Noncausal Affine Processes with Applications to Derivative Pricing

Abstract

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature much more complicated non affine dynamics in calendar time, while still providing (quasi) closed form term structures and derivative pricing formulas. The framework is illustrated with zero-coupon bond and European call option pricing examples.

Noncausal counting processes: A queuing perspective

“…Lemma 2 (See Proposition 3 of [19]). If the noncausal affine process (3) is also affine in calendar time, and is weakly ergodic 4 in both time directions, then it is time reversible.…”

“…where x = p 2 + p(1 − p)v + 1 − p and y = p + (1 − p)u. Under suitable regularity conditions (such as the continuity of g), the only solution of this functional equation is g(x + 1) = e λx , for some positive 19 constant λ. Thus we deduce that (t) and˜ (t + 1) are independent if and only if g(u) = e λ(u−1) , that is if (X t ) is Poisson P(λ) distributed.…”