TAILIEUCHUNG - Lecture Financial modeling - Topic 12: Forward contracts and hedges, simulated correlated random variables

Topic 12 - Forward contracts and hedges, simulated correlated random variables. After completing this unit, you should be able to: Compute no-arbitrage forward prices for equities, currencies, and commodities; compute the payoffs of forward contracts; construct forward hedges using beta and correlation; simulate correlated random variables. | Financial Modeling Topic #12: Forward Contracts and Hedges, Simulated Correlated Random Variables L. Gattis 1 Learning Objectives Compute no-arbitrage forward prices for equities, currencies, and commodities Compute the payoffs of forward contracts Construct forward hedges using beta and correlation Simulate correlated random variables 2 Forward Contract A forward is a contract to buy or sell an asset in the future where the asset, price, quantity, delivery place and location, are specified in the contract. There is generally no up-front payment At maturity, the “seller” is obligated to deliver the asset to the “buyer” and is paid the forward price Forward contract terms are negotiated between counterparties in what is called the over-the-counter (OTC) market which is a network of institutions Futures contracts are forward contracts that trade on exchanges such as the Chicago Mercantile Exchange. 3 Forward Payoffs The “buyer” takes delivery of a quantity (Q) of the asset and pays the forward price. The buyer’s payoff is the difference between the forward price (f0) and the spot price of the asset at delivery (St). The buyer is said to have a long position in the forward, since she profits if the spot price at maturity is above the forward price Long (Buyer) Forward Payoff = (St - f0)Q The “seller” is called the short party of the contract and profits if the spot price falls and the seller can receive a forward price which is above the spot price at maturity. Short (Seller) Forward Payoff = (f0 - St)Q 4 1. Must Buy @ Forward Price 2. Can Sell @ Spot Prices 1. Can Buy @ Spot Price 2. Must Sell @ Forward Price Forward Pricing and Cash and Carry Arbitrage: Stock A cash and carry arbitrage is a risk-free strategy to buy an asset and simultaneously enter into a forward to sell it. ., Buy Non-dividend paying stock in the cash market at S0 today Enter into forward contract to sell stock in t years at price F0,t Finance the purchase at interest rate r for t years. .

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