Janek, Agnieszka (2011): The vanna - volga method for derivatives pricing.
Download (781kB) | Preview
This Master thesis highlights some basic features and applications of the vanna-volga method and its accuracy when pricing plain vanillas and simple barrier options.
In the paper we derive formulas for premiums of vanilla FX options using two versions of the vanna-volga method – the exact vanna-volga method and the simplified vanna-volga method. We review a very common vanna-volga variation used to price the first-generation exotics and the application of the vanna-volga method to construct the implied volatility surface.
Furthermore, we briefly discuss a popular stochastic volatility model that aims to take the smile effect into account – the Heston model. Its accuracy and efficiency is further compared with that of the vanna-volga method.
In the part of the thesis, which is devoted to calibration results, we compare the results obtained by the exact vanna-volga method, the simplified vanna-volga method and the Heston model. We also investigate the accuracy of the vanna-volga method applied to barrier options.
All the plots and graphs in this thesis were produced by programs implemented by the author in MATLAB. These programs are available on request.
|Item Type:||MPRA Paper|
|Original Title:||The vanna - volga method for derivatives pricing.|
|Keywords:||vanna- volga method; implied volatility; volatility smile; Heston model|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63 - Computational Techniques; Simulation Modeling
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
|Depositing User:||Agnieszka Janek|
|Date Deposited:||22. Jan 2012 23:00|
|Last Modified:||11. Mar 2014 15:56|
Bossens, F., Ray´ee, G., Skantzos, N.S. and Deelstra, G. (2010). Vanna-volga methods applied to FX derivatives. From theory to market practice, Working Paper.
Brigo, D. and Mercurio, F. (2007). Interest Rates Models – Theory and Practice with Smile, Inflation and Credit, Springer.
Carr, P., Hogan, A. and Verma, A. (2006). Vanna-volga method for 1st generation exoticsin FX, Bloomberg Research Paper.
Castagna, A. (2009). FX Options and Smile Risk, Wiley Finance.
Castagna, A. and Mercurio, F. (2006). Consistent pricing of FX options, Working Papers Series, Banca IMI.
Castagna, A. and Mercurio, F. (2007). The vanna-volga method for implied volatilities, Risk, January, 106–111.
Cox, J. C., Ingersoll, J. E. and Ross, S. A. (1985). A Theory of the term structure of interest rates, Econometrica 53: 385–407.
Derman, E. and Kani, I. (1996). The ins and outs of barrier options: Part 1, Derivatives Quaterly, Winter 1996, 55–67.
Fisher, T. (2007). Variations on the vanna-volga adjustment, Bloomberg Research Paper
Garman, M. B. and Kohlhagen, S. W. (1983). Foreign currency option values, Journal of International Monet & Finance, 2: 231–237.
Hakala, J., Periss´e, G. and Wystup, U. (2002). The pricing of first generation exotics, Foreign Exchange Risk, Risk Publications.
Haug, E. G. (2007). The Complete Guide To Option Pricing Formulas (2nd ed), McGraw-Hill.
Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 6: 327–343.
Janek, A., Kluge, T., Weron, R. and Wystup, U. (2011). FX Smile in the Heston Model, in Statistical Tools for Finance and Insurance (2nd ed), eds. P. ˇ Ciˇzek, W. H¨ardle, R. Weron, Springer-Verlag, Berlin, 133–162.
Kucharczyk, D. (2011). The Heston model for pricing path dependent options, MSc Thesis, Wroclaw University of Technology.
Lipton, A. and McGhee, W. (2002). Universal barriers, Risk, May, 81–85.
Reiswich, D. andWystup, U. (2010). FX volatility smile construction, Centre for Practical Quantitative Finance Working Paper Series #20, Frankfurt School of Finance and Management.
Shkolnikov, Y. (2009). Generalized vanna-volga method and its applications, NumeriX Research Paper
Weber, A. and Wystup, U. (2009). Pricing Formulae for Foreign Exchange Options, MathFinance.
Weron, A. and Weron, R. (2005). Inżynieria finansowa, WNT (in Polish).
Wystup, U. (2002). Ensuring efficient hedging of barrier options, RISK training course on pricing, hedging and trading exotic derivatives.
Wystup, U. (2003). The market price of one-touch options in foreign exchange markets, Derivatives week, 12(13), 1–4.
Wystup, U. (2006). FX Options and Structured Products, Wiley Finance.
Wystup, U. (2008). Foreign exchange symmetries, Centre for Practical Quantitative Finance Working Paper Series #9, Frankfurt School of Finance and Management.
Wystup, U. (2008). Vanna-volga pricing, Centre for Practical Quantitative Finance Working Paper Series #11, Frankfurt School of Finance and Management.