3
β„Ž = + βˆ’ = 365 = 365 = 365 β„Ž = β„Ž = Γ— β„Ž = Γ— β„Žβ„Ž ! = 2 Γ— Γ— () = = Γ— = 1 + !"# !"#$% !"#$ !"#$%& βˆ’ 1 = Γ— βˆ’ βˆ’ 1 βˆ’ Γ— () = Call Option Buyer Seller Expectation MP↑ MP↓ Loss Limited to OP Unlimited Profit Unlimited Limited to OP Put Option Buyer Seller Expectation MP↓ MP↑ Loss Limited to OP Limited to Stock Price Profit Limited to Stock Price Limited to OP At the money In the Money Out the Money (breakeven) (to exercise) (not to exercise) EP = MP EP < MP: call option EP > MP: put option EP < MP: put option EP > MP: call option 1) Underlying Price 2) Strike Price More in the money Higher OP More out the money Lower OP 3) Volatility More Volatile Higher OP Less Volatile Lower OP 4) Expiration Time Longer Expiration Time Higher OP Shorter Expiration Time Lower OP 5) Interest Rate 6) Dividends

BASFIN 2 Finals reviewer [Computations]

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BASFIN 2 FINALS REVIEWER

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Page 1: BASFIN 2 Finals reviewer [Computations]

πΆπ‘Žπ‘ β„Ž  πΆπ‘¦π‘π‘™π‘’  π‘ƒπ‘’π‘Ÿπ‘–π‘œπ‘‘= π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’  π‘‘π‘Žπ‘¦π‘   π‘–𝑛  π‘–π‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦+ π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’  π‘π‘œπ‘™π‘™π‘’π‘π‘‘π‘–π‘œπ‘›  π‘π‘’π‘Ÿπ‘–π‘œπ‘‘βˆ’ π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’  π‘π‘Žπ‘¦π‘šπ‘’𝑛𝑑  π‘π‘’π‘Ÿπ‘–π‘œπ‘‘  

 

π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’  π‘‘π‘Žπ‘¦π‘   π‘–𝑛  πΌπ‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦ =  π‘†π‘‘π‘Žπ‘Ÿπ‘‘  π‘œπ‘“  πΌπ‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦

𝐢𝑂𝐺𝑆365

 

   

π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’  πΆπ‘œπ‘™π‘™π‘’π‘π‘‘π‘–π‘œπ‘›  π‘ƒπ‘’π‘Ÿπ‘–π‘œπ‘‘ =π‘…π‘’π‘π‘–π‘’π‘£π‘Žπ‘π‘™π‘’  π‘Žπ‘‘  π‘†π‘‘π‘Žπ‘Ÿπ‘‘

π΄π‘›π‘›π‘’π‘Žπ‘™  π‘†π‘Žπ‘™π‘’𝑠365

 

 

π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’  π‘ƒπ‘Žπ‘¦π‘šπ‘’𝑛𝑑  π‘ƒπ‘’π‘Ÿπ‘–π‘œπ‘‘ =  π‘ƒπ‘Žπ‘¦π‘Žπ‘π‘™π‘’𝑠  π‘Žπ‘‘  π‘†π‘‘π‘Žπ‘Ÿπ‘‘

𝐢𝑂𝐺𝑆365

 

 

πΌπ‘›π‘‘π‘’π‘Ÿπ‘›π‘Žπ‘™  π‘”π‘Ÿπ‘œπ‘€π‘‘β„Ž  π‘Ÿπ‘Žπ‘‘𝑒 =π‘Ÿπ‘’π‘‘π‘Žπ‘–π‘›π‘’π‘‘  π‘’π‘Žπ‘Ÿπ‘›π‘–π‘›π‘”

