- 1. “Options” Derivatives Course: “Financial Derivatives
- 2. Outline 1. Background 2. Definition 3. Option and Future Dissimilarities 4. Option and Future Similarities 5. Basic Terms of Option 6. Hedging Risk bidirectionally 7. Types of Option “Outline”----Options Derivatives
- 3. 8. Exercising Styles of Option 9. Positions in Option 10. “Bearish-to-Neutral-to-Bullish” views about the Market movement 11. Moneyness of Option 12. Option Payoffs vs. Option Profit 13. Option Profit and Breakeven 14. Graph Of Call and Put Option 15. Kinship of Option 16. Pricing of Option “Outline”----Options Derivatives
- 4. Background As the Futures Contracts are useful in Hedging risks related to the Price movements of the Underlying shares, they hedge the Risk only in one direction and one can still suffer a large loss in the other direction. So Options were introduced that consists of mechanisms that help eliminate the risk on an underlying asset much more effectively.
- 5. What is an option? (Definition) An Option is a financial Instrument that provides the holder with the right without obligation to buy or sell a specified quantity of an underlying asset at a fixed price (called a strike price or an exercise price) at or before the expiration date of the option. Since it is a right and not an obligation, the holder can choose not to exercise the right and allow the option to expire.
- 6. Options Versus Futures The major difference between options and Futures arise from the phrase “without Obligation” i.e., the holder of an option need not to exercise his right if the price movement of the underlying asset is adverse, the holder of a future contract has to honor the contract even if it means incurring a loss.
- 7. Due to “without obligation” feature of Option Derivatives, the price (which is known as Premium) of Option is much higher than the price of a comparable Future Contract as nothing in the world is free. Options Versus Futures
- 8. Option and Future Similarities Like Futures Contract, Options Contracts too are derived from an underlying asset, which could be a Financial security (shares, indices, bonds/debentures, T.Bills, etc.), a commodity or index. Like Futures, Options are traded in an active secondary market
- 9. Basics Concepts/Terms Of Options Options are a separate instruments from the Stocks Options are created on an “underlying asset” If there is no underlying asset, there is no option There must be price uncertainty (price volatility) Options must have an “expiry date” (due date) Option Exercise price is called “strike price”
- 10. Basics Concepts/Terms (Buyers and Writers of Option) For every option there is both a buyer and a writer Seller is called “Option writer” Buyer is called “Option Holder” The buyer pays the writer for the ability to choose when to exercise, the writer must abide by buyer’s choice Buyer puts up no margin while writer must post margin
- 11. Options vest the RIGHT(without obligation) only upon the BUYER of the CALL or PUT OPTION and not upon the Writer/Seller of the Option. If the buyers of the Option decide to exercise their right, the writers are obliged to honor their commitments. Basics Concepts/Terms (Buyers and Writers of Option)
- 12. Terms of Options Contract T = Exercise date X or K = Exercise price OR Strike Price C = Option Premium is the price paid by the option holder to buy the option Underlying Asset such as shares, indices, bonds, debentures, T-Bills, etc., ST = Market Price of Underlying Asset
- 13. Options –Hedging of Risk in Two Directions Options provide investors with the opportunity to insure the risk arising from Price Fluctuations “How can one insure oneself against the fall in price and yet avail the benefit of a price rise?”
- 14. Assume that one has 4000 shares priced at Rs. 240 each to start with. One can buy an option that gives the right (without obligation) to sell 4000 shares at Rs. 250 each (called exercise price or strike price) three months later. Naturally one pays a price for this option. Suppose the option to sell 4000 shares at Rs. 250 each, three months from now costs Rs. 16000. This is also known as Option Premium. Options –Hedging of Risk in Two Directions
- 15. If Price Rises If three months later the market price of the share is for example Rs. 260, one may decide not to exercise the option as the shares can now be sold in the market at Rs. 260 each, for a total cost of Rs. 10,40,000. Even after deducting Rs. 16,000 towards the option price there is still a gain of Rs. 24000. Options –Hedging of Risk in Two Directions
- 16. If Price Falls If on the other hand, three months later the price falls to Rs. 230, one can exercise the Option to sell the shares at Rs. 250 each , thereby avoiding the possible loss of Rs. 80,000 which one would have suffered if one had not purchased the Option . Thus for a premium of Rs. 16,000 one has effectively insured oneself against all possible losses arising during the three months Options –Hedging of Risk in Two Directions
- 17. Call Option (a right to buy) Put Option (a right to sell) Two Basic Kinds of Options
- 18. A Call Option confers the Right to BUY the underlying asset, at a specified price on or before a certain date in the future A Put Option confers the Right to SELL the underlying asset, at a specified price on or before a certain date in the future. Two Basic Kinds of Options
- 19. Example of Call Option One buy 2000 shares at Rs. 150 (Exercise Price or Strike Price ) at an option premium or call premium e.g. Rs. 4000. If the price of the share three months later rises to Rs. 160, one can exercise the option to buy the shares at Rs. 150. Thus there is a gain of Rs. 16,000 ( Rs. 20,000 profits-Rs. 4000 of premium paid).
