Summary: A STOCHASTIC VOLATILITY MODEL FOR RISK-REVERSALS IN
CLAUDIO ALBANESE AND ALEKSANDAR MIJATOVI´C
Abstract. It is a widely recognised fact that risk-reversals play a central role in pricing of
derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary
stochastically with time. In this paper we introduce a stochastic volatility model with jumps
and local volatility, defined on a continuous time lattice, which provides a way of modeling
this kind of risk using numerically stable and relatively efficient algorithms.
It is generally accepted that in foreign exchange option markets there are at least three
main sources of risk. The first is the stochastic behaviour of the FX rate. The Black-Scholes
model (Black & Scholes 1973) deals with this type of uncertainty.
The second source of risk comes from the nondeterministic nature of the volatility of the
underlying FX rate. There have been many attempts made to incorporate this observation
into the specification of the process driving the FX spot rate. This is usually achieved by
extrinsically specifying a diffusion process which is governing the behavior of the volatility for the
log-returns of the FX rate. Widely used examples of this approach can be found in (Heston 1993)
and (Bates 1996b).
The third source of risk in the foreign exchange option markets comes from the observed
stochasticity of the skewness of the risk neutral distribution of the log-returns for the underlying