114 research outputs found
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
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
Fast Hybrid Schemes for Fractional Riccati Equations (Rough is not so Tough)
We solve a family of fractional Riccati differential equations with constant
(possibly complex) coefficients. These equations arise, e.g., in fractional
Heston stochastic volatility models, that have received great attention in the
recent financial literature thanks to their ability to reproduce a rough
volatility behavior. We first consider the case of a zero initial value
corresponding to the characteristic function of the log-price. Then we
investigate the case of a general starting value associated to a transform also
involving the volatility process. The solution to the fractional Riccati
equation takes the form of power series, whose convergence domain is typically
finite. This naturally suggests a hybrid numerical algorithm to explicitly
obtain the solution also beyond the convergence domain of the power series
representation. Our numerical tests show that the hybrid algorithm turns out to
be extremely fast and stable. When applied to option pricing, our method
largely outperforms the only available alternative in the literature, based on
the Adams method.Comment: 48 pages, 4 figure
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
A Fully Quantization-based Scheme for FBSDEs
We propose a quantization-based numerical scheme for a family of decoupled FBSDEs. We simplify the scheme for the control in Pag\ue8s and Sagna (2018) so that our approach is fully based on recursive marginal quantization and does not involve any Monte Carlo simulation for the computation of conditional expectations. We analyse in detail the numerical error of our scheme and we show through some examples the performance of the whole procedure, which proves to be very effective in view of financial applications
Pricing currency derivatives under the benchmark approach
This paper considers the realistic modelling of derivative contracts on exchange rates. We propose a stochastic
volatility model that recovers not only the typically observed implied volatility smiles and skews
for short dated vanilla foreign exchange options but allows one also to price payoffs in foreign currencies,
lower than possible under classical risk neutral pricing, in particular, for long dated derivatives. The main
reason for this important feature is the strict supermartingale property of benchmarked savings accounts
under the real world probability measure, which the calibrated parameters identify under the proposed
model. Using a real dataset on vanilla option quotes, we calibrate our model on a triangle of currencies
and find that the risk neutral approach fails for the calibrated model, while the benchmark approach still
works
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