Abstract

The main objective of this paper is to propose an alternative valuation framework for pricingforeign currency and cross-currency options, which is capable of  accommodating existing empiricalregularities. The paper generalizes the GARCH option pricing methodology of Duan (1995) to a two-country setting. Specifically, we assume a bivariate nonlinear GARCH system for the exchange rateand the foreign asset price, and generalize the local risk-neutral valuation principle for pricingderivatives. We define an equilibrium price measure in the two-country economy and derive thelocally risk-neutralized GARCH processes for the exchange rate and the foreign asset price. Foreigncurrency options and cross-currency options are then valued using Monte Carlo simulations. Oursetup accommodates rich empirical regularities such as stochastic volatility, fat tailed distributionsand leverage effect extensively documented for financial data series.  Numerical results show  thatour proposed model exhibits properties that are consistent with the documented empirical regularitiesfor foreign currency options and quanto options.

Pricing Foreign Currency and Cross-Currency Options Under GARCH-Duan

ABSTRACT

One of the main sources of uncertainty in the analysis of the risk and return properties of a portfolio of fixed-income securities is the stochastic evolution of the shape of the yield curve.The authors have estimated a model that fits the South African yield curve, using a Kalman filter.The model includes four latent factors and three observable macroeconomic variables (capacity utilisation, inflation and the repo rate). The goal is to capture the dynamic interactions between the macroeconomy and the yield curve in such a way that the resulting model can be used to generate interest-rate scenario trees that are suitable for fixed-income portfolio optimisation. An importantinput into the scenario generator is the investor’s view on the future evolution of the repo rate.In this paper, details of the model are provided and the results of the estimation and scenario generation are reported.

Fixed income portfolio optimization