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1. Of course a swaption will be needed. The major reasons being that Bond A is callable after 3 years and matures in 4 years whereas Bond B matures in 5 years. It is understandable that if interest rates decrease substantially Bond A will be called.
2. First let's glance at the required structure to convert Bond A in to Bond B
(a) To eradicate the credit risk involved in Bond A we need to buy a CDS with 4 year maturity. That will alter the credit of the initial portfolio from AA- to AAA.
(b) Second step involves the conversion of fixed rate in to floating rate. For this we require a (fixed payer) interest rate swap in USD with maturity 5 years.
(c) By utilizing a cross currency swap (floating to floating) we exchange USD floating into DEM floating. Therefore we need a currency swap for 5 years.
(d) Ultimately we need to hedge the risk mentioned in part (c). Consequently we should buy a (Bermudan type) swaption in USD.
how do we get the pvif of a perpetuity
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