DERIVATIVES (F&O) #pdf

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SFM
STRATEGIC FINANCIAL
MANAGEMENT
Summary Booklet for
DERIVATIVES
By CA. Gaurav Jain
100% Conceptual Coverage
With Live Trading Session
Complete Coverage of Study Material, Practice
Manual & Previous year Exam Questions
Registration Office:
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CA. Gaurav Jain
Strategic Financial Management
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100% Coverage with PM, SM & RTP
CA. Gaurav Jain
Strategic Financial Management
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100% Coverage with PM, SM & RTP
CA. Gaurav Jain
Strategic Financial Management
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100% Coverage with PM, SM & RTP
CA. Gaurav Jain
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100% Coverage with PM, SM & RTP
CA. Gaurav Jain
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DERIVATIVES (FUTURES)
Attempt wise Marks Analysis of Chapter
Attempt Marks
May-11 5
Nov-11 13
May-12 10
Nov-12 0
May-13 8
Nov-13 13
May-14 0
Nov-14 0
May-15 8
Nov-15 8
May-16 0
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Concept No. 1: Introduction
Define Forward Contract, Future Contract.
Forward Contract, In Forward Contract one party agrees to buy, and the counterparty to
sell, a physical asset or a security at a specific price on a specific date in the future. If the
future price of the assets increases, the buyer(at the older, lower price) has a gain, and the
seller a loss.
Futures Contract is a standardized and exchange-traded. The main difference with
forwards are that futures are traded in an active secondary market, are regulated, backed
by the clearing house and require a daily settlement of gains and losses.
Future Contracts differ from Forward Contracts in the following ways:
Futures contracts trade on organized exchange. Forwards are private contracts and do
not trade.
DERIVATIVES
Exchange Traded
Future
Contract
Option
Contract
OTC
Derivatives
Forward
Contract
FRA
Cap, Floor &
Collar
Interest
Rate Swap
Currency
Swap
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Future contracts are highly standardized. Forwards are customized contracts satisfying
the needs of the parties involved.
A single clearinghouse is the counterparty to all futures contracts. Forwards are contract
with the originating counterparty.
The government regulates future markets. Forward contracts are usually not regulated.
Concept No. 2: How Future Contract can be terminated at or prior to expiration?
A short can terminate the contract by delivering the goods, and a long can terminate the
Contract by accepting delivery and paying the contract price to the short. This is called
Delivery. The location for delivery (for physical assets), terms of delivery, and details of
exactly what is to be delivered are all specified in the contract.
In a cash-settlement contract, delivery is not an option. The futures account is marked-
to-market based on the settlement price on the last day of trading.
You may make a reverse, or offsetting, trade in the future market. With futures, however,
the other side of your position is held by the clearinghouse- if you make an exact opposite
trade(maturity, quantity, and good) to your current position, the clearinghouse will net your
positions out, leaving you with a zero balance. This is how most futures positions are
settled.
Note:
Future Contracts can be taken for any number of periods like in currency future we can take
12 months Contract.
Current Month + 11 months
Concept No. 3: Position to be taken under Future Market
How to settle/ square-off/ covering/ closing out a position
Long Position should be settled by Short position to calculate Profit/ Loss.
Short Position should be settled by Long position to calculate Profit/ Loss.
Future Market
Long Position
Buying Position
Short Position
Selling Position
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Concept No. 4: Gain or Loss under Future Market
Position If Price on Maturity/ Settlement Price Gain/ Loss
Long Position
Increase Gain
Decrease Loss
Short Position
Increase Loss
Decrease Gain
Note:
Note:
Gain/Loss is net of brokerage charge. Brokerage is paid on both buying & selling.
Security Deposit is not considered while calculating Profit & Loss A/c.
Interest paid on borrowed amount must be deducted while calculating Profit & Loss.
A Future contract is ZERO-SUM Game. Profit of one party is the loss of other party.
Concept No. 5: Difference between Margin in the cash market and Margin in the
future markets and Explain the role of initial margin, maintenance margin
In Cash Market, margin on a stock or bond purchase is 100% of the market value of the
asset.
Initially, 50% of the stock purchase amount may be borrowed and the remaining amount
must be paid in cash (Initial margin).
There is interest charged on the borrowed amount.
Lot Size Required
Cash Market
1.No Lot Size Required
2. An investor can trade
any number of shares
Future Market
1.Lot Size Required.
2. An investor can only trade
as per lot size.
Example:
Lot Size of NIFTY 100
If NIFTY is traded at 5250, then the
value of one NIFTY contract is `
5,25,000.
Lot Size of Reliance 150 shares
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In Future Markets, margin is a performance guarantee i.e. security provided by the client to
the exchange. It is money deposited by both the long and the short. There is no loan
involved and consequently, no interest charges.
The exchange requires traders to post margin and settle their account on a daily basis.
1. Initial Margin
It is the money that must be deposited in a futures account before any trading takes
place and paid by both long and short position.
It is set for each type of underlying asset.
Initial Margin per contract is relatively low and equals about one day’s maximum price
fluctuation on the total value of the contract.
2. Maintenance Margin
It is the amount of margin that must be maintained in a futures account. i.e. It is a limit
below which our closing balance should not fall.
If the initial margin balance in the account falls below the maintenance margin due to the
change in the contract price, additional fund must be deposited to bring the margin
balance back-up to the initial margin requirement.
3. Variation Margin
It is the amount which the trader has to bring when the maintenance margin is breached.
Note:
Any amount, over & above initial margin amount can be withdrawn.
If Initial Margin is not given in the question, then use:
Initial Margin = Daily Absolute Change + 3 Standard Deviation
Concept No. 6: Concept of EAR (Normal Compounding)
The rate of interest that investor actually realize as a result of compounding is known as the
Effective Annual Rate (EAR).
EAR represents the annual rate of return actually being earn after adjustments have been
made for different compounding periods.
EAR = (1+ periodic rate) m – 1
Where:
Periodic rate = stated annual rate
m
m = the number of compounding periods per year
Greater the compounding Frequency, the greater the EAR will be in comparison to stated
rate.
For Normal Compounding use,
FV = PV(1+r
m)
m × n
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Concept No. 7: Concept of e rt & e –rt (Continuous Compounding)
Most of the financial variable such as Stock price, Interest rate, Exchange rate, Commodity
price change on a real time basis. Hence, the concept of Continuous compounding comes in
picture.
Continuous Compounding means compounding every moment. Instead of (1 + r) we will use ert
Under Future & Options Chapter, it is normally assumed that interest rate is compounded
continuously (i.e. infinite times)
FV = PV(1+r
α)
α
FV = PV × e rt
Or present value = FV
ert
Or PV = FV × e -rt
Where r = rate of interest p.a
t = time period
Concept No. 8: Fair future price of security with no income
In case of Normal Compounding
Fair future price = Spot Price (1+r)n
In case of Continuous Compounding
Fair future price = Spot Price × e rt
Where r = risk free interest p.a. with Continuous Compounding.
t = time to maturity in years/ days. (No. of days / 365) or (No. of months / 12)
Concept No. 9: Fair Future Price of Security with Dividend Income
In case of Normal Compounding
Fair Future Price = [Spot Price – PV of Expected Dividend ] ( 1+r)n
In case of Continuous Compounding
Fair Future Price = [Spot Price – PV of Expected Dividend ] × e r t
PV of DI = Present Value of Dividend Income = Dividend × e – r t
Where t = period of dividend payments
Concept No. 10: Fair Future Price of security when income is expressed in
percentage or when dividend yield is given
In case of Normal Compounding
Fair Future Price = Spot Price [1+(r-y)] n
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In case of Continuous Compounding
Fair Future Price = Spot Price × e(r-y) × t
Where y = income expressed in % or dividend Yield
Note:
If percentage income is given, it is assumed to be given on per annum basis.
Concept No. 11: Fair Future Price of Commodity with storage cost
It is applicable in case of Commodity futures.
In case of Normal Compounding
Fair Future Price = [Spot Price + PV of S.C ] ( 1+r) n
In case of Continuous Compounding
Fair Future Price = [Spot Price + PV of S.C ] × e rt
Where PV of S.C = Present Value of Storage Cost
Note: Fair Future Price when Storage Cost is given in percentage(%).
FFP = Spot Price × e (r + s) × t
Where S = Storage cost expressed in percentage.
Concept No. 12: Fair Future Price of commodities with Convenience yield
expressed in % (Similar to Dividend Yield)
Applicable in case of Commodity futures.
The benefit or premium associated with holding an underlying product or physical good
rather than contract or derivative product i.e. extra benefit that an investor receives for
holding a commodity.
In case of Continuous Compounding
Fair Future Price = Spot Price × e(r-c)×t
Note: Fair Future Price when convenience income is expressed in Absolute Amount.
