Créer une présentation
Télécharger la présentation

Download

Download Presentation

EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS Dr Helen Weeds 2013-14, Spring Term

122 Vues
Download Presentation

Télécharger la présentation
## EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETS Dr Helen Weeds 2013-14, Spring Term

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**EC247 FINANCIAL INSTRUMENTS AND CAPITAL MARKETSDr Helen**Weeds2013-14, Spring Term Lecture 7: Futures and options**LEARNING OUTCOMES**• What is a derivative? • Futures and forwards • Explain the nature of forwards and futures • Use of futures in hedging and speculation • Specification of a futures contract • Convergence of futures price to spot price • Margin accounts and marking to market • Options • Explain the nature of financial options • Calls and puts; European and American exercise types • Payoff from call and put options for holder and writer • Option valuation: some simple relationships**What is a derivative?**• General definition of a ‘derivative’ • An asset whose performance is based on (derived from) the value of an underlying asset (the ‘underlying’) • Derivative contracts • give the right (and sometimes the obligation) to buy or sell a quantity of the underlying • or to benefit in another way from a rise or fall in the value of the underlying • The derivative contract is itself an asset, with its own value, and can be purchased or sold • Either on an exchange or ‘over the counter’ (OTC)**Derivatives can be risky…**• Depending on how they are used, derivatives trading can generate enormous losses • In 1994, Proctor & Gamble (!) lost $102m speculating on the movements of future interest rates • In 1995, Barings (Britain’s oldest merchant bank) lost over £800m (and went bankrupt) as a result of trading in derivatives on the Nikkei Index (Japanese share index) by ‘rogue trader’ Nick Leeson • In 1998, Long-Term Capital Management (LTCM) collapsed as a result of its options trading (its bailout was brokered by FRBNY) • In 2008, SociétéGénérale lost €4.9bn due to unauthorised trading by JérômeKerviel, who took out large, unhedged positions in equity indices**FORWARDS AND FUTURES**• Forward contract • An agreement between two parties to undertake an exchange at an agreed future date at a price agreed now • Example • Farmer grows a field of potatoes, to be harvested in 2 months’ time • Crisps producer wants to know how much it will have to pay for potatoes, in order to set its prices and market the product • Market price of potatoes varies over time • Both parties can lock into a price that is agreed now, to reduce uncertainty and limit exposure to unforeseen price shocks • The buyer at the future date is said to take a ‘long’ position • The seller at the future date is said to takea ‘short’ position**Forwards and futures: differences**• Forwards are traded over the counter • Private agreements, not regulated by an exchange • Tailor-made, to suit the requirements of the parties • amounts and delivery dates are flexible • may be written for long-term maturities (e.g. 3 years) • But risk of default by the other party (‘counterparty risk’) • Futures: similar to forwards, but traded on an exchange • The clearing house is the counterparty to the transaction: reduces risk of default • Contract is standardised, and tends to cover shorter maturities only (e.g. up to 1 year) • Contract is easier to trade • Today: focus on exchange-traded derivatives [OTC: next week]**Forwards and futures: development**• Forwards contracts • Holland, late 1500s: fish dealers bought and sold herring before it was caught • Exchange-based trading • England: Royal Exchange in London, 1571 • now the London Metal Exchange (LME) • Japan: Dōjima Rice Exchange, 1710 • USA: Chicago Board of Trade (CBOT), 1848 • now part of the Chicago Mercantile Exchange (CME) • Futures contracts • 1865: CBOT began trading futures contracts (in grain) • These were the first standardised derivatives contracts • Today: most futures exchanges are entirely electronic**Uses of futures**• Hedging • Using a futures contract to offset specific risks • E.g. in April (before planting) a farmer sells a futures contract, committing him to supply a specific quantity of the crop in September (after harvest) at the agreed price • Offsets the risk of a price fall between planting and harvest • Similar considerations for a food processor that buys the futures contract • Speculation • Trading in futures contracts with the intention of profiting from price changes (rather than to hedge specific risks) • E.g. buy a futures contract now, hoping that the price will go up • Speculative trading increases liquidity, which benefits other traders**Hedging with futures**• Spot and forward quotes for the $/£ exchange rate(22 June 2012, $ per £) • ImportCo, based in the US, knows it will