1,721,035 research outputs found
The explicit Laplace transform for the Wishart process
Full text linkWe derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru (1991). 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
The 4/2 Stochastic Volatility Model
No full textWe introduce a new stochastic volatility model that includes, as special instances, the
Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits
important features: first, instantaneous volatility can be uniformly bounded away
from zero, and second, our model is mathematically and computationally tractable,
thereby enabling an efficient pricing procedure. This called for using the Lie symmetries
theory for partial differential equations; doing so allowed us to extend known results
on Bessel processes. Finally, we provide an exact simulation scheme for the model,
which is useful for numerical applications
A flexible matrix Libor model with smiles
Full text linkWe 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. (2011)
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
this 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
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