chapter4-2-金融工程专业无文字.ppt

Chapter 4Futures and Forwards Prices II
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Three kinds of underlying investment assets:
⑴、Investment assets providing no e
⑵、Investment assets providing a known cash e
⑶、Investment assets providing a known dividend yield
Develop pricing models for forwards when the underlying asset has cash flows associated with it during the period of the forward contract.
forward price for an investment asset
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forward price for an investment asset providing a Known Cash e
Intuition 1
To see this, consider a security that had a perfectly predicable set of cash flows that will occur between 0 and T. Denote the present value of those cash flows as I (discounting at the risk free rate). From the short party’s perspective :buy one unit of the asset and enter into a short forward contract to sell it for F0 at time T. This cost S0 and is certain to lead to a cash inflow of F0 at time T and e with a present value of I.
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A formal prove
Assumption:The underlying asset will provide e with a present value of I during the life of a forward contract.
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 and a cash amount of I borrowed at risk-free interest rate.
Clearly A and B once again have the same payoffs at time T, and so once again, setting them equivalent:
Provide e with a present value of I
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Continued
This is the forward price for an investment asset providing a known cash e (present value I).
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Reexamine The Formula
We could attribute this formula to the notion opportunity cost that the short party faced: to induce the short party to enter into the contract the long party must pay them interest at least in the amount that the short could get if they simply sold the asset now and invested it at the risk-free rate.
Recall that we demonstrated that a forward contract on a security that pays no dividends will have, at time 0, a delivery price of:
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Reexamine