chapter4-1無文字金融工程專業(yè)-資料下載頁
2024-09-20 18:14本頁面
【正文】 om the short’s perspective there is no risk in this contract. They pay the current market (spot) price for the asset (S0), they hold it for T years, and then they sell it for K dollars. ? This cost S0 and is certain to lead to a cash inflow of K/F0 at time T. 0SKT0 T?So how would the short party determine the delivery price that they would be willing to enter into? ?Look at it this way, they have to pay S0 dollars today, and they want to earn the riskfree rate on those dollars, so the delivery price K or the forward price at time zero F0 must be F0 = K = S0erT! 39 A formal prove ? Consider the following portfolios(at time 0 ): ? Portfolio A: a long forward contract and a cash amount of on hand. ? Portfolio B: one unit of underlying asset. 0 rTrT eKe ?? KT rTKe?TA unit of asset buy rTKe?40 A formal prove ? Notice, then, that both portfolio’s A and B each give you the same end result or value－ the value of the security at maturity. On condition that there are no arbitrage opportunities, at some earlier time, such as time 0, these two portfolios should be identical too. If not, if AB or BA, then you would short the expensive one and go long the inexpensive on, making money for nothing! ? portfolio A is equivalent to portfolio B 00 SKef rT ?? ?A B 41 forward price for an investment asset providing no ine ? Rearranging: ? Which is the same formula we developed through our intuition earlier. ? Example: Forward on nondividend paying stock maturing in 3 months. ? Stock price is $40, r=.05, Tt=.25, S=40, so: F0 = K = *.25 = rTKeSf ??? 0000 ?fKF ?0 rTeSF 00 ?42 forward price for an investment asset providing no ine ? To see this consider the two alternative possibilities: ? First: F0 S0erT: ? An investor could borrow S0 dollars at the risk free rate and use them to buy the asset at time 0. They could then take a short position in the forward contract. At time T, the asset is sold under the terms of the contract at F0(K), and the investor then pays S0erT to the borrower and s the difference. 0 T S0 F0（ K） rTeS043 forward price for an investment asset providing no ine ? Second: F0 S0 erT ? It’s the exact opposite, take a long position in the forward contract, short the asset and invest the proceeds at the risk free rate. 0 T S0 F0（ K） rTeS0
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