Mfe Formula Sheet 2017

Exam MFE Adapt to Your Exam INTRODUCTION TO DERIVATIVES

INTRODUCTION TO DERIVATIVES

Reasons for Using Derivatives Risk management –––hedging Speculation –––to make a bet rather than to reduce risk Reducing transaction cost Minimizing taxes / avoiding regulatory issues • •

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Bid-ask Spread Bid price: The price: The price at which brokers will buy and end-users -will sell at.  Ask/Offer price: The price:  The price at which brokers will sell and end-users -will buy at. Bid-ask - - spread = Ask price ––– Bid price Round-trip - - transaction cost: difference cost: difference between what you pay and what you receive from a sale using the same set of bid/ask prices. Long vs. Short A long position long position in an asset benefits from an increase in the price of the asset. A short  position  position in an asset benefits from a decrease in the price of the asset.

Short-Selling Borrow an asset from a lender Immediately sell the borrowed asset and receive the proceeds (usually kept by lender or a r r party) designated 3rrd Buy the asset at a later date at the open market to repay the lender (close/cover the short position) Haircut: Additional Haircut: Additional collateral placed with lender by short-seller. -- It belongs to the short-seller. -- Interest rate on haircut is called: short rebate in the stock market  repo rate in the bond market Reasons for short-selling -- assets: assets: Speculation–––To speculate that the price of a particular asset will decline. Financing–––To borrow money for additional financing of a corporation. Hedging–––To hedge the risk of owning an asset or a derivative on the asset. • •

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Option Moneyness In-the-money: -- -Produce a positive a positive payoff  payoff (not necessarily positive profit) if the option is exercised immediately  At-the-money: -- -The spot price is approximately equal  to  to the exercise price Out-of-the-money: -- -- -Produce a negative payoff negative payoff if the option is exercised immediately •

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Option Style European-style -options can only be exercised at expiration.  American-style -options can be exercised at  any  any time during the life of the option. Bermudan-style -options can be exercised during options can bounded periods (i.e. periods  (i.e. specified periods during the life of the option). •

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Zero-coupon Bond Buying zero-coupon -bond = lending money Selling zero-coupon -bond = borrowing money Profit on the bond = 0

FORWARD FORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONS CONTRACTS, CALL OPTIONS, AND PUT OPTIONS Contract     d    r    a    w    r    o     F

Position in Contract Long Forward

Short Forward

Long Call     l     l    a     C

Short Call

Long Put    t    u     P

Short Put

Description Obligation to buy  at  at the forward price Obligation to sell  at the forward price Right (but not obligation) to buy  at  at the strike price Obligation to sell  at the strike price if the call is exercised Right (but not obligation) to sell at the strike price Obligation to buy  at  at the strike price if the put is exercised

Position in Underlying

Payoff

Profit

Maximum Loss

Maximum Gain

Long

"  − %,"

"  − %,"

−%,"

∞

Short

%,"  −  "

%,"  −  "

−∞

%,"

Long

max [0, " − ]

max [0, " − ] − (Prem. (Prem. )

−(Prem. −(Prem. )

∞

Insurance against high underlying price

Short

−max [0, " − ]

−max [0, " − ] + (Prem. (Prem. )

−∞

(Prem.)

Sells insurance against high underlying price

Short

max [0, [0,  − " ]

max [0, [0,  − " ] − (Prem. (Prem. )

−(Prem. −(Prem. )

 −(Prem. −(Prem. )

Insurance against low underlying price

−max [0, [0,  − " ]

− max max 0,  − " + (Prem. (Prem. )

(Prem.)

Sells insurance against low underlying price

Long

Forward 0, T   F 0,

Call  d  r d  w a  o r w   F  n g    L o

        f         f      o      y      a        P

 Prem. −

0

0

S   h o  r t  t F   o r w  wa    r d   d  

Guarantee/lock in purchase price of underlying Guarantee/lock in sale price of underlying

Put   l   l  l  C a  n g   o   L

        f         f      o      y      a        P

Strategy

S   h o  r t  t C   a l   l  

L o  n   g P   u t          f         f      o      y      a        P

0   t   u   t  P   r  o   h   S

0, T  - F 0, 0, T   F 0,

Spot Price at Expiration

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 K 

 K 

Spot Price at Expiration

Spot Price at Expiration

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OPTIONS COMBINATION COMBINATION OPTIONS Put-Call Parity  ,  −   ,    %,"   −  

By rearranging put-call parity:

Synthetic Forward Syn. Long forw. = Long call ( K ) + Short put ( K ) Syn. Short forw. = Short call ( K ) + Long put ( K )  F 0,T 

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Floor = Stock + Put

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Write a covered put = – Stock – Put

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Cap = Call – Stock

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Write a covered call = – Call + Stock

Bull Spread • •

Bear 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

0 S   h o  r t F   o r w  a r d  

•

Bull Spread

 a r d  r w   F o  g   n   L o

        f         f       o       y       a         P

Short call (K 1) + Long call ( K 2), K 1 < K 2 Short put (K 1) + Long put ( K 2), K 1 < K 2

•

        f         f       o       y       a         P

Bear Spread

        f         f       o       y       a         P

- F 0,T   F 0,T 

 K 1

Spot Price at Expiration

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

 K 2 -  K 1

Collar Long put (K 1) + Short call ( K 2), K 1 < K 2 Collar 

        f         f       o      y       a         P

        f         f       o      y       a         P

0

0

0

K 2

Spot Price at Expiration

Ratio Spread

Box Spread

        f         f       o      y       a         P

 K 1

Spot Price at Expiration

 K 1

K 2

Spot Price at Expiration Spot Price at Expiration

Spot Price at Expiration

Collared Stock Long collar + Long stock

Strangle Long put ( K 1) + Long call (K 2), K 1 < K 2

Straddle

Strangle

Collared Stock 

        f         f       o       y       a         P

        f         f       o      y       a         P

       f        f      o      y      a        P

0

0

0

Straddle Long put (K ) + Long call (K )

 K 1

 K 

K 2

Spot Price at Expiration

Spot Price at Expiration

Spot Price at Expiration

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 •

Butterfly Spread

       f        f      o      y      a        P

 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

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Spot Price at Expiration

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