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2017
2017
Coaching
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Adapt to Your Exam
Adapt to Your Exam
Exam MFE
Exam MFE
– – – – --- - –– --rr - - --– – – – – – - - --- - --- - - - ---FORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONS
FORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONS
Contract
Contract PositionPosition in Contract
in Contract DescriptionDescription
Position in Position in Underlying
Underlying Payoff Payoff ProfitProfit
Maximum Maximum Loss Loss Maximum Maximum Gain
Gain StrategyStrategy
F F o o r r w w a a r r d
d Long ForwardLong Forward
Obligation to Obligation to
buy buy at the at the forward price forward price Long Long "" − − %,"%," "" − − %,"%," −−%,"%," ∞∞ Guarantee/lock in Guarantee/lock in purchase price of purchase price of underlying underlying Short Forward Short Forward Obligation to Obligation to sell sell
at the forward at the forward price price Short Short %,"%," − − "" %,"%," − − "" −∞−∞ %,"%," Guarantee/lock in Guarantee/lock in sale price of sale price of underlying underlying C C a a l l l l Long Call Long Call
Right (but not Right (but not obligation) to obligation) to buy
buy at the strike at the strike price price
Long
Long max max [0,[0, "" − ] − ] max max [0,[0, "" − ] − ]
− (P
− (Prem.rem. )) −(Prem−(Prem.. )) ∞∞
Insurance against Insurance against high underlying high underlying price price Short Call Short Call Obligation to Obligation to sell sell
at the strike at the strike price if the call price if the call is exercised is exercised
Short
Short −max −max [0,[0, "" − ] − ]
−max
−max [0,[0, "" − ] − ]
+ (P
+ (Prem.rem. )) −∞−∞ (Prem.)(Prem.)
Sells insurance Sells insurance against against high underlying high underlying price price P P u u t t Long Put Long Put
Right (but not Right (but not obligation) to obligation) to sell
sell at the strikeat the strike price price
Short
Short max [0max [0,, − − ""]]
max [0
max [0,, − − ""]]
− (P
− (Prem.rem. )) −(Prem−(Prem.. ))
−(Prem −(Prem.. )) Insurance against Insurance against low underlying low underlying price price Short Put Short Put Obligation to Obligation to buy
buy at the strike at the strike price if the put price if the put is exercised is exercised
Long
Long −max [−max [0,0, − − ""]]
− − mamax 0,x 0, − − "" + (P + (Prem.rem. )) Prem. Prem. − − (Prem.)(Prem.) Sells insurance Sells insurance against against low underlying low underlying price price Forward
Forward Call Call PutPut
Spot Price at Expiration Spot Price at Expiration
P P a a y y o o f f f f L L o o n n g g F
F o o r r w w a a r r d d 0 0 F F 0,0,T T - F - F 0,0,T T S S h h o o r r t t F F o o r r w w a a r
r d d
F F 0,0,T T
Spot Price at Expiration Spot Price at Expiration
P P a a y y o o f f f f L L o o n n g g C C a a l l l l K K 0 0 S S h h o o r r t t C C a a l l l l
Spot Price at Expiration Spot Price at Expiration
P P a a y y o o f f f f L L o o n n g g P P u u t t K K 0 0 S S h h o o r r t t P P u u t t – – – – --- - –– --rr - - --– – – – – – Option Moneyness Option Moneyness •
• In-the-money: Produce aIn-the-money:Produce a positive positive payoff (not payoff (not
necessarily positive profit) if the option is necessarily positive profit) if the option is exercised immediately
exercised immediately
•
• At-the-money: At-the-money: The spot price is approximatelyThe spot price is approximately
equal
equal to the exercise price to the exercise price
•
• Out-of-the-money: Produce aOut-of-the-money:Produce a negativenegative payoff if payoff if
the option is exercised immediately the option is exercised immediately Option Style
Option Style
•
• European-style optionsEuropean-style options can only be exercised atcan only be exercised at
expiration. expiration.
•
• American-style options American-style options can be exercised at can be exercised at any any
time
time during the life of the option.during the life of the option.
•
• Bermudan-style optionsBermudan-style options can be exercised during can be exercised during
bounded periods
bounded periods (i.e. specified periods during the (i.e. specified periods during the life of the option).
life of the option). Zero-coupon Bond Zero-coupon Bond
Buying zero-coupon bond = lending money Buying zero-coupon bond = lending money Selling zero-coupon bond = borrowing money Selling zero-coupon bond = borrowing money Profit on the bond = 0
Profit on the bond = 0 – – – – --- - –– --Short-Selling Short-Selling •
• Borrow an asset from a lenderBorrow an asset from a lender •
• Immediately sell the borrowed asset and receiveImmediately sell the borrowed asset and receive
the proceeds (usually kept by lender or a the proceeds (usually kept by lender or a designated 3
designated 3rdrd party) party)
•
• Buy the asset at a later date at the open marketBuy the asset at a later date at the open market
to repay the lender (close/cover the short to repay the lender (close/cover the short position)
position) Haircut:
Haircut: Additional collateral placed with lender by Additional collateral placed with lender by short-seller. It belongs to the short-seller.
short-seller. It belongs to the short-seller. Interest rate on haircut is called:
Interest rate on haircut is called:
•
• short rebateshort rebate in the stock market in the stock market •
• repo raterepo rate in the bond marketin the bond market
Reasons for short-selling assets Reasons for short-selling assets::
•
• Speculation – To speculate that the price of aSpeculation – To speculate that the price of a
particular asset will decline. particular asset will decline.