Fair Future Price = [Spot Price - PV of Convenience Income] × e rt
Concept No. 13: Arbitrage Opportunity between Cash and Future Market
Arbitrage is an important concept in valuing (Pricing) derivative securities. In its Purest
sense, arbitrage is riskless.
Arbitrage opportunities arise when assets are mispriced. Trading by Arbitrageurs will
continue until they effect supply and demand enough to bring asset prices to efficient( no
arbitrage) levels.
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Arbitrage is based on “Law of one price”. Two securities or portfolios that have identical
cash flows in future, should have the same price. If A and B have the identical future pay
offs and A is priced lower than B, buy A and sell B. You have an immediate profit.
Difference between Actual Future Price and Fair Future Price?
Fair Future Price is calculated by using the concept of Present Value & Future Value.
Actual Future Price is actually prevailing in the market.
Case Value Future Market Cash Market Borrow/ Invest
FFP < AFP Over-Valued Sell or Short Position Buy Borrow
FFP > AFP Under-Valued Buy or Long Position Sell # Investment
# Here we assume that Arbitrager hold shares
Concept No. 14: Complete Hedging by using Index Futures & Beta
Hedging is the process of taking an opposite position in order to reduce loss caused by
Price fluctuation.
The objective of Hedging is to reduce Loss.
Complete Hedging means profit/ Loss will be Zero.
Position to be taken:
1. Long Position should be hedged by Short Position.
2. Short Position should be hedged by Long Position.
Value of Position to be taken:
Value of Position for Complete hedge should be taken on the basis of Beta through index
futures.
Value of Position for Complete Hedge = Current Value of Portfolio × Existing Stock Beta
Concept No. 15: Value of Hedging/Position for Increasing & Reducing Beta to a
Desired Level
Objective
[Assume Long Position]
Reducing Risk
Position: Short Position
Increasing Risk
Position: Long Position.
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Alternative 1 (Hedging Using Index Future)
Case I: When Existing Beta > Desired Beta
Objective: Reducing Risk
Value of Index Position = Value of Existing Portfolio × [Existing Beta – Desired Beta]
Action: Take Short Position in Index & keep your current position unchanged.
Case II: When Existing Beta < Desired Beta
Objective: Increase Risk
Value of Index Position = Value of Existing Portfolio × [Desired Beta – Existing Beta]
Action: Take Long Position in Index & keep your current position unchanged
Note:
No. of future contracts to be sold or purchased for increasing or reducing Beta to a
Desired Level using Index Futures.
No. of Future Contract to be taken = ����&#-667558875;&#-667558866;&#-667558882; &#-667558872;&#-667558881; ��&#-667558873;&#-667558883;&#-667558882;&#-667558863; ��&#-667558872;&#-667558868;��&#-667558867;��&#-667558872;&#-667558873;
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Alternative 2 (Hedging Using Risk free Investment or Borrowing)
Case 1: Reducing Risk
SELL SOME SECURITIES AND REPLACE WITH RISK-FREE INVESTMENT
Step1: Equate the weighted Average Beta formulae to the new desired Beta
Desire Beta = Beta1 × W1 + Beta2 × W2 ( Beta of Risk free investment is Zero)
Step2: Use the weights and decide
Case 2: Increasing Risk
BUY SOME SECURITIES AND BORROW AT RISK-FREE RATE
Step1: Equate the weighted Average Beta formulae to the new desired Beta
Desire Beta = Beta1 × W1 + Beta2 × W2 ( Beta of Risk free investment is Zero)
Step2: Use the weights and decide
Concept No. 16: Partial Hedge
Value of existing Portfolio × Existing beta × percentage (%) to be Hedge
It result into Over-Hedged or Under-Hedged Position
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There may be profit or loss depending upon the situation.
Concept No. 17: Beta of a Cash and Cash Equivalent
Beta of a cash and Risk free security is Zero.
