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Unformatted text preview: STAT 2820 Chapter 3 Introduction to Options by K.C. Cheung 3.1 Types of Options 3.1.1 A call option gives the holder the right to buy a certain asset by a certain date at a certain price. A put option gives the holder the right to sell a certain asset by a certain date at a certain price. The date specified in an option contract is called the expiration date/maturity date . The price specified in the contract is called the exercise price/strike price . 3.1.2 The main difference between options and forwards/futures is that option holders have the right to buy/sell the underlying assets, depending on the market situation on the expiry date; while forward/futures holders have the obligation to buy/sell the assets no matter how favorable/unfavorable the market is. 3.1.3 Call or put options can be either American or European . The holder of an American option can exercise at any time prior to the expiration date. The holder of a European option can only exercise the option on the expiration date. 3.2 Holding Call Options 3.2.1 Let K be the strike price of a European call option. On the expiration date, if the spot price of the underlying asset S T is greater than K , the option holder will exercise the option: use $ K to buy a unit of the asset, then sell it in the spot market immediately for $ S T , earning a profit of S T K . However, if S T < K , it it unreasonable to buy the asset at $ K because it is selling at a lower price in the spot market. The option is worthless and hence the option holder will walk away. To sum up, the payoff of holding a European call option is Payoff = S T K if S T ≥ K if S T < K = ( S T K ) + , where x + = max( x, 0). For example, 6 + = 6 , 11 . 3 + = 11 . 3 , ( 4) + = 0 , ( 9 . 21) + = 0. STAT 2820 Chapter 3 2 6 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ K S T Payoff of holding a call Example (Payoff of holding call option): On January 1, an investor buys a European call option on 10 units of gold. Expiration date is March 1, strike price is $400 per unit. On March 1: (a) Spot price of gold is $420 Exercise the options, buy 10 units of gold at $400 per unit 4000 Sell 10 units of gold in spot market +4200 Total CF +200 (b) Spot price of gold is $440 Exercise the options, buy 10 units of gold at $400 per unit 4000 Sell 10 units of gold in spot market +4400 Total CF +400 (c) Spot price of gold is $380 Not exercise the option Total CF 3.2.2 Since the payoff at exercise date of holding a call option is always nonnegative, the holder must pay a price to obtain it. In other words, the price of a call option is strictly positive, as opposed to the initial price of a futures, which is zero. That price is called the option price ....
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 Fall '11
 KC

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