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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