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Chapter 3

# Chapter 3 - Notes 3 Finance 5108 1 Financial without...

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Notes 3 Finance 5108 1. Financial without interim cash flows The basic concept in the valuation of futures or forward contracts is the concept of no arbitrage pricing. The basic model is generally called the cost of carry model. The other side of this argument is called the reverse cost of carry model. Greater than risk-free rate moves away from no arbitrage. We make the following assumptions: 1. No transaction cost 2. Tax rate are equal 3. Market participants can borrow or lend at the risk free rate 4. All arbitrage opportunities are taken advantage of as they occur 5. Trading is continuous and the model use continuous time calculations EXAMPLE: Forward contract on zero coupon bonds. The current price of a 6 month forward contract is trading at \$1025. A bond that can be delivered against the forward contract is trading at \$925. Is there an arbitrage assuming the risk free rate is 5%? ANS: If I can borrow to buy the bonds the interest and principle would cost me 925e .05(.5) = \$948.42. The profit would be 1025- 948.42 = \$76.58. This would be a riskless profit that I would gain by borrowing \$925 and buying the bond and then sell (agreeing to make delivery) the forward contract. This would be an arbitrage profit. If the forward contract was trading at \$900, I could then short the bond and invest the money at the risk free rate and buy the forward contract (agree to take delivery in the forward market). My profit would be \$948.42 - \$900 = \$48.42. There would not be an arbitrage profit only if the price of the forward contract was exactly at \$948.42. Reverse is lower limit of arbitrage opportunity. So for no arbitrage to occur the following relationship must hold 0 0 0 0 F = S Where F is the forward price of the contract S is the current price of the underlying asset r is the risk-free rate T is timeto delivery on the forward contract rT e If the current forward price is above or below this number then an arbitrage opportunity exists and would be exploited.

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An alternate structure for this using discrete time model would be ( 29 T 0 0 F = S 1 + r The r is just the opportunity cost of the buying the security. It should be noted that the cost of carry model is the one in which you buy the underlying
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Chapter 3 - Notes 3 Finance 5108 1 Financial without...

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