TITLE:
The Pricing of Dual-Expiry Exotics with Mean Reversion and Jumps
AUTHORS:
Kevin Z. Tong, Dongping Hou, Jianhua Guan
KEYWORDS:
Dual-Expiry Options, Binary Options, Eigenfunction Expansion, Lévy Subordinator, Stochastic Time Change, OU Process, Jump Diffusion
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.9 No.1,
January
29,
2019
ABSTRACT: This paper develops a new class of models for pricing dual-expiry options
that are characterized by two expiry dates. The underlying asset price is modeled
by a time changed exponential Ornstein Uhlenbeck (OU) process, where
the time change process is a Lévy subordinator. The new models can capture
both mean reversion and jumps often observed in various types of underlying
assets of exotics. The pricing method exploits the observation that dual expiry
options have payoffs that can be perfectly replicated by a particular set of first
and second order binary options. The novelty of the paper is that we are able
to derive the analytical solutions to the prices of these binaries through eigenfunction
expansion method. Based on that, we can obtain the formulas for
dual-expiry exotics through static replication. We also numerically investigate
the sensitivities of prices of chooser, compound and extendable options with
respect to the parameters of the models.