Investment Banking Introduction to Derivatives

1. Investment BankingIntroduction to Derivatives

2. Contents Derivatives Derivatives Pricing Derivatives Market in Pakistan

3. Derivatives Some say the world will end in fire, Some say in ice Robert Frost (1874–1963) This is what the Derivative world is?

4. Financial Derivatives • Financial instrument whose price is dependent upon or derived from the value of underlying assets • The underlying not necessarily has to be an asset. It could be any other random/uncertain event like temperature/weather etc. • The most common underlying assets includes: • Stock • Bonds • Commodities • Currencies • Interest rates

5. Financial Derivatives Derivatives are mainly used to mitigate future risks, however they do not add value since hedging is a zero sum game and secondly investors mostly use them on do it yourself alternatives basis. • Derivatives markets can be traced back to middle ages. They were developed to meet the needs of farmers and merchants. First future exchange was established in Japan in 16th century. The Chicago Board of Trade was established in 1848.The international Monetary market was established in 1972 for future trading in foreign currencies • Insurance is a kind of mitigating risk but it has its limitations. To avoid zero NPV it tries to cover administrative costs, adverse selection, and moral hazard risks in its premium. Apart from this simple format, the derivatives on the other hand have lot of varieties, i.e. from simple to highly exotics, creating a world of their own. Size of its activities are manifold as compared to total world GDP

6. International Markets and their risks • In global world, Foreign exchange markets of each country play an important role. The market embodies a spot market with a forward market. The forward market represents the selling and buying committed or due on some future dates. To understand the dynamics of foreign exchange market in Pakistan or in any country we have to understand the difference and relationship between exchange rates and interest rates. This gives birth to four questions i.e. (1) why the dollar rate of interest is different from say PKR (2) Why the forward rate of exchange (F-PKR/$) is different from the spot rate (S-PKR $) (3) What determines next years expected spot rate of exchange between $ and PKR (E (S-PKR/$)) (4) What is the relationship between inflation rate in the US and the inflation rate in Pakistan. Suppose that individuals are not worried about risk or cost to international trade than (a) difference in interest rates =1 + r PKR/ 1+r $ must be equal to expected difference in inflation rates = E (1 + Inf Pak)/ E ( 1 + inf US). Further difference between forward and spot rates = F-PKR per $/S-PKR per $ must be equal to Expected change in spot rate = E (S-PKR per S)/ (S-PKR per $) Prepared by: Farrukh Aleem Mirza

7. International Markets and their Risks • Interest rate parity theory says that the difference in interest rate must be equal to the difference between the forward and spot exchange rates i.e. 1 +r PKR/ 1 + r$ = difference between the forward and spot exchange rates. In case of Pakistan it would give the following results = 1.12/1.01 X 85 = forward rate of PKR/$ after one year = 94.25 • Expectation theory of exchange rates tells us that the difference in % between the forward rate and today's spot rate is equal to the expected change in the spot rate = difference between forward and spot rates = F-PKR per $ / S-PKR per $ = expected change in spot rate E (S PKR per $) / (SPKR per $). • Purchasing power parity implies that difference in the rates of inflation will be offset by a change in the exchange rate =Expected difference in inflation rate = E (1 + Inf-PKR)/ E (1 + Inf-US) = Expected change in spot rate = E (S-PKR/$) / S -PKR/$. This would give a result of Rs 90.77/US$ considering inflation in Pakistan as 10. in US as 3 and spot rate of PKR/US$ as Rs 85. • However life is not very simple and apart from these exercises inflows and outflows mostly dictate the spot and forward rates that can alter. Prepared by: Farrukh Aleem Mirza

8. Derivatives Markets • Exchange Traded Contracts • Over The Counter Market

9. Market Participants Hedger Hedgers face risk associated with the price of an asset. They use futures or options markets to reduce or eliminate this risk Speculators Speculators wish to bet on future movements in the price of an asset. Derivatives can give them an extra leverage to enhance their returns Arbitrageurs Arbitragers work at making profits by taking advantage of discrepancy between prices of the same product across different markets

10. Types of Financial Derivative Can be plain vanilla or exotic • Forward • Futures • Options • Forward Rate Agreement (FRAs) • Swaps

11. Forwards • Forward contract is a binding contract which fixes now the buying/selling rate of the underlying asset to be bought/sold at some time in future. • Long Forward • Binding to buy the asset in future at the predetermined rate. • Short Forward • Binding to sell the asset in future at the predetermined rate.

12. Basic Features • Long/Short • Pay Off • Binding Contract • OTC Transaction/Contract • Risk/Uncertainty Elimination • Zero Cost Product • Credit Risk

13. Pay Off Pay Off = ST – K (for the long forward) Pay Off = K – ST (for the short forward) T = Time to expiry of the contract ST = Spot Price of the underlying asset at time T K = Strike Price or the price at which the asset will be bought/sold

14. Forward Contract Payoff K

15. Futures • A futures contract is a standardized contract, traded on a futures exchange, to buy or sell a certain underlying instrument at a certain date in the future, at a specified price • Specification of a standard contract: Gold • Commodity Name • Exchange Name • Size of Contract : 100 troy ounce • Delivery month: Feb/April/June/Aug/Oct/Dec

16. Forwards Traded in dispersed interbank market 24 hr a day. Lacks price transparency Transactions are customized and flexible to meet customers preferences. Futures Traded in centralized exchanges during specified trading hours. Exhibits price transparency. Transactions are highly standardized to promote trading and liquidity. DISTINCTIONS BETWEEN FUTURES & FORWARDS

17. Forwards Counter party risk is variable No cash flows take place until the final maturity of the contract. Futures Being one of the two parties, the clearing house standardizes the counterparty risk of all contracts. On a daily basis, cash may flow in or out of the margin account, which is marked to market. DISTINCTIONS BETWEEN FUTURES & FORWARDS

18. Margin Requirements/Daily Settlement • Initial Margin An Initial margin is the deposit required to maintain either a short or long position in a futures contract. • Maintenance Margin Maintenance margin is the amount of initial margin that must be maintained for that position before a margin call is generated.

19. Margin Call If the amount actually falls below the maintenance margin, a margin call is given to the investor to replenish the account to the initial margin level, otherwise the account is closed. • Variation Margin The additional funds deposited to make up to the initial margin.

20. Futures’ Price Close to Expiry In the delivery month the Futures’ Price is almost equal to the prevailing Spot Price. Or we can say that with the passage of time the Futures’ Price gradually approaches the prevailing Spot Price. Because of No Arbitrage Principle

21. No Arbitrage Principle • Assume Notations • T = Delivery/Expiry time of the futures’ contract • F0 = Futures Price now to be delivered at time T • ST = Spot Price of the underlying at delivery time T • If F0 > ST there is an arbitrage opportunity • Short the futures contract, buy the asset and make the delivery • Pay Off = F0 - ST > 0

22. If F0 < ST Parties who want to buy the asset, would immediately go long the futures’ contract and wait for the delivery. Because of increased demand for the futures, the futures’ price would go up to the actual market spot price of the asset to remove the anomaly.

23. Hedging Strategies • Short Hedge • When the hedger owns an asset or expects to own an asset in future and wants to sell it. • By shorting an appropriate futures’ contract, the hedger can lock in a price now to sell the asset at some time in future.

24. HEDGING WITH FUTURES • Suppose • Commitment to sell 1000 barrels after 3 months at the then prevailing spot price say ST • Futures Price for delivery after 3 months = 18.75 • Strategy • Go short a 6 months future contract to lock in a price now • At maturity go long a futures to close the position

25. HEDGING WITH FUTURES • Long Hedge • When a company knows it will have to purchase a certain asset in the future and wants to lock in a price now. • By going long an appropriate futures contract the hedger can lock in a price he will be paying after time T to buy the asset.

26. HEDGING WITH FUTURES • Suppose • Commitment to buy 1000 barrels after some time T at the then prevailing spot price say ST • Futures Price = 18.75 • Strategy • Go long a 6 months future contract to lock in a price now • At maturity go short a futures contract to close the position

27. BARINGS BANK A bank with a history of 233 years collapsed because of imprudent use of derivatives. One of the traders Nick Leeson, who was basically responsible to make arbitrage profits on Stock Index Futures on Nikkei 225 on the Singapore and Osaka exchanges. Instead of looking for arbitrage opportunities, the trader started making bets on the index and went long the futures. Unfortunately the market fell by more than 15% in the 1995 leading to margin calls on his positions. Because of his influence on the back office, he was able to hide the actual position and sold options to make for the margin calls. But his view on the market proved to be wrong and losses mounted to an unmanageable amount.

28. METALLGESELLSCHAFT A US Subsidiary of a German Company used hedging strategies, which went against them, resulting in heavy cash outflows. Being an Oil Refinery and Marketing company, they sold forward contracts on oil maturing up to 10 years. To hedge their position, they went long the available futures contracts with maturities up to 1 year. They planned to use “Stack & Roll” strategy to cover their short forwards contracts. But due to decreasing oil prices they had margin calls on their futures contracts. They were unable to meet those heavy cash outflows. Ultimately the US team of the company were kicked out and a new team from Germany came to USA and liquidated the contracts making heavy losses.

