Download Mfe Formula Sheet 2017 PDF

TitleMfe Formula Sheet 2017
TagsOption (Finance) Derivative (Finance) Hedge (Finance) Short (Finance) Moneyness
File Size838.1 KB
Total Pages6
Document Text Contents
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www.coachingactuaries.comwww.coachingactuaries.com Copyright Copyright © © 2017 2017 Coaching Coaching Actuaries. All Actuaries. All Rights Reserved. Rights Reserved. 11

Adapt to Your ExamAdapt to Your Exam
Exam MFEExam MFE

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FORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONSFORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONS

ContractContract
PositionPosition

in Contractin Contract
DescriptionDescription

Position inPosition in
UnderlyingUnderlying

Payoff ProfitPayoff Profit
MaximumMaximum

LossLoss
MaximumMaximum

GainGain
StrategyStrategy

    F    F
   o   o
   r   r
   w   w
   a   a
   r   r
    d    d Long ForwardLong Forward

Obligation toObligation to
buy buy  at the at the

forward priceforward price
LongLong "" −  − %,"%," "" −  − %,"%," −−%,"%," ∞∞

Guarantee/lock inGuarantee/lock in
purchase price ofpurchase price of

underlyingunderlying

Short ForwardShort Forward
Obligation toObligation to sell sell 

at the forwardat the forward

priceprice

ShortShort %,"%," −  − "" %,"%," −  − "" −∞−∞ %,"%,"

Guarantee/lock inGuarantee/lock in
sale price ofsale price of

underlyingunderlying

    C    C
   a   a
    l    l    l    l

Long CallLong Call

Right (but notRight (but not
obligation) toobligation) to

buy buy  at the strike at the strike
priceprice

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

−(Prem−(Prem.. )) ∞∞
Insurance againstInsurance against
high underlyinghigh underlying

priceprice

Short CallShort Call

Obligation toObligation to sell sell 
at the strikeat the strike

price if the callprice if the call
is exercisedis exercised

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

−∞−∞ (Prem.)(Prem.)

Sells insuranceSells insurance
againstagainst

high underlyinghigh underlying
priceprice

    P    P
   u   u
   t   t

Long PutLong Put

Right (but notRight (but not
obligation) toobligation) to

sellsell at the strikeat the strike
priceprice

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

−(Prem−(Prem.. ))


−(Prem−(Prem.. ))

Insurance againstInsurance against
low underlyinglow underlying

priceprice

Short PutShort Put

Obligation toObligation to
buy buy  at the strike at the strike
price if the putprice if the put

is exercisedis exercised

LongLong −max [−max [0,0,  −  − ""]]
−− mamax 0,x 0,  −  − ""
+ (P+ (Prem.rem. ))

 Prem. Prem.
−−

(Prem.)(Prem.)

Sells insuranceSells insurance
againstagainst

low underlyinglow underlying
priceprice

Forward Forward Call Call PutPut

Spot Price at ExpirationSpot 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

00

 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 ExpirationSpot 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 

00
S  S  h h o o r r t t C  C  a a l  l  l  l  

Spot Price at ExpirationSpot 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 

00

  S  S  h  h
 o o  r  r
  t  t  P  P

  u  u  t  t

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Option MoneynessOption Moneyness

•• In-the-money:In-the-money: Produce aProduce a positive positive payoff (not payoff (not

necessarily positive profit) if the option isnecessarily positive profit) if the option is
exercised immediatelyexercised 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:Out-of-the-money: Produce aProduce a negativenegative payoff if payoff if

the option is exercised immediatelythe option is exercised immediately

Option StyleOption 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

timetime 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 periodsbounded periods (i.e. specified periods during the (i.e. specified periods during the
life of the option).life of the option).

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

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Short-SellingShort-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 athe proceeds (usually kept by lender or a
designated 3designated 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 shortto 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 assetsReasons 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.

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INTRODUCTION TO DERIVATIVESINTRODUCTION TO DERIVATIVES

Reasons for Using DerivativesReasons 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

riskrisk

•• Reducing transaction costReducing transaction cost

•• Minimizing taxes / avoiding regulatory issuesMinimizing taxes / avoiding regulatory issues

Bid-ask SpreadBid-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 priceBid-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 salewhat 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. ShortLong vs. Short
AA 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.
AA 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.

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INTRODUCTION TO DERIVATIVESINTRODUCTION TO DERIVATIVES

FORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONSFORWARD CONTRACTS, CALL OPTIONS, AND PUT OPTIONS

Page 2

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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

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