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Financial Mathematics Old FM Forum 

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#74




I've found the formulae here to be almost sufficient for the Aug 2019 exam and just want to add a few here.
Interest Rate Swaps: General: PV(Interest without the swap) =PV(Interest with the swap) Level notional Amount Fixed (Swap) Rate = (P(t1)  P(n)) / (P(t) + P(t+1) + … + P(n)) Where P(t) = Price of a zero coupon bond maturing for $1 in t years which = (1+spot rate for t year investment)^ t Note if swap begins in year 1 (not deferred) then P(t1) = P(0) = 1 McCaulay Price Change approximation (2nd order) Approximation for price of asset at interest rate i, P(i) around a specific i = i(0), McCaulay Duration D and McCaulay Convexity C P(i) ~= P( i(0) )* ( (1+i(0))/(1+i) )^D * (1 + ( (i  i(0))/ (1 +i(0)) )^2 * (C  D^2)/2 ) 1st Order: P(i) ~= P( i(0) )* ( (1+i(0))/(1+i) )^D Last edited by campbellkord; 08222019 at 12:31 PM.. Reason: Correction and change in notation 
#75




hey guys  when given a liability and two assets (one before and one after the liability), i found the shortcut method very helpful.
w = (t2  tL)/(t2  t1) t1 = shorter bond duration t2 = longer bond duration tL = liability duration w = shorter bond's weight 
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