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INTRODUCTION TO FORWARDS AND OPTIONS
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FORWARD CONTRACTForward contract: Agreement that sets today the terms-including price and quantity-at which you buy or sell and asset or commodity at a specific time in the furute.
• Specifies the quantity and exact type f the asset or commodity (underlying asset) the seller must deliver.
• Specifies delivery logistics such as time, date (expiration date) and place.• Specifies the price (forward price) buyer will pay at the time of delivery. • Obligates the seller to sell and the buyer to buy subject to the above specifications.
Forward contract requires no initial premium/payment.
The term long is used to describe the buyer.
The term short is used to describe the seller.
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FORWARD CONTRACT
Payoff to long forward = Spot price at expiration – forward price
Payoff to short forward = Forward price – Spot price at expiration
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FORWARD CONTRACT
Example 2.1
Suppose the non-dividend S&R (Special and Rich) 500 index has a current price of $1000 and the 6-months of forward price is $1020.
What does this means?
• The holder of the long position in the S&R forward contract is obligated to pay $1020 in 6 months for one unit of the index.
• The holder of the short position is obligated to sell one unit of the index for $1020
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FORWARD CONTRACT
S&R index in 6 months S&R forward (Long) S&R forward (Short)
900
950
1000
1020
1050
1100
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FORWARD CONTRACT
Long and short forward positions on the S&R 500 index
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FORWARD CONTRACT
Forward Purchase Investment and Forward Purchase
• Payment is deferred (unfunded)• Borrow to buy physical index with initial cost
$0 at time $0.• Pay $1020 after 6 months and own the
index.
• E.g. Invest $1000 in a zero-coupon bond (Treasury bills). Therefore initial cost is $1000 at time 0.
• Suppose that 6 months interest rate is 2%. After 6 months zero-coupon bond is worth $1020.
• Use the bond to pay forward price of $1020.• Own the index after 6 months.• Investing $1000 at the same time entering
forward contract mimics the effect of buying the index outright (pay in full-funded)
Simple comparison:
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CASH SETTLEMENT
Cash settlement- Buyer and seller settle financially (make net cash payment). No transfer of physical asset which will likely have significant costs. Example 2.2
1) Suppose that S&R index at expiration is $1040.
2) Suppose the S&R index at expiration is $960
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OPTIONS
CALL OPTIONS: is a contract that gives the buyer the right , but not the obligation to sell the underlying asset at a pre-specified price (strike price).
PUT OPTIONS: is a contract that gives buyer the right , but not the obligation to sell the underlying asset at a pre-specified price (strike price).
Option Trading gives buyer/seller the right to walk away from the deal.
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OPTIONS
TERMS
Strike price – the amount can be exchange for underlying asset Exercise – the exchange of the strike price for the underlying asset at the terms
specified in the option contract Expiration – the date beyond which an unexercised option is worthless Exercise style – the circumstances under which an option holder has the right to
exercise an option.i. European style option – exercise only at expirationii. American style option – exercise at anytime during the life of the optioniii. Bermudan style option – can only exercise during specified period, not the
entire life of the option
Option writer – the party with short position in the option
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PURCHASED CALL
• Payoff at expiration • Profit at expiration
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CALL OPTIONS
Example 2.3
Suppose that a buyer purchase a call option to pay $1020 for S&R index in 6 months. What is the payoff if: i. In 6 months, the S&R price is $1100.
ii. In 6 months, the S&R price is $900.
Thus, at the time buyer and seller agree to the contact, buyer must pay the seller initial price (premium). It is to compensates seller for being at a disadvantage at expiration.
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CALL OPTIONS
Example 2.4
Consider a call option on the S&R index with 6 months to expiration and a strike price of $1000.
i. Suppose the index is $1100 in 6 months.
ii. Suppose the index is $900 in 6 months
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CALL OPTIONS
Example 2.5
Consider a call option on the S&R index with 6 months to expiration and a strike price of $1000. Suppose the risk free rate is 2% over 6 months. Assume that the index spot price is $1000 and the premium for the call is $93.81. What is the payoff?
i. Suppose the S&R index price is $1100
ii. Suppose the index is $900 in 6 months
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PUT OPTIONS
Example 2.6
Consider a put option n the S&R index with 6 months to expiration and a strike price of $1000
i. Suppose the S&R index price is $1100
ii. Suppose the index is $900 in 6 months
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PUT OPTIONS
Example 2.6
Consider a put option on the S&R index with 6 months to expiration and a strike price of $1000. Suppose that the risk-free rate is 2% over 6 months. Assume the premium is $74.20.
i. Suppose the S&R index price is $1100
ii. Suppose the index is $900 in 6 months
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PROFIT FOR LONG PUT POSITIONS
• Profit table • Profit diagram
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“MONEYNESS” OF AN OPTION
Options are often describe by their degree of “moneyness”
In-the-money option – call with a strike price < asset price, put with strike price > asset price
Out-of- the-money option – call with a strike price > asset price, put with strike price < asset price
At-the-money option – strike price is approx. equal to asset price
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OPTIONS ARE INSURANCE
Call Option is also insurance. By buying a call, you have bought insurance against an increase in the price
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OPTIONS ARE INSURANCE
Homeowner’s Insurance is a Put Option
• Suppose that you own a house that cost $200,000 (assume that physical damage is the only thing that will affect the market value.
• Buy a $15,000 insurance policy to compensate you for damage • Suppose the deductible is $25,000• If the house suffers $4000 damage from a storm – you pay for all repairs• If the house suffers $45000 damage from a storm – you pay $25,000 and the insurance
company pay $20,000• The insurance company pay damage occurs beyond deductible up to $175,000 because
the house is $200,000 ($175,000+$25,000)
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EQUITY-LINKED CDS
Example 2.7
A simple At maturity, the CD is guaranteed to repay the invested amount, plus 70% of the simple appreciation in the S&P 500 over that time. Suppose the S&P index is 1300 initially and investor invest $10,000. Let say the index is 2200:
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EQUITY-LINKED CDS
CONT…
Suppose the effective annual interest rate is 6% if the index fall below 1300 at expiration,
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OPTIONS AND FORWARD POSITIONS: A SUMMARY
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TUTORIAL
Derivatives Market (THIRD EDITION) Robert L . McDonald
Q2.2, Q2.4, Q2.5, Q2.6, Q2.7, Q2.8, Q2.9, Q2.13