Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486671
Title: Modelling FX smile : from stochastic volatility to skewness
Author: Luo, Lin
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2007
Availability of Full Text:
Access from EThOS:
Full text unavailable from EThOS. Please try the link below.
Access from Institution:
Abstract:
This thesis is concerned with the design and analysis of a tractable model, which can capture the key features ofthe observed implied volatility smile surface in the foreign exchange (FX) market, and is flexible enough to be extended to price path-dependent exotic options. In the first part, we examine the dynamics ofthe exchange rate via the conditional distribution implied from option prices, in which the theory and various techniques for implied distribution are analyzed. We identify three sources of uncertainty that need to be modelled: the stochastic exchange rate process, the stochastic volatility, and the stochastic skewness, which can be observed either from the implied higher moments or from its proxy measure 'C risk reversal. An error correction model (ECM) of these higher moments is then proposed to exploit excess returns in the FX underlying market. In the second part, we follow the instrumental approach to explore a tractable model that can address all three sources of uncertainty and reproduce the current market implied volatility smile. Our review of the local volatility model, stochastic volatility model and jump models indicates that individual model is insufficient to account for the asymptotic behaviour of the entire smile surface.The combined models are interesting yet lack oftractability. CarT & Wu [2005] model, which uses two Levy processes to model the up and down jump to capture stochastic skewness, is restricted to price European options. The identification ofthe Albanese and Mijatovic [2006] model completesthis journey. The model, which combines local volatility and Variance Gammajump with regime -switching controlled by a stochastic volatility process, is defined on a continuous time lattice, thus it is both complicated enough to calibrate to the smile surface, and flexible enough to price both European and exotic options. In .the last part, we investigate the methodology to price the FX barrier options within this lattice framework, in which we propose an algorithm to calculate the exponential for nonnormal matrix.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.486671  DOI: Not available
Share: