11.1 Options and Swaps LECTURE 11

11.2

11.3 Aims and Learning Objectives By the end of this session students should be able to: Understand how the market for options works Compare and contrast futures contracts with option contracts Understand the general principles behind the pricing of options

Introduction An option is a contract giving the holder a right to buy or sell a stated security at a specified price either within a specified period of time or at a specific date Key elements: Strike or exercise price Premium or price Maturity or expiration As with futures, an option contract involves two counterparties: the buyer (purchaser) and seller (writer)

Types of Options Call Options: Gives the holder the right to buy a financial instrument Put Options: Gives the holder the right to sell a financial instrument Can be further classified into: American Options: the option can be exercised at any time before the expiration date European Options : option can only be exercised on the expiration date

11.6 Terminology In the Money - exercise of the option would be profitable Call: market price > exercise price Put: market price < exercise price Out of the Money - exercise of the option would not be profitable Call: market price < exercise price Put: market price > exercise price At the Money - exercise price and price of underlying are equal

11.7 Types of Options Equity Options Index Options Futures Options Foreign Currency Options Interest Rate Options

11.8 Payoff Price of underlying 0 Call Writer Call Holder Payoff Profiles for Calls

11.9 Payoff Profiles for Puts 0 Payoffs Price of underlying Put Writer Put Holder

Combining Options Straddle: purchase both a put and a call on the same underlying, where both options have the same expiration date and exercise price Strip: combine two puts and a call Strap: combining two calls and a put Can also combine options with owning the underlying

11.11 Payoff Profiles for Straddles 0 Payoffs Price of underlying holder of a straddle writer of a straddle

11.12 Payoff Profile for Holding the Underlying and Holding a Put Option 0 Price of underlying Payoff from holding put Payoff from underlying Payoff from put and underlying

11.13 Payoff Profile for Holding the Underlying and Writing a Call Option Payoff Price of underlying 0 Payoff from writing call Payoff from underlying and writing call Payoff from underlying

Comparing Options and Futures Similarities Options are highly geared (leveraged) Few options produce a delivery of the underlying (either “closed out” or left to lapse) - reversing contract Attracts both hedgers and speculators

11.15 Differences Insurance role is similar, but is one sided Cashflow differences Call Option Futures holder writer seller buyer premium Contract price Price at expiration Delivery date price

Pricing Options General Principles of (call) option pricing (premium of an option): (1) Positively related to the cash price of underlying (2) Negatively related to the exercise price (3) Positively related to expiration time (4) Positively related to the volatility of the cash price of the underlying (5) Positively related to the risk-free interest rate

Swaps Swaps involve the exchange of a set of payments Two types: Currency Swaps exchange of currency payments Interest Rate Payments - exchange of interest payments (e.g. convert debt from a fixed rate to a floating rate)

11.18 Example of an Interest Rate Swap Suppose firm A has borrowed money at a floating rate of interest and would like to convert to a fixed rate of interest Possible options available: Issue a fixed interest coupon bond Hedge against the risk by selling a long-term interest rate futures contract Hedge against the risk by writing a call (or buying a put) on interest-rates

11.19 Alternatively, it could swap these liabilities with another firm (say, firm B) who would prefer to pay a floating rate In this case the firms would swap agreements: Firm A would meet Firm B’s fixed interest payments and Firm B would agree to meet Firm A’s floating interest rate payments To overcome possible default risk, swaps are arranged through financial intermediaries Main advantage of swaps over other derivatives is that they can be written for a long period

11.20 Summary In this lecture we have: 1. Described how the market for options and the market for swaps works 2. Compare option contracts with futures contracts 3. Discussed the principles behind the pricing of options