Futures and Options PDF

Futures and Options Options: 1) All derivatives whether futures or options, will have an expiration date After that the contract is Null and Void Options contracts give the buyer a right wrt the underlying asset but impose a contingent obligation on the sellers That is, if the buyer decides to exe...

Futures and Options Options: 1) All derivatives whether futures or options, will have an expiration date After that the contract is Null and Void Options contracts give the buyer a right wrt the underlying asset but impose a contingent obligation on the sellers That is, if the buyer decides to exercise the right, the seller must carry out what is expected from it Options contracts are called Contingent Contracts That is, the transaction may or may not happen Futures contracts are called Commitment contracts Because the transaction must happen When a right is given wrt to an underlying asset There are two possibilities You have bought the right to buy the underlying asset Call Options or you may have bought the right to sell the underlying asset Put Options If the expiration date is the only point in time at which the option can be exercised we call it a European option If the option can be exercised any time at or before expiration we call it an American option So American options give greater flexibility To buy an option the buyer must pay a price to the seller This is called Option Price aka Option Premium What is the logic: If the option is exercised the buyer will get a profit or positive cash flow Else he will get nothing If the option is exercised the seller will get a loss or a negative cash flow Else he will get nothing So buyers may subsequently get a positive or a NIL cash flow Sellers may subsequently get a negative or a NIL cash flow Options are like Insurance products You insure your laptop for 40000 If the laptop falls and breaks you get 40000 Otherwise you get nothing In any case the premium paid by you at the beginning is non-refundable Strike Price of Exercise Price It is the price payable per unit of the underlying asset if the buyer exercises a call It is the price receivable per unit of the underlying asset if the buyer exercises a put An option may or may not be exercised So the strike price enters the picture only if the option is exercised The non-refundable premium is paid upfront Ajay buy a call option from Vijay He has the right to buy 100 shares at 70 per share 7000 The cost of the option is 80 paise per share 80 Assume these are European options expiring after 3 months Case-A: Three months hence the price of the shares is 85 It will be exercised. If Ajay wants the share he will exrcise and buy at 70 case-B: Three months hence the price of the share is 60 The alternative is tro buy spot at 85 What are the cash flows in each case for Ajay and Vijay? If he does not want the share he will take delivery by paying 70 and immediately sell spott at 85 So cash flow =100*(85-70) = 1500 Case-B: The option will not be exercised If he wants the share he can buy spot at 60 instead of 70 If he does not want the shares he will have to buy at 70 and dump at 60 So loss = 1000 So if denote the terminal asset price by ST, a call will be exercised if ST > X, else it will not be exercised Assume all stock options are for 100 shares Cash Flow if exercised = 100*(ST-X) Else it is zero No buyer of an option can subsequently get a negative cash flow CF = 100*max[0, ST-X} Premium = 100*.8 = 80 If ST > X CF = 100*(ST-X) Profit = 100*(ST-X)-80 if ST > X else CF = 0 Else Profit = -80 So if the option is not exercised the holder loses the premium So the premium is the maximum loss for him Profit = 100*max[0,ST-X] - 100*C If the option is exercise the CF for the seller is -100*(85-70)+80 = -1420 If the option is not exercised profit = 80 For sellers the option premium is the maximum profit he get a lower profit or a loss but not more Ajay buy a put option from Vijay He has the right to sell 100 shares at 70 per share The cost of the option is 80 paise per share Assume these are European options expiring after 3 months Case-A: Three months hence the price of the shares is 85 case-B: Three months hence the price of the share is 60 What are the cash flows in each case for Ajay and Vijay? If the share price is 85, the holder will not exercise the put If he has the shares he would rather sell at 85 in the spot market But if the price is 60 he will exercise If he has the shares he would rather sell at 70 than at 60 in the spot market If he does not have the shares he will buy spot at 60 and then exercise and sell at 70 If the option is not exercised payoff = 0 If the option is exercised payoff = 100*(X-ST) 100*max[0,X-ST] What about the profit Buyers; Holders; Longs are the same Profit = 100*max[0,X-ST] - 100*p They are the people who have bought the right in this case p = 80 paise Sellsr; Writers; Shorts are the same Pi = 100*Max[0,X-ST] - 80 They are the people who have sold the option For the put sellers If the marketr price of the asset is greater than the exercise price then holders of put options will not exercise If they have the asset they would rather sell at the market price If they do not have it