- 20. If on the other hand, the price falls to e.g., 130, one would not exercise the option and invest at the lower prevailing price, thus gaining Rs.36000 (Rs. 40,000 saved on the lower price – Premium paid of Rs. 4000). Thus one would have covered ones risk in either direction Example of Call Option
- 21. Option’s Exercise Styles (American Option Vs. European) If the right can be exercised anytime within a specified period then the Option is known as an American Option. If the right can be exercised only on a specific date then the Option is known as an European Option.
- 22. By purchasing the Call Option, one takes the Long Call Position and is called the Long Call Holder, Similarly the Counter-party who sold these Call Options has the Short Call position and is the Call Writer Since long and short positions of an option are opposite counter-parts to each other, the gains of a long position holder are the losses of the short position holder and vice versa Positions in Options
- 23. Positions in Options Four Possible Positions can be taken in Option Derivatives; 1. Long Call Position taken by Call Holder/Buyer 2. Short Call Position taken by Call Writer/Seller 3. Long Put Position taken by Put Holder/Buyer 4. Short Put Position taken by Put Writer/Seller
- 24. Views about the Market movements It is important to understand, “Why anyone would wish to buy or sell either Put or Call Option?”
- 25. Buying or Selling of Put and Call Options indicates the buyer or seller’s View regarding the future market price movement of the underlying asset. At any given point in time there could be Bearish-to-Neutral-to-Bullish views about the Market movement Views about the Market Movement
- 26. The level of confidence in ones view of the market movement determines the position one takes. Whatever may be one view, in order for the trade to materialize there has to be somebody who has an equally confident but opposite view of the market Views about the Market Movement
- 27. Buying a Call/Long Call position indicates that you are BULLISH about the market while the counter party (short call position) has Bearish view about the market. Buying a Put/Long Put position indicates that you are BEARISH view about the market Views about the Market Movement
- 28. FOUR OPTIONS • Sell a Put option • Outlook bullish/ Neutral • Opposite of short calls / long puts • Sell a Call option • Outlook Bearish or Neutral • Opposite of long calls/ short puts • Buy a Put option • Outlook Bearish • Opposite of long calls and short Puts • Buy a call option • Outlook bullish • Opposite of short calls and long put LONG CALLS LONG PUTS SHORT PUTS SHORT CALLS
- 29. Moneyness of Option An important aspect related to the Options is the relationship between the Spot price of Underlying asset and the Exercise Price of Option. Moneyness is the relative position of the current price (or future price) of an underlying asset (e.g., a stock) with respect to the strike price of a derivative So there have three conditions, At-the-money option (ATM) In-the-money option (ITM) Out-of-the-money option (OTM)
- 30. At The Money (ATM): An Option is an ATM Option when strike price is same as current spot price [X = ST], so the decision to exercise becomes irrelevant. In The Money (ITM): when two prices are such that it is profitable for the Option holder to exercise the option. Out of The Money (OTM): when it is better for the holder not to exercise the option. Moneyness of Option
- 31. Call Option Put Option ATM X = ST X = ST ITM X < ST X > ST OTM X > ST X < ST Call and Put Moneyness Terms
- 32. 15-32 Option “Moneyness” Summarizing In-the- Money Out-of-the- Money Call Option S > K S ≤ K Put Option S < K S ≥ K
- 33. Call Option Moneyness Terms At The Money (ATM): when strike price is same as current spot price [X = ST] and payoff from exercising is zero In The Money (ITM): A Call Option will be ITM when strike price is below the current spot price [X < ST] and the payoff from exercising is positive i.e., (St–X) > 0 Out of The Money (OTM): A Call Option will be OTM when the strike price is above the current spot price [X > ST] and the payoff from exercising is zero i.e., (St–X) < 0 so no reason to exercise
- 35. 15-35 Option Payoffs versus Option Profits Option investment strategies involve initial and terminal cash flows. Initial cash flow:- option price (often called the option premium). Terminal cash flow:- the value of an option at expiration (often called the option payoff ). The terminal cash flow can be realized by the option holder by exercising the option. Option Profits = Terminal cash flow − Initial cash flow OR Option Profits = Option Payoff− Option Premium
- 36. Long Call Option Profit = Long Call Option Pay Off (in the Money) – Option Premium = (St–X) – Option Premium Long Put Option Profit = Long Put Option Pay Off (in the Money) – Option Premium = (X–St) – Option Premium Option Payoffs versus Option Profits
- 37. Since long and short positions of an option are opposite counter-parts to each other, the gains of a long position holder are the losses of the short position holder and vice versa Option Payoffs versus Option Profits
- 38. Let us assume that one buys a European Call Option maturing 30 days from today on a certain stock. Assume that strike price is Rs. 125 and the Call Premium is Rs. 10. This is also the Premium Income for the Call Writer/ Short Call Holder. On 30th day, if the underlying share price is for example Rs.140, what are the payoffs for a Long and Short Call? Option Payoffs versus Option Profits An Example of Call Option
- 39. Solution T = Exercise date = 30th X or K = Exercise price OR Strike Price = Rs. 125 C = Call Premium = Rs. 10 ST = S30 = Market Price at 30th day = Rs. 140 Option Payoffs versus Option Profits An Example of Call Option
