FINM3405L3

# FINM3405L3 - Replication and Arbitrage li i d A bi Lecture...

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Lecture 3 aluation of Valuation of Forward and Futures Contracts Replication and Arbitrage ± The way in which derivatives (forwards, futures, ptions) are priced is somewhat different to how options) are priced is somewhat different to how regular financial securities are priced. ± Because derivative securities are based on another underlying security, it is possible to ‘replicate’ the derivative using clever portfolios of more basic ecurities securities ± Our ability to synthetically replicate the derivative security is the key to calculating the correct forward/futures price ± If it has a different price, then an arbitrage opportunity xists exists Aside ± A couple of points before we begin: s noted there are a few minor differences between – As noted, there are a few minor differences between forwards and futures, the main one being marking-to-the- market. It can be shown that if interest rates are constant, then the price of a futures contract is the same as a forward. Thus, futures are often valued as if they were forwards. When we talk about ‘pricing’ a forward contract, we really e e ta about p c g a o a d co t act, e ea y mean determining the correct delivery price F . What if F is Mispriced? ± WBC shares are trading at \$22 e riskless rate of interest is 5% pa ± the riskless rate of interest is 5% pa ± If two people wanted to setup a forward contract for the delivery of WBC shares one year from now, what is the correct forward price F ? ± You might think it is the best guess as to what WBC price will be in one year, but this is totally wrong o e yea , but t s s tota y o g ± We will consider two cases: – Case 1: a forward contract with delivery in one year is arranged ith \$28 with F = \$28 – Case 2: a forward contract with delivery in one year is arranged with F = \$21

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Case 1: Forward Overpriced Action Time 0 Cashflows Time T Cashflows Short forward nil +28.00 Use the WBC to fulfill Buy WBC share -22.00 your obligations under short fwd Borrow +22.00 -23.13 22 exp(0.05 × 1) Net cashflow \$0.00 +\$4.87 Conclusion: F=\$28 is too high Case 2: Forward Underpriced Action Time 0 Cashflows Time T Cashflows Long forward Nil -21.00 Short sell WBC +22.00 Use the WBC share pruchased under long fwd to close-out short sale Invest proceeds -22.00 +23.13 Net cashflow \$0.00 +\$2.13 Conclusion: F=\$21 is too low Conclusion ± Forward prices of \$28 and \$21 are incorrect and ermit arbitrage profits permit arbitrage profits. ± The correct forward price for delivery of WBC in one ear is the ‘ ost of carry’ 23 13 year is the cost of carry \$23.13 ± any other forward price is wrong and allows an rbitrage profit arbitrage profit ± therefore, F = \$23.13 is the no-arbitrage or arbitrage- free forward price ± we have seen enough now to understand the basic rinciple of derivative valuation: principle of derivative valuation: – We seek to identify a portfolio that precisely replicates the derivative (usually, this portfolio involves positions in the underlying asset and the bank account). Then – set up a three-piece strategy containing the replicating
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## This note was uploaded on 08/27/2009 for the course FINM 3405 taught by Professor Philipgray during the Three '09 term at Queensland.

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FINM3405L3 - Replication and Arbitrage li i d A bi Lecture...

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