Concept No. 18: Hedging Commodity Risk Through Futures
Concept No. 19: Calculation of Rate of Return
Increase or Decrease in Stock Price (P1 – P0)
(+) Dividend Received
( - ) Transaction Cost
( - ) Interest Paid on Borrowed Amount
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Rate of return:
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&#-667558893;&#-667558872;&#-667558867;��&#-667558875; ��&#-667558873;��&#-667558867;����&#-667558875; &#-667558908;&#-667558870;&#-667558866;��&#-667558867;&#-667558862; ��&#-667558873;&#-667558865;&#-667558882;&#-667558868;&#-667558867;&#-667558874;&#-667558882;&#-667558873;&#-667558867; ×&#-667557937;&#-667557938;&#-667557938;
Concept No. 20: Hedge Ratio
The Optional Hedge Ratio to minimize the variance of Hedger’s position is given by:-
Hedge Ratio = Corr. (r) σS
σF
σS = S.D of Δ S
σF = S.D of Δ F
r = Correlation between Δ S and Δ F
Δ S = Change in Spot Price
Δ F = Change in Future Price
Hedging
Commodity
Risk
Commodity
Producer
Expected to
fall in Price
Sell Future
Contract
Commodity
Consumer
Expected to
rise in Price
Buy Future
Contract
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DERIVATIVES (OPTIONS)
Attempt wise Marks Analysis of Chapter
Attempt Marks
May-11 5
Nov-11 8
May-12 8
Nov-12 8
May-13 0
Nov-13 0
May-14 4
Nov-14 0
May-15 0
Nov-15 5
May-16 5
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Concept No. 1: Introduction
Option Contract:
An option contract give its owner the right, but not the legal obligation, to conduct a
transaction involving an underlying asset at a pre-determined future date( the exercise date)
and at a pre-determined price (the exercise price or strike price)
Meaning of Long position & Short position under Option Contract
Option Contract
Call Option
Long Call
Right to
Buy
Option
Buyer
Short Call
Obligation
to Sell
Option
Seller
Put Option
Long Put
Right to
Sell
Option
Buyer
Short Put
Obligation
to Buy
Option
Seller
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There are four possible options position
1. Long call: The buyer of a call option has the right to buy an underlying asset.
2. Short call: The writer (seller) of a call option has the obligation to sell the underlying
asset.
3. Long put: The buyer of a put option has the right to sell the underlying asset.
4. Short put: The writer (seller) of a put option has the obligation to buy the underlying
asset.
Note:
If question is silent always assume Long Position.
Exercise Price/ Strike Price:
The fixed price at which buyer of the option can exercise his option to buy/ sell an
underlying asset. It always remain constant throughout the life of contract period.
Option Premium:
To acquire these rights, owner of options must buy them by paying a price called the
Option premium to the seller of the option.
Option Premium is paid by buyer and received by Seller.
Option Premium is non-refundable, non-adjustable deposit.
Note:
The option holder will only exercise their right to act if it is profitable to do so.
The owner of the Option is the one who decides whether to exercise the Option or not.
Concept No. 2: Call Option
When Call Option Contract are exercised:
When CMP > Strike Price Call Buyer Exercise the Option.
When CMP < Strike Price Call Buyer will not Exercise the Option.
Note:
Maximum loss to the call buyer will be equal to option premium paid.
Maximum profit for the call Writer/ Seller will be only option premium received
Maximum profit for call buyer will be unlimited.
Maximum loss for call seller will be unlimited.
Break-even point for the buyer and seller is the price at which profit and loss will be zero.
Break-even Market Price = Exercise Price + Option Premium
The call holder will exercise the option whenever the stock’s price exceeds the strike price
at the expiration date.
The sum of the profits between the Buyer and Seller of the call option is always Zero. Thus,
Option trading is ZERO-SUM GAME. The long profits equal to the short losses.
Position of a Call Seller will be just opposite of the position of Call Buyer.
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In this chapter, we first see whether the Buyer of Option opt or not & then accordingly we
will calculate Profit & Loss
Concept No. 3: Put Option
When Put Option Contract are exercised:
When CMP > Strike Price Put Buyer will not Exercise the Option.
When CMP < Strike Price Put Buyer will Exercise the Option.
Note:
If Actual Market Price falls to Zero, NP = X – S – OP i.e. X – 0 – OP
Maximum Profit = X – OP
Put Buyer will only exercise the option when actual market price is less the exercise price.
Profit of Put Buyer = Loss of Put Seller & vice-versa. Trading Put Option is a Zero-Sum
Game.
Pay-off Diagram
Concept No. 4: Profit or Loss/ Pay off of call Option & Put Option
While calculating profit or loss, always consider option Premium,
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Call Buyers (Long Call)
If S – X > 0
Exercise the option
Net Profit = S – X – OP
If S – X < 0
Not Exercise
Loss = Amount of Premium
Put Buyers (Long Put)
If X – S >0
Exercise the option
Net Profit = X – S –OP
If X – S < 0
Not Exercise
Loss = Amount of Premium
Break-even Market Price for call & Put option
Break – even Market Price is the price at which Profit & loss is Zero.
