Ch 17. Options and other derivatives: Introduction

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Ch 17. Options and other derivatives Introduction

• Overview
• Values at expiration
• Option strategies
• Put-Call parity
• Option-like securities
• Exotic options

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1. Option contract

• Call (put) option gives its holder the right to
  purchase (sell) an asset for a specified price,
  called the exercise or strike price, on or before
  some specified expiration date.
• Key elements
• Exercise or strike price
• Premium or price of option
• price of underlying asset
• Maturity or expiration

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• Call option April call on Alcan with X65,
  C1.90, S63.17, ST67.
• value at expiration ST X2
• profit 2 - 1.90 0.10
• Figure payoff at maturity
• Put option April put on Alcan with X65,
  P6.30, S63.17, ST55.
• value at expiration X - ST 10
• profit 10 - 6.30 3.70
• No need to own the stock to exercise put
• Figure payoff at maturity

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• In the Money - exercise of the option would be
  profitable
• Call S gt X, Put S lt X
• Out of the Money - exercise of the option would
  not be profitable
• Call S lt X, Put S gt X
• At the Money - exercise price and asset price are
  equal
• American - the option can be exercised at any
  time before expiration or maturity
• European - the option can only be exercised on
  the expiration or maturity date

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options trading

• CBOE (Chicago Board Options Exchange)
• ME (Montreal Exchange)
• OTC (overthe-counter) market
• Exchanged-traded options are standardized in
  maturity dates, interval for exercise price, and
  contract size. (1 contract is for 100 shares).
• Exercise prices have an interval of 2.5 or 5
  depending on share prices (35).
• Maturity of options is generally within one year.
  There are LEAPS (long-term equity anticipation
  securities).
• Quote on Montreal Exchange website

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• Exercise prices are adjusted by stock split and
  stock dividend factor e.g., for a ten-for-one
  stock split, exercise price will be 6.50 from
  original exercise price of 65.
• Cash dividends do not affect option contracts.
• Call (put) option values are lower (higher) for
  high-dividend stocks (high-dividend tend to slow
  the rate of stock price increase).

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• OCC (Option Clearing Corporation) in US and CDCC
  (Canadian Derivates Clearing Corporation)
  guarantee contract performance. All buyers and
  sellers (writers) of options deal with the
  clearing corporation.
• Option writes are required to post margin
  amounts.
• Other listed options
• Stock index options
• Foreign currency options
• Futures options
• Interest rate options

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2. Values of options at expiration

• Payoff to call holder
• (ST - X), if ST gtX and
• 0 if ST lt X
• Profit to call holder Payoff - Purchase Price

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• Payoff to put holder
• 0 if ST gt X
• (X - ST), if ST lt X and
• Profit to put holder Payoff - Purchase Price

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Options vs stock investments
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Alcan Stock Price 45 55 65 All
Stock 9,000 11,000 13,000 All
Options 0 10,000 30,000 Lev Equity
9,270 10,270 12,270
All Stock -10.0 10.0 30 All Options -100
0 200 Lev Equity
-7.3 2.7 27.7

• Calls are a leveraged investment on stock.
• Call offers potential insurance.

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3. Option strategies

• Protective Put Buy stock and put to limit loss.
  See Figure 17.7
• Payoff ST lt X ST gt X
• Stock ST ST
• Put X - ST 0

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Covered Call

• Buy stock and sell call. Figure 17.9
• Offers some downside protection at the
• expense of giving up gain potential.
• Payoff ST lt X ST gt X
• Stock ST ST
• Call 0 - ( ST - X)

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Option Strategies

• Straddle Buy call and put with same X.
• Figure 17.10
• Useful for investors who believe that a stock
  will move a lot, but are uncertain about the
  direction of the move.
• It is essentially a bet on volatility.
• Strip one call and two puts
• Strap two calls and one put.

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• Spreads - A combination of two or more call
  options (or put options) on the same asset with
  differing exercise prices or times to expiration
• Figure 17.11
• An example of bullish spread payoff increases
  or unaffected by stock price increases.
• money spread Same maturity, different exercise
  price
• time spread Different maturity dates

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• collars A collar brackets the value of a
  portfolio between two bounds.
• Stock A is selling at 100. Buy put with X90,
  and sell call with X110.

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4. Put-call parity
Suppose you buy a call and write a put with same
X. See Figure 17.12. C P S0 X/(1rf)T
ST lt X ST gt X Payoff of call held 0 ST
- X Payoff of put written -( X - ST)
0 Total Payoff ST - X ST - X
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Arbitrage put call parity

• Since the payoff on a combination of a long call
  and a short put are equivalent to a leveraged
  equity, the prices must be equal.
• C - P S0 - X / (1 rf)T
• If the prices are not equal, an arbitrage will be
  possible.
• Extension PC- S0 PV(X) PV(div)
• only for European options on dividend-paying
  stocks.

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Put-call parity Example

• Stock Price 110 Call Price 17
• Put Price 5 Risk Free 10.25
• Maturity .5 yr X 105
• C - P gt S0 - X / (1 rf)T
• 17- 5 gt 110 - (105/1.05)
• 12 gt 10
• Since the leveraged equity is less expensive, buy
  the low cost alternative and sell the high cost
  alternative

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Put-call parity arbitrage
Immediate Cashflow in Six Months Position Cas
hflow STlt105 STgt 105 Buy Stock -110 ST
ST Borrow X/(1r)T 100 100 -105 -105 Sell
Call 17 0 -(ST-105) Buy Put
-5 105-ST 0 Total 2 0 0
Check put-call parity ME website
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5. Option-like securities

• Callable bonds straight bond plus issuance of
  call by investors to the bond-issuing firm.
• Callable bonds should sell less than straight
  bonds by the value of the call.
• See Figure 17.13

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Convertible securities

• A bond with 1,000 face value has a conversion
  ratio of 10 The bond holder can convert the
  bond to 10 shares.
• If the bond is selling at 920, then bond holders
  will convert the bond, if the share price is
  selling above 92.
• 9210conversion value.
• Two lower bounds
• Conversion value
• Value of straight bond
• See Figure 17.14

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Warrants

• Call options issued by the firm.
• When warrants are exercised,
• the firm issues new shares of stock, and
• cash flows to the firm
• Warrants are often issued with bonds.

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Collateralized loans

• In the event of default of a collateralized loan,
  the lender takes possession of the collateral.
• The borrow has an implicit call option.
• Borrow needs to repay L. The collateral is
  worth S0 today, and ST at maturity.
• Borrower can wait till maturity and repay L only
  if collateral is worth more than L.

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• call option
• Borrower turns over collateral to lender, but
  holds the right to repurchase it for L.
• Turning over the collateral is equivalent to
  payment of S0.
• Borrowers liability is S0 C.
• put option
• Borrower owns the collateral, will repay L with
  no default, and holds the right to sell the
  collateral to the lender for L.
• Borrowers liability is PV(L) P.

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• Borrowers liability
• S0 C or PV(L)P ?
• Recall put-call parity
• S0 C PV(L)P
• See Figure 17.15

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• Financial engineering
• The creation of portfolios with specified payoff
  patterns.
• Example index-linked CD
• 7. Exotic options
• Asian options
• Barrier options
• Lookback options
• Currency translated options
• Binary options