𝑛𝑒𝑑  π‘Žπ‘ π‘ π‘’𝑑𝑠  

 π‘†π‘’π‘π‘ π‘‘π‘Žπ‘›π‘‘π‘–π‘Žπ‘™  π‘”π‘Ÿπ‘œπ‘€π‘‘β„Ž  π‘Ÿπ‘Žπ‘‘𝑒

= π‘π‘™π‘œπ‘€π‘π‘Žπ‘π‘˜  π‘Ÿπ‘Žπ‘‘π‘œ  Γ—  π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘›  π‘œπ‘›  π‘’π‘žπ‘’𝑖𝑑𝑦    π‘†π‘’π‘π‘ π‘‘π‘Žπ‘›π‘‘π‘–π‘Žπ‘™  π‘”π‘Ÿπ‘œπ‘€π‘‘β„Ž  π‘Ÿπ‘Žπ‘‘𝑒

=π‘…π‘’π‘‘π‘Žπ‘–π‘›π‘’π‘‘  πΈπ‘Žπ‘Ÿπ‘–𝑛𝑔𝑠

𝑁𝑒𝑑  πΌπ‘›π‘π‘œπ‘šπ‘’  

Γ—  π‘π‘’𝑑  πΌπ‘›π‘π‘œπ‘šπ‘’

π‘†β„Žπ‘Žπ‘Ÿπ‘’β„Žπ‘œπ‘™π‘‘π‘’π‘Ÿ!𝑠  πΈπ‘žπ‘’𝑖𝑑𝑦  

 πΈπ‘π‘œπ‘›π‘œπ‘šπ‘–𝑐  π‘‚π‘Ÿπ‘‘π‘’π‘Ÿ  π‘„π‘’π‘Žπ‘›π‘‘π‘–π‘‘π‘¦   𝑄

=  2  Γ—  π‘†π‘Žπ‘™π‘’𝑠  Γ—  π‘π‘œπ‘ π‘‘  π‘π‘’π‘Ÿ  π‘œπ‘Ÿπ‘‘π‘’π‘Ÿ

π‘π‘Žπ‘Ÿπ‘Ÿπ‘¦π‘–π‘›π‘”  π‘π‘œπ‘ π‘‘  

 

π‘π‘’π‘šπ‘π‘’π‘Ÿ  π‘œπ‘“  π‘‚π‘Ÿπ‘‘π‘’π‘Ÿ  π‘π‘’π‘Ÿ  π‘¦π‘’π‘Žπ‘Ÿ  (𝑁) =  π‘ π‘Žπ‘™π‘’𝑠𝑄

 

 π΄π‘›π‘›π‘’π‘Žπ‘™  π‘‚π‘Ÿπ‘‘π‘’π‘Ÿ  πΆπ‘œπ‘ π‘‘ =  π‘  Γ—  π‘π‘œπ‘ π‘‘  π‘π‘’π‘Ÿ  π‘œπ‘‘π‘’π‘Ÿ    πΈπ‘“𝑓𝑒𝑐𝑑𝑖𝑣𝑒  π΄π‘›π‘›π‘’π‘Žπ‘™  π‘…π‘Žπ‘‘𝑒

= 1

+π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘

π‘‘π‘–π‘ π‘π‘œπ‘’π‘›π‘‘  π‘π‘Ÿπ‘–𝑐𝑒

!"# !"#$%  !"#$    !"#$%&

βˆ’ 1    πΈπ‘₯𝑝𝑒𝑐𝑑𝑒𝑑  π‘ƒπ‘Ÿπ‘œπ‘“𝑖𝑑

= 𝑝  Γ—  π‘ƒπ‘‰ 𝑅𝑒𝑣 βˆ’ πΆπ‘œπ‘ π‘‘βˆ’ 1 βˆ’ 𝑝  Γ—  π‘ƒπ‘‰ πΆπ‘œπ‘ π‘‘  

 

π΅π‘Ÿπ‘’π‘Žπ‘˜  πΈπ‘£π‘’𝑛  π‘ƒπ‘Ÿπ‘œπ‘π‘Žπ‘π‘–𝑙𝑖𝑑𝑦  (𝑝) =𝑃𝑉 πΆπ‘œπ‘ π‘‘π‘ƒπ‘‰ 𝑅𝑒𝑣

 

       

  Call  Option     Buyer   Seller  

Expectation   MP↑   MP↓  Loss   Limited  to  OP   Unlimited  Profit   Unlimited   Limited  to  OP  

   

