Assessing the effects of variability in interest rate derivative pricing

Interest rate derivatives are financial instruments similar in spirit to stock options. The value of such a derivative depends on the level of a particular interest rate at a designated time. One type of interest rate derivative is an interest rate cap, which pays a notional amount multiplied by the amount by which a specified interest rate exceeds the strike rate at periodic intervals until maturity. Many models exist for pricing interest rate derivatives. This research uses the Hull-White model (Hull, 2003) for the short rate, implemented with a trinomial tree. This model can be used to determine pricing for interest rate derivatives.; The first part of this research explores various spline methods for estimating the term structure of the zero rate curve, one of the inputs into the Hull-White trinomial tree. The zero rate is the interest rate that would be earned on a bond that has no intermediate coupon payments and pays face value at maturity. The zero rate curve is modeled with splines extending an approach developed by Fisher et al. (1994).; The second part of this research uses bootstrap techniques to determine the variability of the zero rate curve at various maturities and to propagate the variability of the zero rate curve into the Hull-White pricing model. The latter bootstrap includes the entire method of derivative pricing from the calculation of a zero curve using a set of bond prices through entering that zero curve into the pricing model, and on to the pricing of a derivative.