Derivative include
Future: - Agreement to buy or sell a
commodity or stock in future.
Forward: - Agreement to buy or sell a
commodity or stock in future but traded Over The Counter (OTC) and actual
execution of contract take place.
Option: - Right to buy or sell.
Option can be
classified in two types
Call Option: - Right to Buy – (Up Side Batting)
Put Option: - Right to Sell – (Downside
Batting)
Strike or
Exercise Price
Strike or Exercise
Price is Price at which contract will execute.
Option Premium
or Option Price
Option premium is
the cost for entering in to option contract. Option Premium is paid by buyer
and received by writer.
Profit for buyer
(Holder) is unlimited and loss is limited to premium paid.
Profit for Seller
(Writer) is limited to premium received and unlimited loss.
Break Even Point
Breakeven is Gain
from option is equal to premium paid.
BEP (Call Option) =
Exercise Price (EP) + Premium Paid
BEP (Put Option) =
Exercise Price (EP) - Premium Paid
BEP for Spread
Strategy
BEP (where Call
option is to be exercised) = EP + Cost of Strategy
BEP (where Put
option is to be exercised) = EP - Cost of Strategy
Option
Strategies
S.
NO.
|
Name
of Strategy
|
Explanation
|
1.
|
Long
Straddle (C+, P+)
|
Buy Call &
Buy Put at same strike price and for same maturity period. Investor Expects
Market will be volatile in either direction
|
2.
|
Short
Straddle (C- , P-)
|
Sell Call &
Sell Put at same strike price and for same maturity period. Investor expects
no volatile in the Market.
|
3.
|
Strip
(2P+, C+)
|
Buy 2 Put &
Buy 1 Call Option at same strike price and for same maturity period. Investor
Expects market will more Bearish than Bullish.
|
4.
|
Strap
(2C+, P+)
|
Buy 2 Call &
Buy 1 Put Option at same strike price and for same maturity period. Investor
Expects market will more Bullish than Bearish.
|
5.
|
Bull
Call Spread (C+, C-)
|
Buy Call &
Sell Call, Buy at Lower Rate and Sell at Higher Rate in Bullish Market.
Premium for Long Call > Premium for Short Call. (Favorable Contract have
higher premium)
|
6.
|
Bull
Put Spread (P+, P-)
|
Buy Put &
Sell Put, Buy at Lower Rate and Sell at Higher Rate in Bullish Market.
Premium for Long Put < Premium for Short Put. (Favorable Contract have
higher premium)
|
7.
|
Bear
Call Spread (C-, C+)
|
Short Call &
Long Call. Sell at lower and Buy at Higher in Bearish Market. Premium for
Short Call > Premium for Long Call (Favorable Contract have higher
premium).
|
8.
|
Bear
Put Spread (P-, P+)
|
Short Put &
Long Put. Sell at lower and Buy at Higher in Bearish Market. Premium for
Short Put < Premium for Long Put (Favorable Contract have higher
premium).
|
9.
|
Protective
Put (S+, P+)
|
Long in Stock and
Long in Put. Put acts as Insurance but Increase Cost of Acquisition.
|
10.
|
Covered
Call (S+, C-)
|
Long in Stock and
Short In Call. Call limits the upside but reduces the cost of Acquisition.
|
Intrinsic Value
Intrinsic Value is
that part of the option premium which represents that extends to which the
option is in the money. Intrinsic Value cannot be negative. If Option is At the
Money or Out of the Money then there is no Intrinsic Value.
Time Value
Time Value is the
difference between option premium and Intrinsic Value. Time value falls with time and falls to zero
on the expiration date.
Moneyness of the
Option
S.
No.
|
Scenario
|
Call
Option
|
Put
Option
|
1.
|
EMP
= EP
|
ATM
Indifference
|
ATM
Indifference
|
2.
|
EMP
> EP
|
ITM
Exercise
|
OTM
Lapse
|
3.
|
EMP
< EP
|
OTM
Lapse
|
ITM
Exercise
|
Investment Value or
Gross Profit = AMP – EP
Initial Margin
Initial Margin is
the Initial Amount which is deposited by buyer and seller of future option.
Initial Margin is the first line of defense for the Clearing House. It is also
known as performance margin.
Maintenance
Margin
Maintenance margin
is the margin required to be kept by the investor in the equity account equal
to or more than a specified percentage of Initial Margin.
Variation Margin
If the account
balance goes below maintenance margin then investor needs bring in so much that
Account balance again reaches Initial Margin Level, this is called Variation
Margin.
Initial Margin = µ
+ 3σ (µ
= Average Change in the Value of Contract)
Maintenance Margin
= Initial Margin x % required to be maintained
Arbitrage Profit
Arbitrage Profit =
Riskless Profit
Arbitragers are the
people who earn arbitrage profit due to difference in Actual Price and
Theoretical Price.
