I have the following problem regarding callable bond replication. Let's define:
A: 7Y Callable bond with fix coupon K%, which is callable exactly in 2Y @par (European feature)
B: 2Y x 5Y Receiver Swaption witk strike=K%
C: 7Y non-callable bond (same as A without call feature)
Textbook replication: A+B=C
However, I'm puzzled with the strike of the swaption. K% coupon is based on a 7Y maturity whereas in 2Y (option expiry) the issuer needs to assess whether there are more favourable conditions than paying K% for the remaining maturity of 5Y. From this perspective, I wonder whether we are really considering the correct strike of K% here?
Additionally, how would you incorporate deterministic credit risk in the pricing of A+B?