•
• Financing – To borrow money for additionalFinancing – To borrow money for additional
financing of a corporation. financing of a corporation.
•
• Hedging – To hedge the risk of owning an assetHedging – To hedge the risk of owning an asset
or a derivative on the asset. or a derivative on the asset.
- - --- - --- - - - - --INTRODUCTION TO DERIVATIVES INTRODUCTION TO DERIVATIVES
Reasons for Using Derivatives Reasons for Using Derivatives
•
• Risk management – hedgingRisk management – hedging •
• Speculation – to make a bet rather than to reduceSpeculation – to make a bet rather than to reduce
risk risk
•
• Reducing transaction costReducing transaction cost •
• Minimizing taxes / avoiding regulatory issuesMinimizing taxes / avoiding regulatory issues
Bid-ask Spread Bid-ask Spread Bid price:
Bid price: The price at which brokers will buy and The price at which brokers will buy and end-users will sell at.
end-users will sell at. Ask/Offer price:
Ask/Offer price: The price at which brokers will sell The price at which brokers will sell and end-users will buy at.
and end-users will buy at.
Bid-ask spread = Ask price – Bid price Bid-ask spread = Ask price – Bid price Round-trip transaction cost:
Round-trip transaction cost: difference between difference between what you pay and what you receive from a sale what you pay and what you receive from a sale using the same set of bid/ask prices.
using the same set of bid/ask prices. Long vs. Short
Long vs. Short A
A longlong position in an asset benefits from an position in an asset benefits from an increaseincrease in the price of the asset.
in the price of the asset. A
A short short position in an asset benefits from a position in an asset benefits from a decreasedecrease in the price of the asset.
in the price of the asset.
rr - - --– – – – – – - - --- - --- - - - - --INTRODUCTION TO DERIVATIVES INTRODUCTION TO DERIVATIVES
FORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONS
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OPTIONS COMBINATION Put-Call Parity
, − , %," −
By rearranging put-call parity:
• Floor = Stock + Put
• Write a covered put = – Stock – Put • Cap = Call – Stock
• Write a covered call = – Call + Stock
Synthetic Forward
Syn. Long forw. = Long call (K ) + Short put (K ) Syn. Short forw. = Short call (K ) + Long put (K )
Bull Spread
• Long call (K 1) + Short call (K 2),K 1 <K 2
• Long put (K 1) + Short put (K 2),K 1 <K 2
Bear Spread
• Short call (K 1) + Long call (K 2),K 1 <K 2
• Short put (K 1) + Long put (K 2),K 1 <K 2
Box Spread
Synthetic long forward (K 1) + Synthetic short
forward (K 2),K 1 <K 2
Ratio Spread
Long and short an unequal number of calls/puts with different strike prices
Collar
Long put (K 1) + Short call (K 2),K 1 <K 2
Collared Stock
Long collar + Long stock
Strangle
Long put (K 1) + Long call (K 2),K 1 <K 2
Straddle
Long put (K ) + Long call (K )
Butterfly Spread
Buy high and low-strike options. Sell middle-strike option. Quantity sold = Quantity bought.
Symmetric
• 1 * Long call (K 1) + 2 * Short call (K 2) + 1 * Long call (K 3),K 1 <K 2 <K 3
• 1 * Long put (K 1) + 2 * Short put (K 2) + 1 * Long put (K 3),K 1 <K 2 <K 3
Asymmetric = − >
= − ?
• * Long call (K 1) + 1 * Short call (K 2) + 1 − * Long call (K 3),K 1 <K 2 <K 3
• * Long put (K 1) + 1 * Short put (K 2) + 1 − * Long put (K 3),K 1 <K 2 <K 3
Spot Price at Expiration
P a y o f f L o n g F o r w a r d 0 F 0,T - F 0,T S h o r t F o r w a r d F 0,T
Spot Price at Expiration
P a y o f f K 1 K 2 Bull Spread
Spot Price at Expiration
P a y o f f Bear Spread K 1 K 2
Spot Price at Expiration
P a y o f f Box Spread 0 K 2 - K 1
Spot Price at Expiration
P a y o f f Ratio Spread 0
Spot Price at Expiration
P a y o f f Collar 0 K 1 K 2
Spot Price at Expiration
P a y o f f Collared Stock 0
Spot Price at Expiration
P a y o f f Strangle 0 K 1 K 2
Spot Price at Expiration
P a y o f f Straddle 0 K
Spot Price at Expiration
P a y o f f Butterfly Spread OPTIONS COMBINATION
