# Seminario Dottorato: Smooth Asymptotics for a DIC option in a Binomial Tree Model

## Wednesday 7 March 2012 - Jose Maria L. Escaner

ARGOMENTI: Seminars Ph.D. Program

SEMINARIO DOTTORATO
Wednesday 7 March 2012 h. 15:00, room 2BC30
Jose Maria L. Escaner (University of the Philippines Diliman)
"Smooth Asymptotics for a DIC option in a Binomial Tree Model"

-Abstract
The talk aims to compute for the smooth asymptotic expansion for a down-and-in call (DIC) barrier option that was modeled using the Cox-Ross-Rubenstein (CRR) binomial tree. For pricing option contracts, the most well-known model used both by practitioners and in the academe is the Black- Scholes continuous time model. Though less accurate, a simpler and easier understood way to model financial derivatives though would be to use discrete time models. Among the many different discrete time models, a simple and widely-used model is the CRR binomial tree model.
It is well-known that the price of the Black-Scholes continuous time model is close to the price obtained with the CRR binomial tree model when the number of time steps is large, as the Black-Scholes price is the limit of the tree model price. As such, it is of interest to measure the convergence of the CRR model using asymptotic expansion. We follow the framework used by Diener and Diener in measuring the asymptotic expansion for the convergence of barrier options. For the purpose of finding the asymptotics, we make use of Andres symmetry principle in order to find the exact pricing formula of the DIC barrier option. By the guidelines set by Joshi, we specify the parameters and define our CRR binomial tree in such a way as to make the pricing formula symmetric. This would allow us to formulate a complete and smooth asymptotic expansion for our DIC barrier option.

Rif. int. C. Marastoni, T. Vargiolu