PT - JOURNAL ARTICLE
AU - Ben-Ameur, Hatem
AU - Karoui, Lotfi
AU - Mnif, Walid
TI - Pricing Interest-Rate Derivatives with Piecewise Multilinear Interpolations and Transition Parameters
AID - 10.3905/jod.2014.22.2.082
DP - 2014 Nov 30
TA - The Journal of Derivatives
PG - 82--109
VI - 22
IP - 2
4099 - http://jod.iijournals.com/content/22/2/82.short
4100 - http://jod.iijournals.com/content/22/2/82.full
AB - Interest-rate derivatives like swaptions are challenging to price because they depend on the term structure of interest rates, which potentially has many degrees of freedom, requiring modeling numerous underlying stochastic factors (often at least three for the level and more if stochastic volatility is allowed). In this article, the authors show how the valuation problem can be streamlined in an affine framework by, effectively, digitizing the derivative productâ€™s terminal density. They assume standard affine dynamics for the state vector X, then divide the state space at option expiration into discrete regions and approximate the payoff in each one, as a constant in the simplest case. They then compute the transition probabilities to move from the initial price to each of the terminal regions, using truncated conditional Laplace transforms. With the probabilities and the set of discrete payoffs, the expected value of the payoff to the derivative product under the forward measure can be computed, which is then discounted to compute the initial value. Examples with two- and three-factor affine term structures show that the procedure is accurate and relatively fast.