slides14 - 14. Options and futures (part 1) Derivatives...

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Unformatted text preview: 14. Options and futures (part 1) Derivatives Derivatives are contracts that have payoffs that depend on the prices of some underlying security. Futures and put and call options are the most commonly traded derivatives, but there are many others. Derivatives are often used to hedge risk. But they can also be traded speculatively . 2 Futures A futures contract is a contract obligating the seller to deliver an asset on a specified date for a specified price (the futures price ). No cash actually changes hands until the time of delivery (in principle, but more on this later). Futures contracts are traded on many kinds of assets, includ- ing pork bellies foreign exchange S&P 500 index Note: See www.cbot.com or www.cme.com for more details. 3 Why might someone want to enter into a futures contract? 4 Delivery Although the futures contract actually specifies delivery of the asset to some specified location, the contract is often settled in cash . At time of maturity, the cash settlement is equal to the dif- ference between the futures price at the time the contract was entered into and the spot price of the underlying asset. Before maturity, the cash settlement is equal to the differ- ence between the futures price at the time the contract was entered into and the current market futures price. 5 Futures payoffs Consider a futures contract specifying a price of $100. The payoff of the contract (for the buyer) at time of maturity is Spot price Payoff 85-15 90-10 95-5 100 105 5 110 10 115 15 6 Pricing a futures contract Suppose there are neither benefits nor costs associated with ownership of the underlying asset. Now, suppose I sell a futures contract, and at the same time buy the underlying asset using borrowed cash. At the time of maturity, I deliver the asset, collect the amount specified in the contract, and pay back the loan. Following this strategy, I am ensured a riskless gain (or loss) equal to the difference between the futures price and the amount required to repay the loan. Since no initial cash was required and no risk is involved, this difference must be zero . (Why?) In other words, the futures price must be equal to the future value of the spot price at the risk-free rate (why use the risk-free rate?). This is referred to as a no-arbitrage pricing model. 7 Example Suppose the spot price of gold is $615 per ounce and one-year risk-free rate is 5%. Assume there are neither costs nor benefits associated with owning gold (is this realistic?)....
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slides14 - 14. Options and futures (part 1) Derivatives...

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