Importance sampling for option pricing with feedforward neural networks
We study the problem of reducing the variance of Monte Carlo estimators through performing suitable changes of the sampling measure which are induced by feedforward neural networks. To this end, building on the concept of vector stochastic integration, we characterize the Cameron-Martin spaces of a large class of Gaussian measures which are induced by vector-valued continuous local martingales with deterministic covariation. We prove that feedforward neural networks enjoy, up to an isometry, the universal approximation property in these topological spaces. We then prove that sampling measures which are generated by feedforward neural networks can approximate the optimal sampling measure arbitrarily well. We conclude with a comprehensive numerical study pricing path-dependent European options for asset price models that incorporate factors such as changing business activity, knock-out barriers, dynamic correlations, and high-dimensional baskets.
Code (1)
Similar Papers 제목 키워드 기반
Pricing options on flow forwards by neural networks in Hilbert space
We propose a new methodology for pricing options on flow forwards by applying infinite-dimensional neural networks. We recast the pricing problem as an optimization problem in a Hilbert space of real-valued function on t…
Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks
We propose a deep Recurrent neural network (RNN) framework for computing prices and deltas of American options in high dimensions. Our proposed framework uses two deep RNNs, where one network learns the price and the oth…
Calibrating the Heston model with deep differential networks
We propose a gradient-based deep learning framework to calibrate the Heston option pricing model (Heston, 1993). Our neural network, henceforth deep differential network (DDN), learns both the Heston pricing formula for …
modelNeural Term Structure of Additive Process for Option Pricing
The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modelin…
Pricing options on the cryptocurrency futures contracts
The cryptocurrency options market is notable for its high volatility and lower liquidity compared to traditional markets. These characteristics introduce significant challenges to traditional option pricing methodologies…