4,060 research outputs found
Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus
This study introduces computation of option sensitivities (Greeks) using the
Malliavin calculus under the assumption that the underlying asset and interest
rate both evolve from a stochastic volatility model and a stochastic interest
rate model, respectively. Therefore, it integrates the recent developments in
the Malliavin calculus for the computation of Greeks: Delta, Vega, and Rho and
it extends the method slightly. The main results show that Malliavin calculus
allows a running Monte Carlo (MC) algorithm to present numerical
implementations and to illustrate its effectiveness. The main advantage of this
method is that once the algorithms are constructed, they can be used for
numerous types of option, even if their payoff functions are not
differentiable.Comment: Published at https://doi.org/10.15559/18-VMSTA100 in the Modern
Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA)
by VTeX (http://www.vtex.lt/
Option Pricing with Orthogonal Polynomial Expansions
We derive analytic series representations for European option prices in
polynomial stochastic volatility models. This includes the Jacobi, Heston,
Stein-Stein, and Hull-White models, for which we provide numerical case
studies. We find that our polynomial option price series expansion performs as
efficiently and accurately as the Fourier transform based method in the nested
affine cases. We also derive and numerically validate series representations
for option Greeks. We depict an extension of our approach to exotic options
whose payoffs depend on a finite number of prices.Comment: forthcoming in Mathematical Finance, 38 pages, 3 tables, 7 figure
A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options
We present a parallel algorithm for solving backward stochastic differential
equations (BSDEs in short) which are very useful theoretic tools to deal with
many financial problems ranging from option pricing option to risk management.
Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs
and non linear partial differential equations (PDEs in short) and hence enables
to solve high dimensional non linear PDEs. In this work, we apply it to the
pricing and hedging of American options in high dimensional local volatility
models, which remains very computationally demanding. We have tested our
algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear
speedups which proves the scalability of our implementationComment: 25 page
Modelling FX smile : from stochastic volatility to skewness
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