29. SOCIÉTÉ GÉNÉRALE • On January 24, 2008, the bank announced that a single futures trader at the bank had fraudulently caused a loss of4.9 billion Euros to the bank, the largest such loss in history. • Jerome Kerviel, went far beyond his role -- taking "massive fraudulent directional positions" in various futures contracts. • He got caught when markets dropped, exposing him in contracts where he had bet on a rise. • Due to the loss, credit rating agencies reduced the bank's long term debt ratings: from AA to AA- by Fitch; and from Aa1/B to Aa2/B- by Moody's. • The alleged fraud was much larger than the transactions by Nick Leeson that brought down Barings Bank.

30. Options • An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specific price on or before a certain date • Unlike a forward/future, this contract gives the right but not the obligation. So its not a binding contract. • The holder will exercise the option only if it is profitable.

31. Types Of Options On the basis of payoff structures Call option • A call gives the holder the right to buy an asset at a certain price within a specific period of time. Put option • A put gives the holder the right to sell an asset at a certain price within a specific period of time.

32. Strike Price Terminology The type of option and the relationship between the spot price of the underlying asset and the strike price of the option determine whether an option is in-the-money, at-the-money or out-of-the-money. Exercising an in-the-money call or in-the-money put will result in a payoff. Neither a call nor put that is at-the-money will produce a payoff.

33. Pay-Offs

34. Types Of Options On the basis of exercise options American options • Can be exercised at any time between the date of purchase and the expiration date. Mostly American options are exercised at the time of maturity. But when the underlying makes cash payments during the life of option, early exercise can be worthwhile. European options • Can only be exercised at the end of their lives

35. Types Of Options On the basis of versatility Vanilla Option • A normal option with no special or unusual features Exotic Option • A type of option that differs from common American or European options in terms of the underlying asset or the calculation of how or when the investor receives a certain payoff.

36. Types of Exotic options Bermuda OptionA type of option that can only be exercised on predetermined dates, usually every month Compound Option An option for which the underlying is another option. Therefore, there are two strike prices and two exercise dates. These are the four types of compound options:- Call on a call- Put on a put- Call on a put- Put on a call

37. Asian OptionAn option whose payoff depends on the average price of the underlying asset over a certain period of time as opposed to at maturity. Also known as an average option. Digital Option An option whose payout is fixed after the underlying stock exceeds the predetermined threshold or strike price. Also referred to as "binary" or "all-or-nothing option."

38. Shout Option An exotic option that allows the holder to lock in a defined profit while maintaining the right to continue participating in gains without a loss of locked-in monies. Barrier Option A type of option whose payoff depends on whether or not the underlying asset has reached or exceeded a predetermined price.

39. Chooser Option An option where the investor has the opportunity to choose whether the option is a put or call at a certain point in time during the life of the option Quantity-Adjusting Option (Quanto Option) A cash-settled, cross-currency derivative in which the underlying asset is denominated in a currency other than the currency in which the option is settled. Quantos are settled at a fixed rate of exchange, providing investors with shelter from exchange-rate risk. 

40. Trading Strategies Involving Options

41. Bull Spreads Buy a Call Option with strike X 1, and sell a call option with strike X2 (whereas X2>X1). Date of maturity for both the options is same Pay Off • If ST ≤ X1 : Zero • If X1 < ST ≤ X2 : ST – X1 • If ST > X2 : ST – X1 – (ST – X2) = X2 – X1

42. Bull Spread

43. Bear Spreads • Buy a Put Option at strike price X2 and sell a put option at a lower strike price of X1. Both options have same expiry Pay Off • If ST ≥ X2 : Zero • If X1 ≤ ST < X2 : X2 - ST • If ST < X1 : X2 - ST – ( X1 - ST)

44. Bear Spread

45. Butterfly Spreads • Buy a call option at strike price X1 , and buy another call option at a higher strike price of X2 . Sell 2 call options at strike price X3 , exactly halfway between X1 and X2 Pay Off • If ST ≤ X1 : Zero • If X1 < ST ≤ X3: ST – X1 • If X3 < ST ≤ X2: ST – X1 – 2(ST – X3) = X2 - ST • If ST > X2: Zero

46. Butterfly Spread

47. Straddle • Buy a call option and a put option both at strike price X Pay Off • If ST > X : ST – X • If ST < X : X- ST • If ST = X : Zero

48. Straddle

49. Strangle • Buy a Put Option with strike price K1= and buy a Call Option at strike price K2 > K1 Pay Off • If ST > K2 : ST – K2 • If ST < K1 : K1 - ST • If K1 ≤ ST ≤ K2 : Zero

50. Strangle