then, buying at the market and then exercising will lead to a loss So in this case the put will not be exercised But if the market price is less than X The put will be exercised If the holder does not want to hold the stock he will exercise and sell at 70 rather than sell spot at 60 If he does not have the stock he will buy at 60 in the spot market and then exercise and sell at 70 Call Holders Profit = 100*max[0,ST-X] - 100*c Call writers Profit = -100*max[0,ST-X] + 100*c = 100*min[0, X-ST] + 100*c So options are zero sum games The buyer's profit/loss = sellers' loss/profit All that happens is that wealth is transferred from one party to another Taken together nobody makes money Put Holders Profit = 100*max[0,X-ST] - 100*p Put Writers =100*Min[0,ST-X] + 100*p Forward contracts are always OTC Futures contracts are always exchange traded Options are both OTC as well as exchange traded products It it is OTC: The contract can have any size; any exercise price; and any expiration date if both parties agree But for exchange traded options the exchange will give a limited choice wrt to exercise price and expiration date The contract size is fixed by the exchange In India the contract size varies from one underlying company to another In the US whether it is IBM or 3M or MS it is 100 shares per contract In the US the options expire on the third Friday of the month So assume we are on 1 October 20XX which is a Thursday That month's option will expire on 16 October Now when options are introduced for a given company the company is assigned to a quarterly cycle There are three cycles January, February and March January: January/April/July/October February: February/May/August/November Marchg: March/June/September/December Assume a company XYZ is allotted to the February cycle On a given date you will have contracts for the current month; the next month; and the next two months of the cycle to which the company belongs So on 1 October 20XX: The available months will be: October(current); November (next); February(20XX+1); May(20XX+1) We move to 1 November: November (Current); December(next); February and May next year We move to 1 December: December; January; February and May on 1 January January (current); February (next); may and August0 In India we have the current month the nextr month and the following month 1 october: tata steel: october; November; and December When October expires; November; December and January Ajay bought call options by paying a premium of 80 paise per share The exercise price was 70 Should Ajay exercise if ST > 70 or only if ST > 70.80 Suppose ST = 70.45 Profit if Exercised: -35 If not exercised -80 Better to lose a smaller amount So a call will be exercised if ST > X, it is not necessary that ST > X+c A put will be exercised if ST < X it is not necessary that ST < X-p Sunk costs should not be counted If ST is ST is 70.45 and X is 70 If you exercise you get 45 Rupees for 100 shares Logic says exercise because you are getting a positive cash flow If you factor in the cost of the option then your total cash flow is -35 If you go by this logic you should not exercise But if you don't exercise you lose 80 It is better to lose 35 than 80 So sunk costs distort the decision making process Hence while taking investment decisions, previously incurred expenses should not be factored in Call: if St > X It is in the money Puts out of the money If St = X At the money At the money If St < X Out of the money In the money When will an option be exercises: when it is in the In the money CALL Only ITM calls and puts will be exercised In the Money = Spot > Strike = St > X ATM and OTM calls and puts will not be exercised At the Money = St = X But suppose you are are holding an OTM call, what are your options? Out of the Money = St< X He can hold on hoping it goes in the money or he can sell it somebody who is more optimistic, at the prevailing premium When the call was bought X = 70 and c = 80 paise Todat ST = 60 and the call it OTM, the current premium is 55 paise So since it is OTM it will not be exercised If there are two months left to maturity the holder can hold on hoping it move to an ITM position Else he can sell and get 100*55 = 55 He bought it for 80 So loss = 25 Rupees You are offered an American option with a premium of Rs. 2.50 per share 250 The current stock price is 104 and the exercise price is 100 Curreent stock price is 104; Exercise price of the put is 110 He will first buy by paying 250 Rupees (each contract is for 100 shares) Premium is rs 4 per share and will immediately exercise What will an investor do? He will get 100*(104-100) = 400 He will first pay 400 and buy the put His assured profit is 400-250 = 150 he will immediately exercise and get 100*(110-104) = 600 This is an arbitrage profit So there is an assured profit of 200 because he has not taken any risk To sure out arbitrage p>= Max[0,X-ST] So for American calls c >=max[0,St-X] p >= max[0,110-104] = 6 c>=Max[0,4] So the put should be priced at at least 6 rupees So to rule out arbitrage the premium must be atleast 4 Rupees anything lower like 2.50 is an arbitrage opportunity current stock 10400 excercise price 10000 8500 buy at 70 6000 > Strike = St > X