advanced Strategies for Forward-Pricing with
Options

• B. ___________________________ Producers can use
  short (___________) and long (___________) moving
  averages as safety nets when target prices are
  never offered in the market.
• C. ___________________________ If producers and
  managers can fit trend lines early enough in
  their campaign they can predict the direction of
  price movements when ____________
• ___________________________

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Advanced Strategies for Forward-Pricing with
Options

• 2. Intermediate Hedging Strategies
• 3. Sophisticated Hedging Strategies

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Examples of Fencing

• Selling a call and buying a put
• Suppose both have the same strike price of 60
  and premium of 2. What happens at the
  expiration date if futures price is below the
  strike price? What happens if future price is
  above the strike price? Present this in a
  diagram?
• This strategy is equivalent to ________________
• __________________________________________________
  __________________________________.