have to pay £10m on 22 Sept 2012 for goods imported from a supplier in the UK • It can hedge this risk by buying £10m on a 3-month forward contract at 1.5585 (‘offer’ price), costing it $15,585,000 • ExportCo, based in the US, is exporting goods to the UK; on 22 June 2012 it knows it will receive £30m in 3 months’ time • It can hedge this risk by selling £30m on a 3-month forward contract at 1.5579 (the ‘bid’ price), gaining it $46,737,000**Speculating with futures**• Suppose a speculator thinks £ will strengthen relative to $ over the next 2 months • Two possible strategies • Purchase £250,000 now, in the spot market, at $1.5470 • £250,000 can be deposited in an interest-bearing account • Take a long position in futures contracts maturing 2 months, at $1.5410 • this requires a (refundable) margin payment to be deposited up-front, say $20,000 • Difference is in the size of up-front investment required • futures allow the speculator to obtain leverage , i.e. to take out a large speculative position with a small stake**Specification of a futures contract**• Asset • e.g. a commodity, of specified grade or quality • Contract size • amount of the asset to be delivered • Delivery • delivery month • arrangements for delivery (e.g. location) • Price • how prices are quoted (currency and unit size, e.g. US$ and cents) • exchange usually imposes limits on daily price movements • Position limits • maximum number of contracts an individual can hold • aims to prevent undue influence on the market (‘cornering’)**Convergence to the spot price**• As the delivery period approaches, the futures price converges to the spot price of the underlying asset • Otherwise there would be an arbitrage opportunity • E.g. if futures price > spot price • sell (i.e. short) a futures contract • buy the asset • make delivery, and realise a profit**Margin accounts**• Default risk (counterparty risk) • Each party to a futures contract (or the central exchange) faces a risk that the counterparty might back out of the deal, or be unable to pay • Margin accounts are used to mitigate counterparty risk • Initial margin: investor deposits a certain sum of money per contract in their margin account at the exchange/clearing house • e.g. initial margin of $6,000 per contract for gold futures (for 100oz at a current futures price of $1,650/oz) • Marking to market: at the end of each trading day, the margin account is adjusted to reflect the investors gain/loss • e.g. if futures price falls from $1,650/oz to $1,641/oz, the investor has a loss of $9 x 100 = $900: margin account is reduced by $900 • Maintenance margin: if the balance in the investor’s margin account falls below this level (lower than the initial margin), it must be topped up to the initial level • the investor faces a margin call • the extra funds deposited are called a variation margin**OPTIONS**• What is an option? • The holder has the right, but not the obligation, to buy/sell the underlying asset at a given price, on or before a specified date • The option writer is obliged to carry out the trade if the holder wishes to do so • The holder pays the writer a non-returnable premium for the option • Hence if the option expires unexercised, the writer makes a profit**Call and put options**• Call option • Gives the holder the right to buy the underlying asset, at a given price, at or before a specified date • Put option • Gives the holder the right to sellthe underlying asset, at a given price, at or before a specified date • Features • ‘Underlying’: could be a stock, index, commodity, currency, etc. • ‘Strike price’ • ‘Expiration’ or ‘maturity’ date • Each option comes in two exercise types • ‘European’: may be exercised only at the expiration date itself • ‘American’: may be exercised at any time before or at expiration • American option value value of equivalent European option • NB: an American option on a non-dividend paying stock is never exercised early, and has the same value as the European equivalent**OPTION PAYOFFS**• Consider payoffs from different options and to the two parties • European call option • Option holder’s payoff at expiration/maturity • Holder’s total profit, taking account of option premium paid • Option writer’s profit • European put option • Similar analysis**Example 1: European call option**• An investor buys a call option to purchase 100 shares with the following features • strike price, E = £100 • current stock price, S = £98 • price of an option to buy 1 share, C = £5 • i.e. initial premium paid = £5 x 100 = £500 • At expiration, the stock price is £115 • £115 > £100: the option is exercised • total gain = (£115 £100) x 100 = £1,500 • Taking account of the option premium paid initially • net gain = £1,500 £500 = £1,000**What happens at expiration?