For Call Buyer &Call Seller For Put Buyer &Put Seller
Net Profit = S – X – OP Net Profit = X – S – OP
If NP = 0
S = X + OP
If NP = 0
S = X – OP
Where S = Stock Price
X = Exercise Price
OP = Option Premium
Concept No. 5: Concept of Moneyness of an Option
Moneyness refers to whether an option is In-the money or Out- of the money.
Case I
If immediate exercise of the option would generate a positive pay-off, it is in the money
Case II
If immediate exercise would result in loss (negative pay-off), it is out of the money.
Case III
When current Asset Price = Exercise Price, exercise will generate neither gain nor loss
and the option is at the money.
Call Option Put Option
Case 1 S – X > 0 In-the-Money X - S > 0
Case 2 S – X < 0 Out-of- the-Money X - S < 0
Case 3 S = X At-the-Money X = S
Note:
Do not consider option premium while Calculating Moneyness of the Option.
Concept No. 6: European & American Options
American Option : American Option may be exercised at any time upto and including the
contract’s expiration date.
European Option : European Options can be exercised only on the contract’s expiration date.
The name of the Option does not imply where the option trades – they are just names.
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Concept No. 7: Action to be taken under Option Market
If expected Market Price is Call Put
Going to rise Long Call Short Put
Going to fall Short Call Long Put
Concept No. 8: Option Strategies
Combination of Call & Put is known as OPTION STRATEGIES.
Types of Option Strategies:
Some important Option Strategies are as follows:
1. Straddle Position
2. Strangle Strategy
3. Strip Strategy
4. Strap Strategy
5. Butterfly Spread
1. Straddle Position:
Straddle may be of 2 types:-
Long Straddle Short Straddle
Buy a Call and Buy a Put on the same stock
with both the options having the same
exercise price.
Option: Buy One Call and Buy One Put
Exercise Date: Same of Both
Strike Price/ Exercise Price: Same of Both
Note:
A Long Straddle investor pays premium on
both Call & Put.
Sell a Call and Sell a Put with same exercise
price and same exercise date.
Option: Sell One Call and Sell One Put
Exercise Date: Same of Both
Strike Price/ Exercise Price: Same of Both
Note:
A Short Straddle investor receive premium on
both Call and Put.
Note:
When an investor is not sure whether the price will go up or go down, then in such case we
should create a straddle position.
If Question is Silent, always assume Long Straddle.
2. Strangle Strategy
An option strategy, where the investor holds a position in both a call and a put with
different strike prices but with the same maturity and underlying asset is called Strangles
Strategy.
Selling a call option and a put option is called seller of strangle (i.e. Short Strangle).
Buying a call and a put is called Buyer of Strangle (i.e. Long Strangle).
If there is a large price movement in the near future but unsure of which way the price
movement will be, this is a Good Strategy.
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3. Strip Strategy (Bear Strategy) 4. Strap Strategy (Bull Strategy)
Buy Two Put and Buy One Call Option of
the same stock at the same exercise price
and for the same period.
Strip Position is applicable when decrease
in price is more likely than increase.
Option: Buy One Call and Buy Two Put
Exercise Date: Same of Both
Strike Price/ Exercise Price: Same of Both
Buy Two Calls and Buy One Put when the
buyer feels that the stock is more likely to
rise Steeply than to fall.
Strap Position is applicable when increase
in price is more likely than decrease.
Option: Buy Two Calls and Buy One Put
Exercise Date: Same of Both
Strike Price/ Exercise Price: Same of Both
5. Butterfly Spread
In Butterfly spread position, an investor will undertake 4 call option with respect to 3 different
strike price or exercise price.
It can be constructed in following manner:
Buy One Call Option at High exercise Price (S1)
Buy One Call Option at Low exercise Price (S2)
Sell two Call Option (S1+ S2
2)
Calculation of Option Value
Value of Option
Simple
Valuation
Rules
When Strike
Price and
expected price
of underlying
asset is given.
Binomial
Method
When Expected
price of
Underlying
Assets will either
high price or low
price
Using Risk
Neutral
Approach
Perfectly Hedge
Situation i.e.
using Hedge
Ratio
Black -
Scholes Model
When Standard
Deviation with
other
information is
given
Put Call
Parity
When information
of Call Option is
given and value of
Put Option to be
calculated and
Vice-versa
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Concept No. 9: Intrinsic Value & Time Value of Option
Option value (Premium) can be divided into two parts:-
(i) Intrinsic Value
(ii) Time Value of an Option (Extrinsic Value)
Option Premium = Intrinsic Value + Time Value of Option
Intrinsic Value:
An Option’s intrinsic Value is the amount by which the option is In-the-money. It is the
amount that the option owner would receive if the option were exercised.
