formula rm

7/31/2019 Formula RM

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1. Forwards and FuturesA. Pay-off for Long Position b) Pay-off for Long Position

2. Calculation of Initial Margin:i) When only amount is Given

IM=Amount of Initial Margin*Number of contract

MM= Amount of MM* Number of contract

II) When only Unit Price and Contract Price is givenIM= Unit Price*Contract size

MM= (3/4)th

of Initial Margin

III) When % of Initial Margin is Given:IM= (Unit Price* Contract size* Number of contract)* % given

MM= (3/4) th of Initial Margin

3. Theoretical Futures Price Using No Arbitrage Principle & Valuation of Index FuturesI) Securities providing no Income: F=So ertII) Securities providing Known Income: F= (So-I) ert Where I= Income* e-rt

III) Securities providing Known Income: F=So e(r-y) t Where y=Income in %

Formula S>E S=E S


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7. Futures Hedging Strategiesa) To hedge & Modify Market risk of the portfolio.b) To hedge against fall in specific stock price.c) To gain by buying futures ahead of stock purchases or To trade directionsd) To speculate.e) To Arbitrage.

2. Options1. Types of options

i) Call Option: Long Call, Short Callii)Put Option: Long Put , Short Put

Maximum Profit: Unlimited Maximum Profit: Premium Received

Maximum Loss: Premium Paid Maximum Loss: Unlimited

Maximum Profit: Unlimited Maximum Profit: Premium ReceivedMaximum Loss: Premium Paid Maximum Loss: Unlimited

2. Option Strategiesa) Long Stock, Long Put.b) Long Stock, Short Call.c) Short Stock, Short Call.d) Short Stock, Short Put.

Long CallBuyer of a Call

Has Right to Buy, but no Obligation

Pay-off:(S-E)-P

Short CallSeller of a Call

Has obligation to sell when buyer exercis

Pay-off:(E-S) +P

Long PutSeller of Put

Has Right to sell, but no obligation

Pay-off:(E-S)-P

Short PutBuyer of a Put

Has obligation to buy when buyer exerc

Pay-off:(S-E) +P


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3. Spreads and CombinationsSpreads

a) Bulls Spreads:Position Condition Expiry Date

Long Call (E1)

i) Bulls Spreads with call options: & E2>E1 Same

Short Call (E2)

Long Put (E1)

ii) Bulls Spreads with put option: & E2>E1 SameShort Put (E2)

b) Bear Spreads:Position Condition Expiry Date

Long Call (E1)

i) Bear Spreads with call options: & E1>E2 Same

Short Call (E2)

Long Put (E1)

ii) Bear Spreads with put option: & E1>E2 Same

Short Put (E2)

Long Call (E1)

c) Butterfly Spreads: 2 Short Call (E2) E3>E1 &Same

Long Call (E3) E2= Avg of E1&E3

Combinations

a)StraddleShort Call (E1)i) Top Straddle/Write Straddle: & E1=E2 SameShort Put (E2)

Long Call (E1)

ii) Bottom Straddle/Straddle Purchase: & E1=E2 SameLong Put (E2)


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b) Strangle Position Condition Expiry DateLong Call (E1)

i) Long Strangle: & E1=E2 SameLong Put (E2)

Short Call (E1)

ii) Short Strangle: & E1=E2 SameShort Put (E2)

Long Call (E1)

c) Strips: & E1=E2 Same2 Long Put (E2)

2Long Call (E1)

d) Straps: & E1=E2 SameLong Put (E2)

2 Long Call (E1)

e) Condor : & E2>E1 Same2 Short Call (E1)

Option Pricing

a) Put- Call ParityP+S=C+PV(X)

When P+S C+PV(X) Leads to Arbitrage

Let Assume

P+S=Portfolio-A

C+PV(X)= Portfolio-B


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i) Determination of Arbitrage Profit: When A>B

i) Determination of Arbitrage Profit: When A>B

b)Option Valuation Model:i) Binomial Modelii) Black-Scholes Model

i) Binomial Model:Cu-Cd = Number of Shares to be Purchased

= Cu= Max (uSo-E, 0)So (u-d) Cd= Max (dSo-E, 0)

U= 1+% change in stock Price if stock price increases

d= 1+% change in stock Price if stock price decreases

Cash Flow@ t=0 Cash Flow@ t=1

Portfolio S1=Lower Price S2=Higher Price

2 Short call 2C (E-S) (E-S)

Long Stock -S S1 S2

Borrow ? - -Total X 0 0

i-d u-i C= Call Price

Cu u-d + Cd u-d i= (1+r/n)

C=

i

Pay-off From Expiration

Portfolio S=E SE

Long Call 0 0 S-E

Short Stock S -S -S

Short Put 0 - (E-S) 0

Total SorE -E -E

Pay-off From Expiration

Portfolio S=E SE

Long Stock S S S

Long Put 0 (E-S) -(S-E)

Short Call 0 0 0Total SorE E E


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ii) Black-Scholes Model:C=So N (d1)-E e

-rtN (d2) P=Ee

-rtN (-d2)-So N (-d1)

Where C= Call PriceP= Put Price

ln (So/E) +(r-0.52)td1= d2=d1- t

tNote: When Dividend is given in Rupees then

S*=So-Do

Derivatives of Black-Scholes Model

a) Delta(): P=-C+ N (d1) So

Z (d1) e-d1

2/2

b)Gamma(): = Where Z (d1)=So t 2

t

c) Theta():So Z (d1)

i) (Call)= - Ee-rt r N(d2)2 t

So Z (d1)


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formula rm

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