- 40. Call Option Profits = Call Payoff− Option Premium Call Option Profit = (St–X) – Option Premium Call Option Profit = (140–125) – 10 Call Option Profit = (15) – 10 Call Option Profit = Rs.5 (Note:- If Rs.5 is Long Call Option Profit, then at the same time Rs. 5 is Short Call Option Loss) Option Payoffs versus Option Profits An Example of Call Option
- 41. One must remember that actual benefit on the contract only occurs when the underlying share price moves beyond the Breakeven Level Call Option Breakeven = (Strike + Premium) Call Option Profit = St - Call Option Breakeven Put Option Breakeven = Strike – Premium Put Option Profit = Put Option Breakeven – St “Option Profits and Breakeven”
- 42. Call Option Profit occurs if ST > Call Option Breakeven S30 > (Strike + Premium) 140 > (125 + 10) 140 > 135 As the above condition is fulfilled so Call Option is at Profit Call Option Profit = ST - Call Option Breakeven = 140 – 135 = Rs. 5 “Option Profits and Breakeven” An Example of Call Option
- 43. An Example of Call Option
- 44. Graph of Call Option
- 45. An Example of Put Option
- 46. Graph of Put Option
- 47. Summary of Call vs Put Call Options Right to buy Bullish position Breakeven = Strike + Premium Stock must move up for profitable option ITM when stock price > strike price Put Option Right to sell Bearish position Breakeven = Strike – Premium Stock must move down to be profitable ITM when strike price < stock price
- 48. Convertible Debentures & Call Options Kinship Convertible Debentures is simply an Option to purchase a given number of shares in exchange for the Value of Debenture (akin to exercise price) Dissimilarity includes;- Unlike an Option, Convertible Bond has an independent existence of its own and is useful in mobilizing funds in the Primary Market.
- 49. Warrants are frequently used as sweetener by the corporate while selling their public issues. A share Warrant also involves an option of purchasing a given number of Equity shares by paying a predetermined Exercise Price Warrants & Call Options Kinship
- 50. Warrants (continued) The issuer settles up with the holder when a warrant is exercised When call warrants are issued by a corporation on its own stock, exercise will usually lead to new treasury stock being issued
- 51. Employee Stock Options Employee stock options are a form of remuneration issued by a company to its executives They are usually at the money when issued When options are exercised the company issues more stock and sells it to the option holder for the strike price Expensed on the income statement
- 52. “How are Option Premium Priced ?” Option Pricing
- 53. I. Boundary Conditions II. Minimum & Maximum Values III. Lower Bounds IV. The Variables affecting the Option premium (B) Models of Option Premium Option Pricing (A) Principles of Options Pricing:
- 54. 1. Principles of Options Pricing I. Boundary Conditions
- 55. The minimum value of any option is zero. We state this formally as: Co > O, Po > O No option can sell for less than zero, for in that case the writer would have to pay the buyer. Now consider the maximum value of an option. It differs somewhat depending on whether the option is a call or a put and whether it is European or American. The maximum value of a call is the current value of the underlying: Co < So A call is a means of buying the underlying. It would not make sense to pay more for the right to buy the underlying than the value of the underlying itself. II. Minimum & Maximum Values
- 56. For a put, it makes a difference whether the put is European or American. One way to see the maximum value for puts is to consider the best possible outcome for the put holder. The best outcome is that the underlying goes to a value of zero. Then the put holder could sell a worthless asset for X. For an American put, the holder could sell it immediately and capture a value of X. The maximum value of an American put is the exercise price, Po < X Cont…
- 57. Cont…
- 58. Fortunately, we can tighten the range up a little on the low side: We can establish a lower bound on the option price. For American options, which are exercisable immediately, we can state that the lower bound of an American option price is its current intrinsic value: III. Lower Bounds
- 59. IV-“Variables affecting the Option Premium” Time to Expiry Volatility of Underlying Asset Price Current short term interest rate Dividends to be paid in the underlying share
- 60. Variables affecting the Option Premium Time to Expiry: Option prices are affected by the time to expiration of the option lesser the time to expiry ,lesser the time value of an option and lesser the price of the option and vice versa A longer term option has more time for the underlying to make a favorable move Volatility of Underlying Asset Price High beta stocks are more volatile and so they are highly priced and vice versa
- 61. Variables affecting the Option Premium Current short term interest rate Short term interest rate also affects the Option Premium because premium paid has an opportunity cost in terms of time value. In other words if one did not buy an option, one could have earned some interest on the premium amount by investing it in a risk-free opportunity. So higher the rate of interest, higher is the opportunity loss of buying an option and
- 62. Variables affecting the Option Premium Dividends to be paid in the underlying share If the underlying asset is likely to pay out dividends during the period of option, this will also affect the premium. This is because when a company declares a dividend its market price falls ex-dividend, thus impacting the underlying share price.
