802 research outputs found
FX Smile in the Heston Model
The Heston model stands out from the class of stochastic volatility (SV)
models mainly for two reasons. Firstly, the process for the volatility is
non-negative and mean-reverting, which is what we observe in the markets.
Secondly, there exists a fast and easily implemented semi-analytical solution
for European options. In this article we adapt the original work of Heston
(1993) to a foreign exchange (FX) setting. We discuss the computational aspects
of using the semi-analytical formulas, performing Monte Carlo simulations,
checking the Feller condition, and option pricing with FFT. In an empirical
study we show that the smile of vanilla options can be reproduced by suitably
calibrating three out of five model parameters.Comment: Chapter prepared for the 2nd edition of Statistical Tools for Finance
and Insurance, P.Cizek, W.Haerdle, R.Weron (eds.), Springer-Verlag,
forthcoming in 201
FX Smile in the Heston Model
The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical solution for European options. In this article we adapt the original work of Heston (1993) to a foreign exchange (FX) setting. We discuss the computational aspects of using the semi-analytical formulas, performing Monte Carlo simulations, checking the Feller condition, and option pricing with FFT. In an empirical study we show that the smile of vanilla options can be reproduced by suitably calibrating three out of five model parameters.Heston model; vanilla option; stochastic volatility; Monte Carlo simulation; Feller condition; option pricing with FFT;
Smiles all around: FX joint calibration in a multi-Heston model
We introduce a novel multi-factor Heston-based stochastic volatility model,
which is able to reproduce consistently typical multi-dimensional FX vanilla
markets, while retaining the (semi)-analytical tractability typical of affine
models and relying on a reasonable number of parameters. A successful joint
calibration to real market data is presented together with various in- and
out-of-sample calibration exercises to highlight the robustness of the
parameters estimation. The proposed model preserves the natural inversion and
triangulation symmetries of FX spot rates and its functional form, irrespective
of choice of the risk-free currency. That is, all currencies are treated in the
same way.Comment: Journal of Banking and Finance. Accepte
Vanna-Volga methods applied to FX derivatives : from theory to market practice
We study Vanna-Volga methods which are used to price first generation exotic
options in the Foreign Exchange market. They are based on a rescaling of the
correction to the Black-Scholes price through the so-called `probability of
survival' and the `expected first exit time'. Since the methods rely heavily on
the appropriate treatment of market data we also provide a summary of the
relevant conventions. We offer a justification of the core technique for the
case of vanilla options and show how to adapt it to the pricing of exotic
options. Our results are compared to a large collection of indicative market
prices and to more sophisticated models. Finally we propose a simple
calibration method based on one-touch prices that allows the Vanna-Volga
results to be in line with our pool of market data
An Analysis of the Heston Stochastic Volatility Model: Implementation and Calibration using Matlab
This paper analyses the implementation and calibration of the Heston
Stochastic Volatility Model. We first explain how characteristic functions can
be used to estimate option prices. Then we consider the implementation of the
Heston model, showing that relatively simple solutions can lead to fast and
accurate vanilla option prices. We also perform several calibration tests,
using both local and global optimization. Our analyses show that
straightforward setups deliver good calibration results. All calculations are
carried out in Matlab and numerical examples are included in the paper to
facilitate the understanding of mathematical concepts.Comment: 34 page
- …