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Ethic Essay

2428 words - 10 pages

Introduction to

Options Markets
Chap 9
Options, Futures, and Other Derivatives, 8th Edition, John C. Hull 2011


Review of Option Types
• A call is an option to buy • A put is an option to sell • A European option can be exercised only at the end of its life • An American option can be exercised at any time


Derivatives - Options
 Give the holder the right to buy or sell the underlying at a certain date for a certain price. (European options)

• • •
• •

Right to buy  call option Right to sell  put option Payoff function: call: C(T)= max{S(T)-K, 0}, put: P(T)=max{K-S(T),0} Cash settlement Exchanges: CBOE, CBOT, Eurex, LIFFE, ...view middle of the document...

Derivatives - Options
• • • ...view middle of the document...

Payoff function: f(S) = max(0,S(T) – K)

Payoffs from Options
What is the Option Position in Each Case?
K = Strike price, ST = Price of asset at maturity
Long call

Short call




Long put


Short put

(long position = Buyer)  (short position = Seller

• Payoff diagram of a short position = negative of payoff diagram of a long position Why trade contingent claims, i.e. derivatives, for example, forward、call & put options? • ANS:Speculate, hedge, and arbitrage!

How to Use Options: Arbitrage
Example You have no idea about that the prices of S will raise or down, but find prices of options are not reasonable & want to profit from that. Call with strike 105 costs 2€ each Put with strike 110 costs 2€ each (same maturity) Action: Buy 100 calls and 100 puts. Result at T: Costs = 200*2€ = 400€ Income ≥ (110€-105€)*100 = 500€ Riskless profit (arbitrage) : at least max (S-105,0)+max(110-S,0)-4=1

How to Use Options : Hedge
Example :
Now(1/1): 100 shares of S, each 80 € Maturity(T=6/30): must pay 7500€ (by selling the shares) Problem: price of shares could fall under 75€ Solution: buy 100 puts with strike 77 each option costs 2 Result: S(T) > 77 S(T) < 77  you have > 7700€ -200€ = 7500€  you have = 7700€ -200€ = 7500€

• A US airline has a contract to buy a French airplane for a price fixed in €, payable one year from now. This company can hedge the exchange rate in the following ways: [1] Long a forward for €(payable in $). [2] Long a call for €

• A US airline has a contract to buy a French airplane for a price fixed in €, payable one year from now. This company can hedge the exchange rate in the following way: [1]Long a forward for €(payable in $).

unlimited downside risk

• A US airline has a contract to buy a French airplane for a price fixed in €, payable one year from now. This company can hedge the exchange rate in the following way: [2]Long a call for €
no unlimited downside risk, with some cost

Assets Underlying

Exchange-Traded Options
• • • • Stocks Foreign Currency Stock Indices Futures

P. 199


Specification of Exchange-Traded Options
• • • •


Expiration date Strike price European or American Call or Put (option class)


Moneyness :
• • • • • •


At-the-money option: payoff=0 In-the-money option: payoff>0 Out-of-the-money option: payoff0, buy a call, sell a stock, and deposit Ke –rT . At time T, there are two cases. When ST0. When ST≧K, we get (ST-K)+K-ST=0.




c =S

c  S - Ke- rT

p  Ke -rT–S0

Puts: An Arbitrage Opportunity?
• Suppose that
p= 1 T = 0.5 K = 40 S0 = 37 r =5% D =0

• Is there an arbitrage opportunity?


Lower Bound for European Put Prices; No Dividends
(Equation 10.5, page 221)

p  Ke -rT–S0


Lower Bound for European Put Prices; No Dividends (page 221)
p ...

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