刚刚有复习了下SAP TRM 模块提供的敏感度指标，包括有Macaulay duration 麦考利久期, Fisher-Weil duration FW久期, convexity凸度, basis point sensitivity基点价值, modified duration修正久期和到期收益率YTM。
Macaulay duration is not calculated for options and FX, since this is not relevant from a business perspective.
The Macaulay duration of a fixed-rate transaction is the quotient of the total of the cash flows weighted at the points in time of the payments, and the NPV of the transaction on the horizon.
where CF i are the cash flows of the transaction at time point t i , t horizon is the horizon date, and d i the discount factors of time point t i for horizon date t horizon .
The basis point value describes the change in the market value in the event of an increase in market interest rates for all terms, each by one basis point (0.01%). It specifies absolute changes.
PVBP = NPV(+e) - NPV
Fisher-Weil duration describes the elasticity of the NPV to interest rate changes.
The system calculates the Fisher-Weil duration as the difference quotient of the NPVs by shifting the underlying market rates:
where NPV is the net present value of the transaction, and NPV(+ e ) and NPV(- e ) is the NPV of the transaction after the market rates have been shifted upwards or downwards. A basis point is used as the value of the shift (= 0.01% = 0.0001). The system calculates the Fisher-Weil duration in years.
计算发现 Macaulay duration 和 Fisher-Weil Duration 的值一致，
If the Continuous Compounding indicator is set, then the system uses the constant interest calculation method, regardless of the term of the cash flow:
MD = term
FWD = term = MD
The convexity is the sensitivity of the NPV to changes in the interest rate described by the curvature of the price curve.
The system calculates the convexity as the difference quotients by shifting the underlying market interest rates:
where NPV is the net present value of the transaction, and NPV(+ e ) and NPV(- e ) is the NPV of the transaction after the market rates have been shifted upwards or downwards. A basis point is used as the value of the shift (= 0.01% = 0.0001). The factor 10 -2 is the standardization.
The convexity of a portfolio is the mean value of the convexities calculated for the individual transactions and weighted by their NPVs.
The Yield to Maturity (YTM) is the interest rate at which the net present value of the future cash flows is equal to the actual market value of the investment.
The system calculates the YTM by solving the equation specified below:
Modified duration is an adjusted measure of the duration of an investment, in which Macaulay's duration value is adjusted with the yield to maturity (YTM) of the investment.
For fixed-rate/variable-rate transactions other than a swap, the system calculates the modified duration as follows:
MODDUR = MD / (1 + YTM)
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