chapter4-1无文字 金融工程专业.ppt

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Chapter 4Futures and Forwards Prices Ι
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Our objective is to link the price of the futures or forward contract to the price of the underlying instrument and to identify factors that influence the relationship between these prices.
Objective of this chapter
Forward and futures prices
Spot price of the underlying asset
relationship
?
Forward prices
relationship
?
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1、PRELIMINARIES
⑴ for many of the contracts that are traded in the market, it can be argued that the forward price and futures price of an asset are very close to each other when the maturities of the two contracts are the same.
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1、PRELIMINARIES
⑵ notation
We will use a lot of notation, so let’s be very clear about what each symbol means:
T = maturity date of the forward contract
t = current time
St = price of underlying at time t
ST= Price of underlying at time T
K = delivery price in the forward contract
Ft= forward price at time t
f = value of a long forward contract at time t.
r = risk free rate
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1、PRELIMINARIES
⑶. pound interest is paid on the original principal and on the accumulated past interest.
Notation:
T: Investment period(years)
PV: Present Value of initial investment
FV: Future Value of initial investment
R: Nominal interest rate per annum
m: Compounding frequency
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Continued
When the interest pounded once a year for T years:
What if interest is paid more frequently? Here are a few examples of the formula:
m=1
m=4
m=12
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continued
Consider an amount PV invested for T years at an interest rate of R per annum.
Compounding frequency(m)
m=1
m>1
m→
Future value after n years
(FV)
The limit as m tends to infinity is known as pounding
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示例
例:假设存款金额为100,名义年利率为10%,存款期限为1年,在年度计息的条件下,明年的期末存款余额为:
100× = 110
半年计息一次:
100×× =
每季度计息一次:
100×=
连续复利:
100×=
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实际利率与计息次数
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continued
The limit as m tends to infinity is known as pounding
The standard future and present value formulas are:
PV→FV:PV* eRT= FV
FV→PV:F