373 research outputs found
An analytic multi-currency model with stochastic volatility and stochastic interest rates
We introduce a tractable multi-currency model with stochastic volatility and
correlated stochastic interest rates that takes into account the smile in the
FX market and the evolution of yield curves. The pricing of vanilla options on
FX rates can be performed effciently through the FFT methodology thanks to the
affinity of the model Our framework is also able to describe many non trivial
links between FX rates and interest rates: a second calibration exercise
highlights the ability of the model to fit simultaneously FX implied
volatilities while being coherent with interest rate products
The explicit Laplace transform for the Wishart process
We derive the explicit formula for the joint Laplace transform of the Wishart
process and its time integral which extends the original approach of Bru. We
compare our methodology with the alternative results given by the variation of
constants method, the linearization of the Matrix Riccati ODE's and the
Runge-Kutta algorithm. The new formula turns out to be fast and accurate.Comment: Accepted on: Journal of Applied Probability 51(3), 201
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
A flexible matrix Libor model with smiles
We present a flexible approach for the valuation of interest rate derivatives
based on Affine Processes. We extend the methodology proposed in Keller-Ressel
et al. (2009) by changing the choice of the state space. We provide
semi-closed-form solutions for the pricing of caps and floors. We then show
that it is possible to price swaptions in a multifactor setting with a good
degree of analytical tractability. This is done via the Edgeworth expansion
approach developed in Collin-Dufresne and Goldstein (2002). A numerical
exercise illustrates the flexibility of Wishart Libor model in describing the
movements of the implied volatility surface
Cross Currency Valuation and Hedging in the Multiple Curve Framework
We generalize the results of Bielecki and Rutkowski (2015) on funding and collateraliza- tion to a multi-currency framework and link their results with those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al. (2010b).In doing this, we provide a complete study of absence of arbitrage in a multi-currency market where, in each single monetary area, multiple interest rates coexist. We first characterize absence of arbitrage in the case without collateral.After that we study collateralization schemes in a very general situation: the cash flows of the contingent claim and those associated to the collateral agreement can be specified in any currency. We study both segregation and rehypothecation and allow for cash and risky collateral in arbitrary currency specifications. Absence of arbitrage and pricing in the presence of collateral are discussed under all possible combinations of conventions.Our work provides a reference for the analysis of wealth dynamics, we also provide valuation formulas that are a useful foundation for cross-currency curve construction techniques. Our framework provides also a solid foundation for the construction of multi-currency simulation models for the generation of exposure profiles in the context of xVA calculations
Cross Currency Valuation and Hedging in the Multiple Curve Framework
We generalize the results of Bielecki and Rutkowski (2015) on funding and
collateralization to a multi-currency framework and link their results with
those of Piterbarg (2012), Moreni and Pallavicini (2017), and Fujii et al.
(2010b).
In doing this, we provide a complete study of absence of arbitrage in a
multi-currency market where, in each single monetary area, multiple interest
rates coexist. We first characterize absence of arbitrage in the case without
collateral.
After that we study collateralization schemes in a very general situation:
the cash flows of the contingent claim and those associated to the collateral
agreement can be specified in any currency. We study both segregation and
rehypothecation and allow for cash and risky collateral in arbitrary currency
specifications. Absence of arbitrage and pricing in the presence of collateral
are discussed under all possible combinations of conventions.
Our work provides a reference for the analysis of wealth dynamics, we also
provide valuation formulas that are a useful foundation for cross-currency
curve construction techniques. Our framework provides also a solid foundation
for the construction of multi-currency simulation models for the generation of
exposure profiles in the context of xVA calculations.Comment: 42 page
Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting
We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments. We allow for indices on any asset class, featuring collateralization in arbitrary currency denominations. The framework is pivotal for describing portfolios of interest rate products which are denominated in multiple currencies. The benchmark transition has created significant discrepancies among the market conventions of different currency areas: our framework simultaneously covers forward-looking risky IBOR rates, such as EURIBOR, and backward-looking rates based on overnight rates, such as SOFR. In view of this, we provide a thorough study of cross-currency markets in the presence of collateral, where the cash flows of the contract and the margin account can be denominated in arbitrary combinations of currencies. We finally consider cross-currency swap contracts as an example of a contract simultaneously depending on all the risk factors that we describe within our framework
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