Research

I research machine learning methods for Finance. More specifically, I develop fast and accurate methods for option valuation and calibration. In my research, I combine classical option theory methods with modern methods such as neural networks, tree regression, and differential machine learning to produce powerful tools for trading and risk management. I hope these tools can improve solutions to complex, real-world problems, changing the world.

Papers

Gas Storage Valuation using Delta Least Squares Monte Carlo Method

We propose the Delta least squares Monte Carlo method (Delta LSM), a novel method for estimating spot-based trading strategies for gas storage management. We analytically prove that Delta LSM’s cross-sectional regression estimator is unbiased. Furthermore, numerical experiments show the method leads to less overfitting (reduced variance) compared to the widely adopted least squares Monte Carlo method (LSM). As a result, Delta LSM outperforms LSM across various sample sizes and volatilities environments, exhibiting a consistently higher Sharpe ratio.

Preprint available online here.

Delta Least Squares Monte Carlo Pricing of American Options

We present a new simulation-based American option pricing method, Delta least squares Monte Carlo (Delta LSM). Whereas the classical LSM method from Longstaff & Schwartz (2001) uses only the discounted payoff to learn the continuation value, Delta LSM uses both the discounted payoff and its derivative (Delta) to estimate regression coefficients. The Delta LSM is straightforward to implement and comes at a little extra numerical cost. It is quite literally an add-on to the LSM method. Our numerical experiments show that irrespective of your speed/safety preference – and robustly across market scenarios – Delta LSM gives a marked improvement over classical LSM.

Preprint available online here.

NN de-Americanization: A Fast and Efficient Calibration Method for American-Style Options

Neural network (NN) de-Americanization produces fast and accurate pseudo-European option prices from American option market prices, facilitating the calibration of derivative models. The industry approach binomial de-Americanization takes a flat volatility surface as input. In contrast, the NN de-Americanization method takes the detailed shape of the volatility surface as an input; this is critical for the accurate evaluation of the early exercise premium (EEP) when interest rates are not close to zero.

Preprint available online here.

Overcoming the Feature Selection Issue in the Pricing of American Options

The feedforward neural network Monte Carlo method (FNNMC) exhibits more robustness and accuracy than the state-of-the-art least squares Monte Carlo method (LSM) in pricing several American-style options. Specifically, the FNNMC price estimates are accurate for basket options, where the FNNMC price errors are more than four times smaller than the LSM with the best choice of basis functions. By training the neural network the FNNMC avoids the issue of choosing a proper set of basis functions. Hence we circumvent manually engineering the features for each type of option. Furthermore, we explore in-depth the hyperparameter selection for the FNNMC. In the exploration, we use a novel approach called price grid search, where the search is done at the price level instead of at the usual regression level.

Preprint available online here.