DERIVATIVES AN INTRODUCTION PETER BAYLISS

CONTENTS Definitions History and development Forward contracts Futures Swaps Options Controversy Summary

HISTORY AND DEVELOPMENT early historical evidence for forwards and options. futures contracts were developed in the 19th Century, though financial futures were only introduced in 1973  swaps were first traded as recently as 1981  primary purpose – (initially) management of risk - (now) … speculation

OVER-THE-COUNTER MARKETS VS EXCHANGE TRADED OTC – bilateral agreements (bespoke) Exchange traded – mediated and standardised 4

Forward contracts - a purchase/sale agreement where the implementation or settlement of the contract is deferred to some mutually agreed date in the future  Futures contracts – per forwards, but exchange traded. Swaps - two parties to a swap agree to exchange a set of predetermined cash flows based on a predetermined formula.  Options - give the holder (or buyer) of the option the right but not the obligation to buy or sell the underlier at a specific price at or before a specific date.  DEFINITIONS

A forward contract is a very simple commercial agreement A forward contract is a very simple commercial agreement. It involves two parties, a buyer and a seller, agreeing a price at which a quantity of a product, commodity or other item will be exchanged for a given amount of money on an agreed date. OTC. Very flexible and can provide perfect hedge, but… Substantial counter party risk, so varieties have evolved to reduce this in some instances [forward rate agreements, for example, which are based on the interest rates applicable in a future period, but engineered to have reduced settlement risk] FORWARD CONTRACTS

FUTURES Same structure as a forward, but … - exchange traded - standardised terms and dates - mediated - margin required - no settlement risk - enable price discovery SAFEs (synthetic agreement for forward exchange) - other notional principal contracts but enabling hedging of interest rates and or currency movements

Swaps have the same symmetric or linear payoff profile as forwards and futures. However, they differ from forwards and futures in that there is a multiplicity of cash flows between the two counterparties over the life of the swap. Very adaptable. Any set of cash flows which can be contractually predetermined can form one side of a swap. Swaps permit market participants to modify sets of connected cash flows in attractive ways and thus have become an important tool for asset–liability management. SWAPS

Options - give the holder (or buyer) of the option the right but not the obligation to buy or sell the underlier at a specific price at or before a specific date Asymmetrical payoff (insurance) Writer / Holder Call Put American / European OPTIONS

BSOPM, FOR A SIMPLE EUROPEAN CALL OPTION 10

(SOME OF) THE PROBLEMS WITH PRICING Frictionless markets – no transaction costs, no tax and perfect liquidity. Continuous trading – trades can be performed at any time and in any amount. Unlimited short selling and borrowing are possible and the proceeds are immediately available. There are no arbitrage opportunities. Specifying the form of the probability distribution for the variable at future times – most frequently normal or lognormal distributions are used. Specifying the evolution in time of the distribution – including drift, mean reversion and volatility term structure. 

LOBO LOANS LOBO stands for Lender Option Borrower Option. A LOBO loan is typically a very long-term loan – for example 40 to 70 years. The interest rate is initially fixed, but the lender has the “option” to propose or impose, on pre-determined future dates, such as every 5 years, a new fixed rate. The borrower has the ”option” to either accept the new rate or repay the entire loan.