  Put  Option     Buyer   Seller  

Expectation   MP↓   MP↑  Loss   Limited  to  OP   Limited  to  Stock  Price  Profit   Limited  to  Stock  Price   Limited  to  OP  

 At  the  money   In  the  Money   Out  the  Money  (breakeven)   (to  exercise)   (not  to  exercise)  EP  =  MP   EP  <  MP:  call  option  

EP  >  MP:  put  option  EP  <  MP:  put  option  EP  >  MP:  call  option  

   1)  Underlying  Price  

   2)  Strike  Price  

More  in  the  money   Higher  OP  More  out  the  money   Lower  OP  

 3)  Volatility  

More  Volatile   Higher  OP  Less  Volatile   Lower  OP  

 4)  Expiration  Time  

Longer  Expiration  Time   Higher  OP  Shorter  Expiration  Time   Lower  OP  

 5)  Interest  Rate  

   6)  Dividends  

               

Page 2: BASFIN 2 Finals reviewer [Computations]

   

π΅π‘Ÿπ‘’π‘Žπ‘˜  πΈπ‘£π‘’𝑛 =π΅π‘Ÿπ‘’π‘Žπ‘˜π‘’π‘£π‘’π‘›  πΏπ‘’π‘Žπ‘ π‘’  π‘Žπ‘“π‘‘π‘’π‘Ÿ  π‘‡π‘Žπ‘₯  (𝐢)

(1 + π‘‘π‘Žπ‘₯  π‘Ÿπ‘Žπ‘‘𝑒)  

 π΅π‘Ÿπ‘’π‘Žπ‘˜π‘’π‘£π‘’π‘›  π‘…𝑒𝑛𝑑  π΄π‘“π‘‘π‘’π‘Ÿ  π‘‡π‘Žπ‘₯

= 𝐢1π‘Ÿβˆ’

1π‘Ÿ 1 + π‘Ÿ

1 + π‘Ÿ  

 π‘ƒπ‘Ÿπ‘’𝑠𝑒𝑛𝑑  π‘‰π‘Žπ‘™π‘’𝑒  π‘œπ‘“  πΆπ‘Žπ‘ β„Ž  πΉπ‘™π‘œπ‘€

= 𝐢! +𝐢!

1 + π‘Ÿ ! +𝐢!

1 + π‘Ÿ ! +β‹―

+𝐢!

1 + π‘Ÿ !  

   π΄π‘‘𝑗𝑒𝑠𝑑𝑒𝑑  π·π‘–π‘ π‘π‘œπ‘’𝑛𝑑  π‘…π‘Žπ‘‘𝑒

= 𝑇!"#$%&'( 1 βˆ’ 𝑇!"#$"#%&'"(      π·π‘’π‘π‘Ÿπ‘–π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›  π‘‡π‘Žπ‘₯  π‘†β„Žπ‘–𝑒𝑙𝑑

= π·π‘’π‘π‘Ÿπ‘–π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›  π΄π‘šπ‘œπ‘’𝑛𝑑  Γ—  π‘‘π‘Žπ‘₯  π‘Ÿπ‘Žπ‘‘𝑒    π·π‘’π‘π‘Ÿπ‘–π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›  π΄π‘šπ‘œπ‘’𝑛𝑑

= π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™  π‘π‘œπ‘ π‘‘  Γ—  π‘‘π‘’π‘π‘Ÿπ‘–π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›  π‘Ÿπ‘Žπ‘‘𝑒    π΄π‘“π‘‘π‘’π‘Ÿ  π‘‡π‘Žπ‘₯  π‘ƒπ‘Žπ‘¦π‘šπ‘’𝑛𝑑

= π‘ƒπ‘Ÿπ‘’  π‘‡π‘Žπ‘₯  π‘ƒπ‘Žπ‘¦π‘šπ‘’𝑛𝑑   1 βˆ’ π‘‘π‘Žπ‘₯  π‘Ÿπ‘Žπ‘‘𝑒    

π΅π‘’π‘“π‘œπ‘Ÿπ‘’  π‘‡π‘Žπ‘₯  π‘ƒπ‘Žπ‘¦π‘’π‘šπ‘’π‘›π‘‘ =π‘Žπ‘“π‘‘π‘’π‘Ÿ  π‘‘π‘Žπ‘₯  π‘π‘Žπ‘¦π‘šπ‘’𝑛𝑑