Intrinsic Value is the minimum amount charged by seller from buyer at the time of selling the
right.
An Option has ZERO Intrinsic Value if it is At-the-Money or Out-of-the-Money, regardless of
whether it is a call or a Put Option.
The Intrinsic Value of a Call Option is the greater of (S – X) or 0. That is
C = Max [0, S –X]
Similarly, the Intrinsic Value of a Put Option is (X - S) or 0. Whichever is greater. That is:
P = Max [0, X - S]
Time Value of an Option (Extrinsic Value):
The Time Value of an Option is the amount by which the option premium exceeds the
intrinsic Value.
Time Value of Option = Option Premium – Intrinsic Value
When an Option reaches expiration there is no “Time” remaining and the time value is
ZERO.
The longer the time to expiration, the greater the time value and, other things equal, the
greater the option’s Premium (price).
Concept No. 10: Fair Option Premium/ Fair Value/ Fair Price of a Call on Expiration
Fair Premium of Call on Expiry:
= Maximum of [(S – X), 0]
Note:
Option Premium can never be Negative. It can be Zero or greater than Zero.
Concept No. 11 Fair Option Premium/ Fair Value/ Fair Price of a Put on Expiration
Fair Premium of Put on Expiry:
= Maximum of [(X – S), 0]
Concept No. 12: Fair Option Premium/ Theoretical Option Premium/ Price of a Call
before Expiry or at the time of entering into contract or As on Today
Fair Premium of Call = Current Market Price – Present Value of Exercise Price
Or
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= [&#-667558894; − ��
(&#-667557937;+&#-667558895;&#-667558907;&#-667558895;)&#-667558893; ,0] Max
Or
= [S – X e – rt,0] Max
RFR (r) = Risk-free rate
T = Time to expiration
Concept No. 13: Fair Option Premium/ Theoretical Option Premium/ Price of a Put
before Expiry or at the time of entering into contract or As on Today
Fair Premium of Put = Present Value of Exercise Price – Current Market Price
Or
= [��
(&#-667557937;+&#-667558895;&#-667558907;&#-667558895;)&#-667558893; – &#-667558894;,&#-667557938;] Max
Or
= [�� &#-667558882; – &#-667558869;&#-667558867; – &#-667558894;,&#-667557938;] Max
Concept No. 14: Arbitrage Opportunity in Option Contract
When Arbitrage is possible under Option Contract?
Fair Option Premium ≠ Actual Option Premium
Arbitrage Opportunity on Call Before Expiry
FP = Fair Premium AP = Actual Premium
Case I Value Option Market Cash Market Invest
FP > AP Under-Valued Long Call Sell # Net Amount
# Assume investor is already holding the required shares.
Case 2 Value Option Market Cash Market Borrow
FP < AP Over-Valued Short Call Buy Net Amount
* Arbitrage is not possible Because we can also incur loss in this case
Arbitrage Opportunity on Put Before Expiry
Case I Value Option Market Cash Market Borrow
FP > AP Under-Valued Long Put Buy Net Amount
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Case 2 Value Option Market Cash Market Invest
FP < AP Over-Valued Short Put Sell Net Amount
* Arbitrage is not possible Because we can also incur loss in this case
Concept No. 15: Expected Value of an Option on expiry
Under this approach, we will calculate the amount of Option premium on the basis of Probability.
Value of Option at expiry × Probability = Expected value of an option at Expiry
Concept No. 16: Risk Neutral Approach for Call & Put Option(Binomial Model)
Under this approach, we will calculate Fair Option Premium of Call & Put as on Today.
The basic assumption of this model is that share price on expiry may be higher or may be
lower than current price.
Step 1: Calculate Value of Call or Put as on expiry at high price & low price
Value of Call as on expiry = Max [( S – X),0]
Value of Put as on expiry = Max [(X – S), 0]
Step 2: Calculate Probability of High Price & Low Price
Probability of High Price = CMP (1+r)n− S2
S1 − S2 or Probability of High Price = CMP (e rt)− S2
S1 − S2
Step 3: Calculate expected Value/ Premium as on expiry by using Probability
Step 4: Calculate Premium as on Today
By Using normal Compounding
= Expected Premium as on expiry
(1+r)t
By Using Continuous Compounding
= Premium as on expiry × e – rt
Concept No. 17: Two Period Binomial Model
We divide the option period into two equal parts and we are provided with binomial projections
for each path. We then calculate value of the option on maturity. We then apply backward
induction technique to compute the value of option at each nodes.
