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1 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: 1/50, Lalita park, Laxmi Nagar – Delhi 92 Contact Details: 08860017983, 09654899608 Mail Id: gjainca@gmail.com Web Site: www.sfmclasses.com FB Page: https://www.facebook.com/CaGauravJainSfmClasses CA. Gaurav Jain Strategic Financial Management 2 100% Coverage with PM, SM & RTP CA. Gaurav Jain Strategic Financial Management 3 100% Coverage with PM, SM & RTP CA. Gaurav Jain Strategic Financial Management 4 100% Coverage with PM, SM & RTP CA. Gaurav Jain Strategic Financial Management 5 100% Coverage with PM, SM & RTP CA. Gaurav Jain Strategic Financial Management 6 100% Coverage with PM, SM & RTP CA. Gaurav Jain Strategic Financial Management 7 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 8 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 9 100% Coverage with PM, SM & RTP  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 CA. Gaurav Jain Strategic Financial Management 10 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 11 100% Coverage with PM, SM & RTP  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 CA. Gaurav Jain Strategic Financial Management 12 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 13 100% Coverage with PM, SM & RTP 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. CA. Gaurav Jain Strategic Financial Management 14 100% Coverage with PM, SM & RTP  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. CA. Gaurav Jain Strategic Financial Management 15 100% Coverage with PM, SM & RTP 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; ����&#-667558875;&#-667558866;&#-667558882; &#-667558872;&#-667558881; &#-667558872;&#-667558873;&#-667558882; &#-667558907;&#-667558866;&#-667558867;&#-667558866;&#-667558869;&#-667558882; &#-667558910;&#-667558872;&#-667558873;&#-667558867;&#-667558869;��&#-667558884;&#-667558867; 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 CA. Gaurav Jain Strategic Financial Management 16 100% Coverage with PM, SM & RTP  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 ��&#-667558882;&#-667558867; ��&#-667558874;&#-667558872;&#-667558866;&#-667558873;&#-667558867; &#-667558895;&#-667558882;&#-667558884;&#-667558882;��&#-667558865;&#-667558882;&#-667558883;̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ Rate of return: ��&#-667558882;&#-667558867; ��&#-667558874;&#-667558872;&#-667558866;&#-667558873;&#-667558867; &#-667558895;&#-667558882;&#-667558884;&#-667558882;��&#-667558865;&#-667558882;&#-667558883; &#-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 CA. Gaurav Jain Strategic Financial Management 17 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 18 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 19 100% Coverage with PM, SM & RTP  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. CA. Gaurav Jain Strategic Financial Management 20 100% Coverage with PM, SM & RTP  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, CA. Gaurav Jain Strategic Financial Management 21 100% Coverage with PM, SM & RTP 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. CA. Gaurav Jain Strategic Financial Management 22 100% Coverage with PM, SM & RTP 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. CA. Gaurav Jain Strategic Financial Management 23 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 24 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 25 100% Coverage with PM, SM & RTP = [&#-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 CA. Gaurav Jain Strategic Financial Management 26 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 27 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 28 100% Coverage with PM, SM & RTP 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) CA. Gaurav Jain Strategic Financial Management 29 100% Coverage with PM, SM & RTP 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. CA. Gaurav Jain Strategic Financial Management 30 100% Coverage with PM, SM & RTP 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 CA. Gaurav Jain Strategic Financial Management 31 100% Coverage with PM, SM & RTP 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. CA. Gaurav Jain Strategic Financial Management 32 100% Coverage with PM, SM & RTP




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