Keep on smiling? The pricing of Quanto options when all covariances are stochastic

Professorship/Faculty: Lehrstuhl für Betriebswirtschaftslehre, insbesondere Banking und Finanzcontrolling 
Author(s): Branger, Nicole; Muck, Matthias
Title of the Journal: Journal of Banking & Finance
Publisher Information: Amsterdam : Elsevier North-Holland
Year of publication: 2012
Volume: 36
Issue: 6
Pages / Size: 1577-1591 : graph. Darst.
Language(s): English
Licence: German Act on Copyright 
Document Type: Article
The paper introduces a model for the joint dynamics of asset prices which can capture both a stochastic correlation between stock returns as well as between stock returns and volatilities (stochastic leverage). By relying on two factors for stochastic volatility, the model allows for stochastic leverage and is thus able to explain time-varying slopes of the smiles. The use of Wishart processes for the covariance matrix of returns enables the model to also capture stochastic correlations between the assets. Our model offers an integrated pricing approach for both Quanto and plain-vanilla options on the stock as well as the foreign exchange rate. We derive semi-closed form solutions for option prices and analyze the impact of state variables. Quanto options offer a significant exposure to the stochastic covariance between stock prices and exchange rates. In contrast to standard models, the smile of stock options, the smile of currency options, and the price differences between Quanto options and plain-vanilla options can change independently of each other.
Keywords: Stochastic volatility ; Stochastic correlation ; Quantos ; Wishart processes
Release Date: 17. September 2012