Financial Risk Manager Handbook by Philippe Jorion

By Philippe Jorion

I've got used this publication as a textual content for a graduate point monetary hazard administration direction, in coaching for the GARP FRM examination (which I passed), and as a reference professionally. The instruction manual supplies precisely what it says it's going to, and serves as an outstanding primer ahead of moving into the heavier, extra specific assigned readings (this isn't an assigned analyzing for the FRM examination, brain you).

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We consider a 10-year bond paying a 6% coupon semiannually. Initially, the yield is also at 6% and, as a result, the price of the bond is at par, at $100. The graph compares three lines representing the following: 1. The actual, exact price 2. The duration estimate 3. The duration and convexity estimate P = f (y0 + y) P = P0 − D ∗ P0 y P = P0 − D ∗ P0 y + (1/2)C P0 ( y)2 The actual price curve shows an increase in the bond price if the yield falls and, conversely, a depreciation if the yield increases.

This is also called a cumulative distribution function. When the variable X takes discrete values, this distribution is obtained by summing the step values less than or equal to x. ). Here, f (x) is the probability of observing x. This function is characterized by its shape as well as fixed parameters, θ. 4) Often, the random variable will be described interchangeably by its distribution or its density. These functions have notable properties. The density f (u) must be positive for all u. 1 gives an example of a density function f (x), on the top panel, and of a cumulative distribution function F (x) on the bottom panel.

9733. 1. 20) uses the two extreme points. 21) uses the difference between the dollar durations for the upmove and downmove. Note that convexity is positive if duration increases as yields fall, or if D− > D+ . 56. 13, and would be even closer if the step y was smaller. 48. Finally, this numerical approach can be applied to get an estimate of the duration of a bond by considering bonds with the same maturity but different coupons. If interest rates decrease by 1%, the market price of a 6% bond should go up to a value close to that of a 7% bond.

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