Concept No. 18: Put Call Parity Theory (PCPT)
Put Call Parity is based on Pay-offs of two portfolio combination, a fiduciary call and a protective
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put.
Fiduciary Call
A Fiduciary Call is a combination of a pure-discount, riskless bond that pays X at maturity and a
Call.
Protective Put
A Protective Put is a share of stock together with a put option on the stock.
PCPT Value of Call + ��
(&#-667557937;+&#-667558895;&#-667558907;&#-667558895;)&#-667558893; = Value of Put + S
Through this theory, we can calculate either Value of Call or Value of Put provided other Three
information is given.
Assumptions:
Exercise Price of both Call & Put Option are same.
Maturity Period of both Call & Put are Same.
Concept No. 19: Put - Call Parity Theory ARBITRAGE
As per PCPT,
Value of Call + X
(1+RFR)T = Value of Put + S
LHS RHS
Case I
If LHS = RHS, no arbitrage is possible.
Case II
If LHS ≠ RHS, arbitrage is possible.
A. If LHS > RHS, Call is Over-Valued & Put is Under-Valued
Option Market Cash Market Net Amount
Short Call
i.e. Obligation to sell &
receive Option Premium
Long Put
i.e. Right to sell & pay
Option Premium
Buy
i.e. Buy one share
Borrow
B. If LHS < RHS, Call is Under-Valued & Put is Over-Valued
Option Market Cash Market Net Amount
Long Call
i.e. Right to Buy & pay
Option Premium
Short Put
i.e. Obligation to Buy &
receive Option Premium
Sell
i.e. Sell one share
Invest
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Concept No. 20: Binomial Model (Delta Hedging / Perfectly Hedged technique) for
Call Writer
Under this concept, we will calculate option premium for call option.
It is assumed that expected price on expiry may be greater than Current Market Price or
less than Current Market Price.
Spot Price
On Maturity S1 (High Price) S 2( Low Price)
This model involves 3 Steps:
Step 1: Compute the Option Value on Expiry Date at high price and at low price
Value of Call as on expiry = Max [(S – X),0]
Step 2: Buy ‘Delta’ No. of shares ‘Δ’ at Current Market Price as on Today. Delta ‘Δ ’ also known
as Hedge Ratio.
Hedge Ratio or ‘Δ’ = Change in Option Premium
Change in Price of Underlying Asset
OR
= Value of call on expiry at High Price –Value of call on expiry at Low Price
High Price −Low Price
= C1− C2
S1− S2
Step 3: Construct a Delta Hedge Portfolio i.e. Risk-less portfolio / Perfectly Hedge Portfolio
Sell one call option i.e. Short Call ,Buy Delta no. of shares and borrow net amount.
Step 4: Borrow the net Amount required for the above steps
B = 1
1+r [Δ× S2− C2]
Or
B = 1
1+r [Δ× S1− C1]
Where r = rate of interest adjusted for period
Step 5: Calculate Value of call as on today
Borrowed Amount = Amount required to purchase of share – Option Premium Received
B = Δ × CMP – OP
Or
(Option Premium = Δ × CMP – Borrowed Amount)
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Note: Calculation of Cash flow Position/ Value of holding after 1 year
If on Maturity Actual Market Price is S1
Cash Flow = ∆ × S1 – C1
If on Maturity Actual Market Price is S2
Cash Flow = ∆ × S2 – C2
Cash Flow at S1 and S2 will always be same.
Concept No. 21: Black & Scholes Model
The BSM Model uses five variables to value a call option:
1. The price of the Underlying Stock (S)
2. The exercise price of the option (X)
3. The time remaining to the expiration of the option (t)
4. The riskless rate of return (r)
5. The volatility of the underlying stock price (σ)
For Call:
Value of a Call Option/ Premium on Call = &#-667558894;×��(&#-667558883;&#-667557937;) - ��
&#-667558882;&#-667558869;&#-667558867; × ��(&#-667558883;&#-667557936;)
Where N(d1) and N(d2) are statistical term which takes into account standard deviation,
logarithm (ln) and other relevant factors (It denotes Probability).
