Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

Jain, Shashi; Leitao, Álvaro; Oosterlee, Cornelis W.

doi:10.1016/j.jocs.2019.03.001

Cited by 11 publications

(3 citation statements)

References 22 publications

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“…Often in computations with stochastic variables, we wish to determine the derivatives of the variables of interest, the so-called pathwise sensitivities. This is generally not a trivial exercise in a Monte Carlo setting, see, for example, the discussions in (Capriotti 2010;Giles and Glasserman 2006;Jain et al 2019;Oosterlee and Grzelak 2019). With our new large time step schemes, we determine the pathwise sensitivities of the computed stochastic variables in a natural way, based on the available information in the (conditional) SC points and the interpolation.…”

Section: Pathwise Sensitivitymentioning

confidence: 99%

The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations

Liu

Grzelak

Oosterlee

2022

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We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these SC points, we can perform Monte Carlo simulations with large time steps. Basic error analysis indicates that this data-driven scheme results in accurate SDE solutions in the sense of strong convergence, provided the learning methodology is robust and accurate. With a method variant called the compression–decompression collocation and interpolation technique, we can drastically reduce the number of neural network functions that have to be learned, so that computational speed is enhanced. As a proof of concept, 1D numerical experiments confirm a high-quality strong convergence error when using large time steps, and the novel scheme outperforms some classical numerical SDE discretizations. Some applications, here in financial option valuation, are also presented.

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Section: Pathwise Sensitivitymentioning

confidence: 99%

The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations

Liu

Grzelak

Oosterlee

2022

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“…The resulting values are shown in Table 8, where a regular arithmetic Asian call is priced and we have employed the same parameter configuration as in the previous experiments corresponding to each dynamics. The reference values are computed by the data-driven COS method [35] and Rolling Adjoints method [36], for Lévy and square-root dynamics, respectively. These Monte Carlo-based techniques provide stable and accurate sensitivities.…”

Section: Greeksmentioning

confidence: 99%

SWIFT valuation of discretely monitored arithmetic Asian options

Leitao

Ortiz-Gracia

Wagner

2018

Journal of Computational Science

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In this work, we propose an efficient and robust valuation of discretely monitored arithmetic Asian options based on Shannon wavelets. We employ the so-called SWIFT method, a Fourier inversion numerical technique with several important advantages with respect to the existing related methods. Particularly interesting is that SWIFT provides mechanisms to determine all the free-parameters in the method, based on a prescribed precision in the density approximation. The method is applied to two general classes of dynamics: exponential Lévy models and squareroot diffusions. Through the numerical experiments, we show that SWIFT outperforms state-ofthe-art methods in terms of accuracy and robustness, and shows an impressive speed in execution time.

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“…More recently Bender and Schweizer [2019] propose the regression anytime, which combines the regress later and the regress now approaches. In Jain et al [2019b] the regress later approach is extended to compute path-wise forward Greeks.…”

Section: Introductionmentioning

confidence: 99%

Neural Network for Pricing and Universal Static Hedging of Contingent Claims

Lokeshwar¹,

Bhardawaj²,

Jain³

2019

SSRN Journal

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We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for interpretability of the model, a feature that is often desirable in the financial context. Specifically, the interpretation leads us to demonstrate that any contingent claim -possibly high dimensional and pathdependent-under Markovian and no-arbitrage assumptions, can be semi-statically hedged using a portfolio of short maturity options. We show how the method can be used to obtain an upper and lower bound to the true price, where the lower bound is obtained by following a sub-optimal policy, while the upper bound by exploiting the dual formulation. Unlike other duality based upper bounds where one typically has to resort to nested simulation for constructing super-martingales, the martingales in the current approach come at no extra cost, without the need for any sub-simulations. We demonstrate through numerical examples the simplicity and efficiency of the method for both pricing and semi-static hedging of path-dependent options. * shashijain@iisc.ac.in

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Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

Cited by 11 publications

References 22 publications

The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations

The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations

SWIFT valuation of discretely monitored arithmetic Asian options

Neural Network for Pricing and Universal Static Hedging of Contingent Claims

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