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KIC000003

KIC000003 - 'I Price Volatility is a Function of Duration...

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'I Price Volatility is a Function of Duration and Convexity The larger the Duration, the more volatility in prices from changes in yields. Duration always stated as a positive number. Convexity matters most when change in yield is big. M 1 2 - ""-D!:"y+-CM(!:"y) P 2 Approximating Duration and Convexity Approximate Duration '" P -P+ 2(P o )(Lly) Approximate Convexity", P++P_ -2P o P"(Lly)' Valuation of Defaultable Bonds vow take a bond with face value F and samt-annuarccupcn payments equal to C maturing T semi-annual periods ahead. Suppose: _ there is d probability of default at any given payment date. _ in case of default bondholders receive a recovery value R<F at the time of default, instead of the remaining promised cash-flows. Ifthe discount rate (expected return) for the bond's cash flows is r per semi-annual period, what is the fair price of the bond? - 3

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Expected Loss Expected loss = F - ((l-d)*F + d*R) = F*(l-(l-d»)- d*R = d*F - d*R = d*(F - R) Expected Loss = (Probability
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KIC000003 - 'I Price Volatility is a Function of Duration...

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