N(d1) and N(d2) can be calculated by Using d1 and d2
Calculation of d1 and d2
d1 =
&#-667558875;&#-667558873;[&#-667558894;
��]+ [&#-667558869; +&#-667557938;.��&#-667557938;��&#-667557936;]×&#-667558867;
��× √&#-667558867;
where
S = Current Market Price
X = Exercise Price
r = risk-free interest rate
t = time until option expiration
σ = Standard Deviation of Continuously Compounded annual return
d2 = d1 – σ √&#-667558867;
Or
d2 =
&#-667558875;&#-667558873;[&#-667558894;
��]+ [&#-667558869; − &#-667557938;.��&#-667557938;��&#-667557936;]×&#-667558867;
��× √&#-667558867;
For Put:
Value of a Put Option/ Premium on Put = ��
&#-667558882;&#-667558869;&#-667558867; × [ &#-667557937;−��(&#-667558883;&#-667557936;)]− &#-667558894;×[&#-667557937;−��(&#-667558883;&#-667557937;)]
Where,
S = Current Market Price
X = Exercise Price
Note:
Value or Premium of Put can either be calculated by using PCPT or BSM. However if value of
Call is given or calculated, then in such case PCPT is preferred.
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Concept No. 22: BSM when dividend amount is given in the question
Adjust Spot Price (S) or CMP
[Spot Price – PV of Dividend Income]
Value of a Call Option/ Premium on Call
= [&#-667558894;−���� &#-667558872;&#-667558881; &#-667558909;��&#-667558865;��&#-667558883;&#-667558882;&#-667558873;&#-667558883; ��&#-667558873;&#-667558884;&#-667558872;&#-667558874;&#-667558882;]×��(&#-667558883;&#-667557937;) - ��
&#-667558882;&#-667558869;&#-667558867; × ��(&#-667558883;&#-667557936;)
d1 =
&#-667558875;&#-667558873;[&#-667558894;−���� &#-667558872;&#-667558881; &#-667558909;��&#-667558865;��&#-667558883;&#-667558882;&#-667558873;&#-667558883; ��&#-667558873;&#-667558884;&#-667558872;&#-667558874;&#-667558882;
��]+ [&#-667558869; +&#-667557938;.��&#-667557938;��&#-667557936;]×&#-667558867;
��× √&#-667558867;
d2 = d1 – σ √&#-667558867;
Concept No. 23: High Profit & High Losses under Future & Option
By investing in Future & Options we have huge profits with low initial investments in comparison
to cash markets but at the same time we can also have huge losses.
Concept No. 24: Put-Call Ratio
Put- Call Ratio = Volume of Put Traded
Volume of Call Traded
The ratio of the volume of put options traded to the volume of Call options traded, which is
used as an indicator of investor’s sentiment (bullish or bearish)
The put-call Ratio to determine the market sentiments, with high ratio indicating a bearish
sentiment and a low ratio indicating a bullish sentiment.
Concept No. 25: Option Greek Parameters
Option price depends on 5 factors:
Option Price = f [S, X, t, r, σ], out of these factors X is constant and other causing a change in
the price of option.
We will find out a rate of change of option price with respect to each factor at a time, keeping
others constant.
Delta: It is the degree to which an option price will move given a small change in the underlying
stock price. For example, an option with a delta of 0.5 will move half a rupee for every full rupee
movement in the underlying stock.
The delta is often called the hedge ratio i.e. if you have a portfolio short ‘n’ options (e.g. you
have written n calls) then n multiplied by the delta gives you the number of shares (i.e. units of
the underlying) you would need to create a riskless position - i.e. a portfolio which would be
worth the same whether the stock price rose by a very small amount or fell by a very small
amount.
Gamma: It measures how fast the delta changes for small changes in the underlying stock price
i.e. the delta of the delta. If you are hedging a portfolio using the delta-hedge technique
described under "Delta", then you will want to keep gamma as small as possible, the smaller it
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is the less often you will have to adjust the hedge to maintain a delta neutral position. If gamma
is too large, a small change in stock price could wreck your hedge. Adjusting gamma, however,
can be tricky and is generally done using options.
Vega: Sensitivity of option value to change in volatility. Vega indicates an absolute change in
option value for a one percentage change in volatility.
Rho: The change in option price given a one percentage point change in the risk-free interest
rate. It is sensitivity of option value to change in interest rate. Rho indicates the absolute change
in option value for a one percent change in the interest rate.
Theta: It is a rate change of option value with respect to the passage of time, other things
remaining constant. It is generally negative.
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