chapter4-1无文字 金融工程专业.ppt

1 Chapter 4 Futures and Forwards Prices Ι 2 ? 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 ? 31、 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. 41、 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 51、 PRELIMINARIES ?⑶. pounding ? Compound 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 6 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: TR PV FV)1(??) )4 1( poundin quarterly R PV FV T( ???) )12 1( poundin monthly R PV FV T( ??? m=1 m=4 m=12 7 continued ? Consider an amount PV invested for T years at an interest rate of R per annum. Compounding Compounding frequency(m) frequency(m) Future value after Future value after n years n years (FV) (FV) m=1 m=1 m>1 m>1 m m→→ mT)m R PV(1 ? RT PV e ? T R) 1 PV( ? The limit as m tends to infinity is known as pounding 8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 × = 1