Derivatives Markets

For buyer, no other commitment than premium payments, then margins are not ... Value of a Put option at expiration date = max [strike price - stock price at ...
332KB taille 5 téléchargements 339 vues
Derivatives Markets: V l ti Valuation and d Risk Ri k M Management g t

©D Duc Nguyen - Fimarkets - Fall 2007

Topic 6

184

O Overview i off th the ttopic i 185

…

D i i ? Derivatives? † †

…

Where we are going: † †

…

Derivatives are instruments based on some underlying assets They can be traded either on organized markets (options & futures) or on OTC markets (Swaps & Forwards)

Options Futures

Topics discussed: † † †

Key terms and concepts Trading strategies Applications ©Duc Nguyen - Fimarkets - Fall 2007

O ti Options: key k tterms and d concepts t 186

…

What is an option? †

…

A contract that gives the owner the right, not the obligation, to buy b or sell ll an underlying d l i asset at a particular i l price i ((strike ik price) on or before a certain date (exercise date)

Two basic types of options

©Duc Nguyen - Fimarkets - Fall 2007

O ti Options: key k tterms and d concepts t 187

…

U d l i assets Underlying t † † † †

† †

Shares of publicly traded corporations (equity options) Fixed-income securities (interest rate options) Specified indexes (stock index options) Foreign currency (ex., options on sterling traded on the Chicago g Mercantile Exchange) g ) Futures contracts (options on futures) Options (compound options)

©Duc Nguyen - Fimarkets - Fall 2007

O ti Options: key k tterms and d concepts t 188

…

Strike (or exercise) price

†

…

Exercise dates

† † † †

…

The strike price is the contractual price at which the underlying asset will be purchased (sold) in the event that the option is exercised The date on which the option is exercised The last trading date is called the expiration date American exercise if executed on or before the exercise date European exercise if exercised only on exercise date

P ti i Participants t iin th the options ti market k t

† †

Buyers (sellers) of calls, buyers (sellers) of puts Option buyers = holders; option sellers = writers ©Duc Nguyen - Fimarkets - Fall 2007

O ti Options: key k tterms and d concepts t 189

…

Positions: long or short † †

…

Buyers are said to be long an option contract Sellers are said to be short an option contract

Value of option †

The value of an option at expiration date is a function of the stock price and the strike price

†

Example: option values given a strike price of $85

©Duc Nguyen - Fimarkets - Fall 2007

O ti Options: key k tterms and d concepts t 190

…

Value of option †

Notions of in-the-money, at-the-money, and out-of-themoney

©Duc Nguyen - Fimarkets - Fall 2007

O ti Options: key k tterms and d concepts t 191

…

At a premium i † † † † †

…

Purchase price, paid in full by the buyer Ass beg begins, s, net e deb debit for o buye buyer a and d net e ccredit ed for o se seller e Time-varying value Premium = intrinsic value + time value The longer the amount of time for market conditions to work to your benefit, the greater is the time value

Margins i † †

For buyer, no other commitment than premium payments, then g are not obligatory g y margins For seller, obligation to deliver the underlying asset, then margin (or good-faith margin) deposits are required to insure the transaction ©Duc Nguyen - Fimarkets - Fall 2007

O i Options: ffour b basic i positions ii 192

…

Value of a Call at expiration date †

Long Call & Short Call (European-style)

†

Value of a Call option at expiration date = max [stock price at exercise date – strike price; 0]

©Duc Nguyen - Fimarkets - Fall 2007

O i Options: ffour b basic i position ii 193

…

Value of a Put at expiration date †

Long Put & Short Put (European-style)

†

Value of a Put option at expiration date = max [strike price stock price at exercise date; 0]

©Duc Nguyen - Fimarkets - Fall 2007

O i Options: ffour b basic i position ii 194

…

Real example: payoffs of an option †

May 1st, the stock price of Cory's Tequila Co. is $67 and the premium i ((cost) t) iis $3 $3.15 15 for f aJ July l 70 C Call ll „ „ „ „ „ „

Underlying asset: Cory’s Tequila Co. ($67) Price of an option: $3.15 Total price of the option contract: 3.15 x 100 Strike price: $70 Expiration p date: 3 3rd Fridayy of Julyy Break-even price: $70 + $3.15

©Duc Nguyen - Fimarkets - Fall 2007

O i Options: price’s i ’ determinants d i 195 …

C Current stock k price i

…

Strike price

…

Time to expiration

…

Volatility of stock price

…

Risk-free Risk free rate

…

Dividend expected during the life of option Variable

European Call

European Put

American Call

American Put

Stock price

+

-

+

-

Strike price

-

+

-

+

Ti to expiration Time i i

?

?

+

+

Volatility

+

+

+

+

Risk-free rate

+

-

+

-

Dividends

-

+

-

+

©Duc Nguyen - Fimarkets - Fall 2007

O i Options: valuation l i purpose 196

…

N t ti Notations Notations

…

Factors

S0

C Current t stock t k price i

ST

Stock price at time T

X

Strike price

T

Time of expiration

r

Risk-free rate for maturity T

C

Value of American-style Call option to buy one share

P

Value of American-style Put option to sell one share

c

Value of European-style Call option to buy one share

p

Value of European-style Put option to sell one share

General assumptions †

No transaction cost, no arbitrage g opportunities, pp p possibilityy of lending or borrowing at risk-free rate (nominal rate) ©Duc Nguyen - Fimarkets - Fall 2007

O i Options: valuation l i purpose 197

…

F Four simple i l b bounds d †

Option values are always non negative since no obligation to exercise

†

C >= c ; P >= p (more opportunities before T)

†

C