Consider the following MBS pass through with principle $300 million. The original mortgage pool has a WAM = 360 months (30 years) and a WAC = %7.00%. The pass through security pays a coupon equal to 6.5%. Assume a flat term structure of interest rates of 6% (continously compounded).
(a) What is the price of the pass through? Assume a constant PSA = 150%
(b) Compute the duration of this security assuming that the PSA remains constant at 150%.
(c) compute the effective duration of this security assuming that the PSA increases to 200% if the term structure shifts down by 50 basis points, while it decreases to 120% if the term structure shifts up by 50 basis points. Comment on any difference compared to your result in (b).
(d) Compute the effective convexity of this secuirty under the same PSA assumptions as in part (c). Interpret your results.