1 βˆ’ π‘‘π‘Žπ‘₯  π‘Ÿπ‘Žπ‘‘𝑒  

   π‘‡π‘œπ‘‘π‘Žπ‘™  πΆπ‘Žπ‘ β„Ž  πΉπ‘™π‘œπ‘€

= π‘–π‘›π‘–π‘‘π‘–π‘Žπ‘™  π‘π‘œπ‘ π‘‘+ π‘‘π‘’π‘π‘Ÿπ‘–π‘π‘–π‘Žπ‘‘π‘–π‘œπ‘›  π‘‘π‘Žπ‘₯  π‘ β„Žπ‘–𝑒𝑙𝑓+ π‘Žπ‘“π‘‘π‘’π‘Ÿ  π‘‘π‘Žπ‘₯  π‘Žπ‘‘π‘šπ‘–π‘›  π‘π‘œπ‘ π‘‘  

                               

   BINOMIAL  TREE      

   

           

 

         REPLICATING  PORTFOLIO    

CALL  OPTION   PUT  OPTION  

βˆ†!"##  =  π‘‰! βˆ’ 0π‘ˆ βˆ’ 𝐷   βˆ†!"#  =  

0βˆ’ 𝑉!π‘ˆ βˆ’ 𝐷  

𝐡!"##  =  βˆ† π‘ˆ βˆ’ 𝑉!

𝑅   𝐡!"#  =  βˆ’βˆ† 𝐷 βˆ’ 𝑉!

𝑅  

𝐢   =  βˆ†π‘† βˆ’ 𝐡   𝑃   =  βˆ†π‘† + 𝐡  

 RISK  NEUTRAL    

CALL  OPTION   PUT  OPTION  

𝑝 =  π‘… βˆ’ 𝑆!𝑆! βˆ’ 𝑆!

  𝑝 =  π‘… βˆ’ 𝑆!𝑆! βˆ’ 𝑆!

 

𝐡!"##  =  π‘ 𝑉! + (1 βˆ’ 𝑝)(0)   𝐡!"#  =  π‘ 0 + (1 βˆ’ 𝑝)(𝑉!)  

𝐢 =𝐡𝑅   𝑃 =

𝐡𝑅  

       

Stock  Price  

MP  Rise  (U)  

EP  β€“  MP  Fall  =  Vd  

MP  Rise  β€“  EP  =  Vu  

MP  Fall  (D)  

Stock  Price  

MP  Rise  (U)    

Stock  Price  

=  Sd  

=  Su  

MP  Fall  (D)    

Stock  Price  

Page 3: BASFIN 2 Finals reviewer [Computations]

PUT  CALL  PARTY    π‘ƒ = 𝐢 + 𝑃𝑉 π‘₯ βˆ’ 𝑆    

𝑃𝑉 π‘₯ =  π‘‹π‘…  

 P  =  put  value  C  =  call  value  PV(x)  =  present  value  of  exercise  price  S  =  stock  price  X  =  exercise  price    BLACK  SCHOLE  

β€’ Only  for  European  option    π΅π‘™π‘Žπ‘π‘˜  π‘†π‘β„Žπ‘œπ‘™π‘’𝑠 = 𝑆𝑁 𝑑! βˆ’ 𝐾𝑒!!"𝑁 𝑑!    N(d1)  =  probability  of  what  you  get  S  =  stock  price  K  =  exercise  price  /  strike  price  e-­‐rt  =  discount  factor  N(d2)  =  probability  of  what  you  give    To  get  the  two  probabilities  (d1  and  d2)      

𝑑! = 𝑙𝑛

𝑆𝐾 + π‘Ÿ + 𝜎

!

2 𝑑

𝜎 𝑑  

   

𝑑! = 𝑙𝑛

𝑆𝐾 + π‘Ÿ βˆ’ 𝜎

!

2 𝑑

𝜎 𝑑    

 OR    π‘‘! =  π‘‘! βˆ’ 𝜎 𝑑                              

                                                     


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