Theoretical
Future Price: -
Theoretical Future
Price (TFP) is price calculated using cost of carry model. Cost of Carry Model
means there should such relationship between spot price (Cash Market Price) and
Future Price (Price in Derivative Market) that there should not arise no
arbitrage profit.
S.
No.
|
Cases
|
Non
– Continues Compounding
|
Continues
Compounding
|
1.
|
No
Dividend Income
|
TFP
= SP + COC
|
TFP
= SP x ert
|
2.
|
Dividend
Income
|
TFP
= SP + COC – Dividend Income
|
TFP
= (SP – PV of Dividend Income) x ert
|
3.
|
Dividend
Yield is Given
|
TFPS
= SP + COC – SP x Yield Rate
|
TFP
= SP x e(r – y)t
|
Limitation of
Arbitrage in Real Life
Transaction cost is
ignored.
Margin Money is
ignored.
Dividend Risk
Taxes are ignored.
Short selling is
not allowed in Cash Market.
Basis = Spot Price - Future Price
Contango Market is
such a market in which the basis is
decided solely by the Cost of Carry (COC).
Beta Management
Using Index Future
Portfolio Managers
generally do not sell their existing holding if they expects short term
fluctuation in the market. Rather they would like to adjust their Portfolio
Beta based on their assessment of any volatile movement in share market.
If portfolio
manager expects that market will decline then –
He would like to
decrease Portfolio Beta (Hedging).
If Portfolio
Manager expects that market will rise then –
He would like to
increase Portfolio Beta.
Hedging (Beta is
also known as Hedge Ratio)
Existing
Position
|
Future
Position
|
Long
in Stock (S+)
|
Short
in Future (F-)
|
Short
in Stock (S-)
|
Long
in Future (F+)
|
No
of Contract to be Bought or Sold = VP x (βD – βP)
Nifty Future x Lot Size
|
|
Option Valuation
Binomial Model
Formula
|
Remarks
|
VOC = P x Cu +
(1 – P) x Cd
R
|
Where,
R = 1 + Rf
Cu = Call Upside
Gain
Cd = Call Downside Gain
Pu = Put Upside
Gain
Pd = Put Downside Gain
d = ds (expected downside price divided by spot
price)
s
u = us (expected upside price divided by spot price)
s
|
VOC = P x Pu +
(1 – P) x Pd
R
|
|
P = R – d
U – d
|
|
Value of American
Option = Max of Discounted Value or Intrinsic Value
|
Put Call Parity
Theory (PCPT)
Spot Price + Value
of Put = Value of Call + Present Value of Exercise/Strike Price
PCPT is the
relationship between European Call and Put Option on the same stock, the
maturity period and EP is same.
The PCPT equation
is made to prevent arbitrage profit. If LHS ≠ RHS, then there would arise
arbitrage profit.
LHS Þ SP + VOP (Protective Put – S+, P+)
RHS Þ VOC + PV of EP (Fiduciary Call – C+, ZCB+)
Risk Neutral
Valuation
The Price of an
option is independent of the risk preference of Investor Called risk-neutral
valuation.
Black Scholes
Model
Formula
|
Remarks
|
European Call
Option = SP x N (d1) – PV of EP x N (d2)
|
Where,
Ln = Natural Log
SP = Spot Price
EP = Exercise
Price
R= Rate of
Interest
T = time
|
d1 = ln
(SP) + (r + .5 σ2) x
t
EP………………..
σ√t
|
|
d2 = d1
- σ√t
|
|
Assumption of Block
Scholes Model
European options
are considered.
No Transaction
Costs.
Short Term
interest rates are known and constant.
Stocks don’t pay
dividend.
Stock Price
Movement is similar to random walk.
Stock returns are
normally distributed over a period of time.
Variance of
return is constant over the life of an option.
|
|
When Probability
distribution or probable market price is given for market price of share on
expiration then value of option will be calculated as follows: -
Value of Option = (AMP
–EP) x Probability + (AMP – EP) x Probability + ……………….. (.i.e. we should check
individually)
Future/(1 + Rf)
= Spot Price + PV of Storage – PV of Convince Yield
Performance
Analysis of Stock in terms of Percentage of Greeks
Delta
Delta is the degree
to which an option price will move in given underlying stock price. A deeply
out of the Money call will have a delta very close to zero and a deeply in the
money call will have a delta very close to 1.
Gamma
Gamma measure how
fast the delta changes for small change in the underlying stock price. It is
the delta of the data.
Theta
The Change in
Option Price on given day will decrease in the time to expiration. It is a
measure of time decays.
Rho
The change in the
option price a one percentage point change in the risk frees Interest Rate.
Vega
Vega is the Sensitivity
of Option Value to Change in Volatility.
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