- 63. Dividends to be paid in the underlying share When market price falls, it reduces the benefit to call holder while increasing the benefit to a put holder To compensate for this loss or gain, the call option premium reduces, while the put option premium increases Variables affecting the Option Premium
- 64. “Models of Option Premium” There are two different models for valuing the two kinds of Options: 1) Black-Scholes Option Pricing formula for pricing the European Options 2) Binomial Tree Model (also called Lattice Approach) for pricing the American Options
- 65. The Black-Scholes-Merton Formula Black-Scholes approach forms the core of much of Option pricing. This formula was initially developed by Fisher Black and Myron Scholes, Robert Merton contributed significantly to its later development. What the model does is to price a European call on non-dividend paying stock.
- 66. Assumptions of the Model 1) The stock prices are assumed to follow a random walk, just as gas particles in a closed chamber do. This means that the proportional change in stock prices in a brief period of time follow a normal distribution. This is the same as saying “Underlying Stock Prices follow a log- normal probability distribution” For example, if a stock moves from 100 to 110, the return is 10 percent but the log return is ln(l.lO) = 0.0953 or 9.53 percent.
- 67. Assumptions of the Model 2) The volatility (standard deviation) of stock price is denoted by σ 3) Securities may be short sold with access to full proceeds without any transaction cost 4) The stock pays no dividend during the life of option 5) The risk free rate of interest r is constant and remains the same for all maturities 6) The market is efficient and hence arbitrage opportunities are virtually absent
- 68. The Black-Scholes-Merton formulae for the prices of call and put options are: d2 = dl - σ√T Model
- 69. Where, So is the price of the underlying, X is the exercise price, rC is the continuously compounded risk-free rate, T is the time to expiration. σ is the standard deviation of the log return on the asset and it depicts the volatility of stock The Black-Scholes-Merton Formula
- 70. e=2.7182 N(dl) and N(d2) represent normal probabilities based on the values of dl and d2. Normal probability table is used after computing the values for dl and d2 from formula The Black-Scholes-Merton Formula
- 71. Consider the following example. The underlying price is 52.75 and has a volatility of 0.35. The continuously compounded risk-free rate is 4.88 percent. The option expires in nine months; therefore, T = 9/12 = 0.75. The exercise price is 50. First we calculate the values of dl and d2: Example
- 73. The Binomial Model The word "binomial“ refers to the fact that there are only two outcomes. In other words, we let the underlying price move to only one of two possible new prices. We let S be the current underlying price. One period later, it can move up to S+ or down to S-. We let X be the exercise price of the option and r be the one period risk-free
- 74. The Model
- 75. So that u and d represent 1 plus the rate of return if the underlying goes up and down, respectively. Thus, S+ = Su and S- = Sd.
- 76. Example If shares of a company are currently quoting at Rs. 130 each. Let us assume that the prices of theshare three months from now is expected to be either Rs. 143.67 or Rs. 117.63 per share. If exercise price is Rs. 140, three months to expiration, Risk free rate is 6%, σ= 0.20, What would be the Price of European call option?
- 77. uS=143.67 C3 = 3.67 dS = 117.63 C3 = 0 T = 0 u = 1.1052 d = 0.9048 p = 0.5505 P=55.05% (1-p)= 44.95% T = 3 months
- 78. The expected value of call option at the end of three months is Rs. 2.023 (=0.5505 * 3.67 + 0.4495* 0)
- 79. THANK YOU