Smiles All Around: FX Joint Calibration in a Multi-Heston Model

Col, Alvise De; Gnoatto, Alessandro; Grasselli, Martino

doi:10.2139/ssrn.1982092

Cited by 8 publications

(6 citation statements)

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“…Results in Tables (5) and (10) refer to the stochastic volatility model for currencies of Section 4.3. We take the parameters from Table 1 in De Col et al (2013), which features the result of a calibration performed on market data as of July 23rd 2010. Taking the perspective of a Japanese investor who seeks protections against fluctuations of both EUR-JPY and USD-JPY, we evaluate the payoff…”

Section: Numerical Resultsmentioning

confidence: 99%

“…To provide a coherent framework for the evaluation of FX basket options, we consider the model by De Col et al (2013). The idea is to introduce a foreign exchange market featuring n currencies.…”

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

“…The idea is to introduce a foreign exchange market featuring n currencies. De Col et al (2013) start by considering the value of each of these currencies in units of an artificial currency that can be viewed as a universal numéraire. The model is initially introduced under the risk neutral measure defined by the artificial currency.…”

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

“…Each artificial exchange rate S 0,i is modeled via a multi-variate stochastic volatility model with d independent squareroot components, V(t) ∈ R d . According to De Col et al (2013), the dimension d can be chosen according to the specific problem. A further assumption is that the stochastic volatility components are common between the different S 0,i .…”

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

“…The valuation of vanilla FX options can be performed using standard Fourier based techniques, see De Col et al (2013). In the sequel, we provide the characteristic function of the log-returns in order to approximate FX basket options.…”

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

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General closed-form basket option pricing bounds

Caldana

Fusai

Gnoatto

et al. 2015

Quantitative Finance

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This is the accepted version of the paper.This version of the publication may differ from the final published version. This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms, hence they do not suffer from the curse of dimensionality and can be applied also to high dimensional problems where most existing methods fail. In particular we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate. Permanent repository link

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

Section: Fx Stochastic Volatility Modelmentioning

confidence: 99%

See 3 more Smart Citations

General closed-form basket option pricing bounds

Caldana

Fusai

Gnoatto

et al. 2015

Quantitative Finance

Self Cite

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Pricing Multi-Dimensional FX Derivatives via Stochastic Local Correlations

Col¹,

Kuppinger²

2014

Wilmott

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We present a hybrid Heston local correlation model for pricing multi-dimensional FX derivatives. The model is symmetric under inversion and triangulation and yields prices that are consistent with the one-dimensional vanilla markets of both main and cross FX rates. Irrespective of the choice of numeraire, the model retains its functional form. Important for practitioners, the model is easy to calibrate and can be scaled to any desired dimensionality (i.e., it can include an arbitrary amount of FX rates). The strength of the model -pricing both typical terminal and path-dependent options such as worst-ofs, quanto double no-touches, and third currency barrier options -is shown in test results comparing the Heston local correlation model with other multi-dimensional FX models. Keywordscorrelation, FX, stochastic-local volatility, triangular relation In troductionPricing financial derivatives with multiple underlying components, such as basket options [1], requires a sound modeling of the correlations among the individual underliers. Unfortunately, for most asset classes these correlations are not observable in the market. This leads to material uncertainties and complications in the valuation and risk management of even rather simple multi-component derivatives. Nevertheless, there exists a notable example in which the market actually allows us to infer significant information about the correlation structure: derivatives depending on multiple FX rates. In the FX framework, the market yields potentially more information on where correlations trade than any standard model (e.g., a Gaussian copula model) can handle. This valuable information can be extracted from the FX vanilla markets by making use of the fact that appropriate multiplications and divisions of FX rates are still FX rates and, hence, their implied volatilities are often traded and observable in the market. In order to capture the market implied correlation structure, we need a model that is capable of consistently pricing vanilla options across different FX pairs. At the same time, given the potential high dimensionality of the problem, we seek to retain analytical tractability. Here, we discuss several approaches to model correlations between FX rates and present a multi-dimensional extension of the hybrid Heston plus local volatility model presented in [2,3].Neglecting volatility smiles, the standard Black-Scholes (BS) model can easily be extended to model multi-dimensional FX rate pairs. As an example, we may consider an FX triangle, consisting of three underlying FX rates like EURUSD, GBPUSD, and EURGBP (we shall use the standard FX terminology where the notation ccy1ccy2 stands for the amount of ccy2 paid per unit of ccy1). We then obtain the following relationship between the three FX rates S EURUSD (t), S GBPUSD (t), and S EURGBP (t): S EURGBP (t) = S EURUSD (t) / S GBPUSD (t). From the perspective of a USD investor, we denote EURUSD and GBPUSD as the main FX rates and EURGBP as the cross FX rate. As shown in detail in [3, p. 226], we may...

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A New Class of Local Correlation Models

Guyon

2013

SSRN Journal

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Smiles All Around: FX Joint Calibration in a Multi-Heston Model

Cited by 8 publications

References 43 publications

General closed-form basket option pricing bounds

General closed-form basket option pricing bounds

Pricing Multi-Dimensional FX Derivatives via Stochastic Local Correlations

A New Class of Local Correlation Models

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