Intro to options

Intro to options - Intro to options • Definition :...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Intro to options • Definition : contractual agreement giving owner the right (not obligation) to buy or sell an asset at a pre-determined price on or before a specified date • Features: • To buy ( call option; c); to sell ( put option; p) • (pre-determined) exercise price , E (i.e., strike) • Specified ( expiration ) date, T • If can be exercise before T; American option • If can be exercised only at T; European option When to exercise…. • Call options: owner will exercise if the asset price, S, is greater than E • Put options: owner will exercise if asset price S is less than E • Call: in-the-money if S>E at T; else out-of- money • Put option: in-the-money if S<E at T; else out-of-money Why options? • First traded on the CBOE in 1973 • seminal academic paper by Black & Scholes 1973 (rejected at top-journal) • Scholes gets N.P; Black ineligible – widely used in managerial “compensation” packages – buy a call if belief asset price will rise – buy a put if own asset and belief price may fall – Buy a combination as speculative strategy Value of call option at expiration S T E Value of a put option at expiration E S T Example • Suppose you purchased a 3 month call option on INTEL at $8; the exercise price is $26; current price of INTL is $28 • Graph the value of the call at T=3 • Graph the profit function • Find the break-even price • Graph the seller’s payoff Example: the buyer’s position S T 26 34 pr of it S if S if S T T T =- -- ≤ 26 8 26 8 26 26 Seller’s (short) position….. 26 34 S T prof it if S S if S T T T = <- - - ≥ 8 26 26 8 26 ( ) American vs. European options….. • At expiration, the two types have the same value • But American can be exercised before expiration – If any time t, S<E, do not exercise – But if S>E at any t<T, not always optimal to exercise; value embedded from waiting could be higher – So valuation of American is complicated Lower bound for call price • Assumption: – asset pays no dividend – assume a risk free rate of return of r% • Let c=call price, S t =current price of asset; E=exercise price; and T=expiration date • Then; • Proof: A standard proof …create and compare values of two portfolios c S Ee t rT ≥ -- Strategies:… • Portfolio A: one European call option plus cash of $(Ee-rT ) invested in risk-free asset – Value of portfolio A: $(c+ Ee-rT ) • Portfolio B: a unit of the stock – Value S t • At time T, either (i) S T >E, or (ii) S T <E – Case (i) “A” is worth $S T ; “B” is worth $S T – Case (ii) “A” is worth $E; “B” is worth $S T • So “A” must be worth at least “B” now. Example… • Find the lower bound for the price of a European call option on a non-dividend paying stock if the stock price is $51, E=$50 and has 6 months to expire. Let r=12% • Ans: • Exx: Show that lower bound for a European put on a non-dividend paying stock is: c S Ee e t rT ≥ - = - =- - 51 50 91 0 12 2 ( . )/ $3 ....
View Full Document

This note was uploaded on 03/26/2008 for the course EC 150 taught by Professor Kutsoati during the Spring '08 term at Tufts.

Page1 / 66

Intro to options - Intro to options • Definition :...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online