The Valuation of Callable Bonds with Floored CMS-Spread Coupons

A new type of structured bond has recently been introduced with enormous success–primarily among private investors–in many countries in Europe. The bonds are medium term and with fixed and very high initial coupons. The remaining coupons are determined as a constant multiplier times the spread between a long and a short swap interest rate. These coupons are floored at or near zero, and the bond investment can thus be seen as a bet on the steepening of future term structure curves. However, if the term structure becomes too steep, the bonds may be called by the issuer. The paper studies the pricing and the optimal call strategy of these highly exotic bonds in a stochastic interest rate framework. We implement two versions of the LIBOR Market Model as well as a Gaussian two-factor short rate model. We show how to adapt the Least-Squares Monte Carlo procedure to handle the callability of the product in a numerically efficient manner. We also calculate lower bounds for the product as well as delta and vega ratios