**• The call option holder’s decision to exercise or not depends on the stock price at expiration, • ‘In the money’: > E • profitable to exercise the option • payoff (ignoring option premium) = E • ‘Out of the money’: < E • not profitable to exercise the option • payoff (ignoring option premium) = 0**Profit of call option holder**• To calculate the holder’s profit, we need to take account of • initial premium paid for the option, C • payoff at expiration, • Profit**Writer of the call option**• The writer of the contract is obliged to trade if asked to do so • Option is ‘zero sum’: what one side gains, the other loses • Writer’s profit is the mirror image of the holder’s profit, around the horizontal axis • Writer’s loss is potentially unlimited as the stock price goes up**Example 2: European put option**• An investor buys a put option to sell 100 shares with the following features • strike price, E = £70 • current stock price, S = £65 • price of an option to buy 1 share, P = £7 • i.e. initial premium paid = £7 x 100 = £700 • At expiration, the stock price is £55 • £55 < £70: the option is exercised • total gain = (£70 £55) x 100 = £1,500 • Taking account of the option premium paid initially • net gain = £1,500 £700 = £800**What happens at expiration?**• The put option holder’s decision to exercise or not depends on the stock price at expiration, • ‘Out of the money’: > E • not profitable to exercise the option • payoff (ignoring option premium) = 0 • ‘In the money’: < E • profitable to exercise the option • payoff (ignoring option premium) = E**Profit of put option holder**• To calculate the holder’s profit, we need to take account of • initial premium paid for the option, P • payoff at expiration, • Profit**Writer of the put option**• The writer of the contract is obliged to trade if asked to do so • As before, writer’s profit is the mirror image of the holder’s profit, around the horizontal axis • Writer’s maximum possible loss is P – E**OPTION VALUATION**• What is the value of an option before it is exercised? • Sophisticated answer: the Black-Scholes model [Robert Merton & Myron Scholes: Nobel prize 1997] • Underlying asset value S follows a random walk • Values an option over Sby constructing a (fully) hedged portfolio, which must then earn the risk-free interest rate • Solution for a European call/put: the Black-Scholes formula • ‘No arbitrage’ principle • Two assets (or portfolios of assets) which have the same payoffs in all possible cases must sell at the same market price • ‘No free lunch’ • Using this principle some simple results can be derived • Upper and lower bounds on price of a European call option • Put-call parity**Upper bound on call option price**For a European call option on non-dividend paying stock • Upper bound: , the current price of the stock • Call option gives the holder the right to buy one share of a stock at a given price • The call option can never be worth more than the stock • ‘No-arbitrage principle’: if then an arbitrageur could make a riskless profit by buying the stock at and selling the option at C • Compare two portfolios • A: one call option, C • B: one share in the underlying stock, S • Payoffs at maturity • A: payoff = 0 if ; otherwise • B: payoff = : this is greater than portfolio A**Lower bound on call option price**• Lower bound: • Compare two portfolios • A: one call option, C+ a bond providing payoff E at time T • B: one share in the stock, S • Payoffs at maturity • A: payoff = • bond matures to give E • option’s payoff is • B: payoff = : this is the same as or less than portfolio A • Value of portfolio A must be weakly greater than portfolio B • The (discounted) value of the bond today is • Thus: • Rearrange:**Six factors affect option prices**• Current stock price, S • Call: +ve Put: ve • Strike price, E • Call: ve Put: +ve • Time to expiration, T • Call & put: +ve (assuming no dividend payments) • Volatility (variance) of the stock price, • Call & put: +ve (‘option’ curtails downside risk while keeping upside) • Risk-free interest rate, r • Call: +ve Put: ve (PV of future cash amount is less) • Any dividends that are expected to be paid • Call: ve Put: +ve (dividend payment lowers S)**Effect of volatility**• Greater variance increases dispersion of future stock prices • Option cuts off one side of the distribution: (call) option holder does not exercise when • When , wider distribution gives greater probabilities of higher payoffs: increases value of option**Put-call parity**• A relationship between the prices of European call and put options with the same strike price E and time to maturity T • Consider two portfolios • A: one call option, C + a bond providing payoff E at time T • B: one put option, P + one share of the stock, S • Payoffs at maturity • A: payoff = • bond matures to give E • option’s payoff is • B: payoff = • option’s payoff is • value of the stock is • No arbitrage principle: portfolios have the same price, i.e.: ‘Put-call parity’