Derivatives

A New Way: Kronecker-Factored Approximate Curvature Deep Hedging and its Benefits ArXiv ID: 2411.15002 “View on arXiv” Authors: Unknown Abstract This paper advances the computational efficiency of Deep Hedging frameworks through the novel integration of Kronecker-Factored Approximate Curvature (K-FAC) optimization. While recent literature has established Deep Hedging as a data-driven alternative to traditional risk management strategies, the computational burden of training neural networks with first-order methods remains a significant impediment to practical implementation. The proposed architecture couples Long Short-Term Memory (LSTM) networks with K-FAC second-order optimization, specifically addressing the challenges of sequential financial data and curvature estimation in recurrent networks. Empirical validation using simulated paths from a calibrated Heston stochastic volatility model demonstrates that the K-FAC implementation achieves marked improvements in convergence dynamics and hedging efficacy. The methodology yields a 78.3% reduction in transaction costs ($t = 56.88$, $p < 0.001$) and a 34.4% decrease in profit and loss (P&L) variance compared to Adam optimization. Moreover, the K-FAC-enhanced model exhibits superior risk-adjusted performance with a Sharpe ratio of 0.0401, contrasting with $-0.0025$ for the baseline model. These results provide compelling evidence that second-order optimization methods can materially enhance the tractability of Deep Hedging implementations. The findings contribute to the growing literature on computational methods in quantitative finance while highlighting the potential for advanced optimization techniques to bridge the gap between theoretical frameworks and practical applications in financial markets. ...

Markov-Functional Models with Local Drift ArXiv ID: 2411.15053 “View on arXiv” Authors: Unknown Abstract We introduce a Markov-functional approach to construct local volatility models that are calibrated to a discrete set of marginal distributions. The method is inspired by and extends the volatility interpolation of Bass (1983) and Conze and Henry-Labordère (2022). The method is illustrated with efficient numerical algorithms in the cases where the constructed local volatility functions are: (1) time-homogeneous between or (2) continuous across, the successive maturities. The step-wise time-homogeneous construction produces a parsimonious representation of the local volatility term structure. ...

Path weighting sensitivities ArXiv ID: 2411.13403 “View on arXiv” Authors: Unknown Abstract In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to address the large variance happening when the first simulation time step is small. We also propose a covariance inflation technique to addresses the degenerator case when the covariance matrix is singular. The stock dynamics we consider is given in a general functional form, which includes the classical Black-Scholes model, the implied distribution model, and the local volatility model. ...

Inferring Option Movements Through Residual Transactions: A Quantitative Model ArXiv ID: 2410.16563 “View on arXiv” Authors: Unknown Abstract This research presents a novel approach to predicting option movements by analyzing residual transactions, which are trades that deviate from standard hedging activities. Unlike traditional methods that primarily focus on open interest and trading volume, this study argues that residuals can reveal nuanced insights into institutional sentiment and strategic positioning. By examining these deviations, the model identifies early indicators of market trends, providing a refined framework for forecasting option prices. The proposed model integrates classical machine learning and regression techniques to analyze patterns in high frequency trading data, capturing complex, non linear relationships. This predictive framework allows traders to anticipate shifts in option values, enhancing strategies for better market timing, risk management, and portfolio optimization. The model’s adaptability, driven by real time data processing, makes it particularly effective in fast paced trading environments, where early detection of institutional behavior is crucial for gaining a competitive edge. Overall, this research contributes to the field of options trading by offering a strategic tool that detects early market signals, optimizing trading decisions based on predictive insights derived from residual trading patterns. This approach bridges the gap between conventional metrics and the subtle behaviors of institutional players, marking a significant advancement in options market analysis. ...

Robust forward investment and consumption under drift and volatility uncertainties: A randomization approach ArXiv ID: 2410.01378 “View on arXiv” Authors: Unknown Abstract This paper studies robust forward investment and consumption preferences and optimal strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with drift and volatility uncertainties. We focus on non-zero volatility and constant relative risk aversion forward preferences. Given the non-convexity of the Hamiltonian with respect to uncertain volatilities, we first construct robust randomized forward preferences through endogenous randomization in an auxiliary market. {“Therein, w”}e derive the corresponding optimal and robust investment and consumption strategies. Furthermore, we show that such forward preferences and strategies, developed in the auxiliary market, remain optimal and robust in the physical market, offering a comprehensive {“analysis”} for forward investment and consumption under model uncertainty. ...

KANOP: A Data-Efficient Option Pricing Model using Kolmogorov-Arnold Networks ArXiv ID: 2410.00419 “View on arXiv” Authors: Unknown Abstract Inspired by the recently proposed Kolmogorov-Arnold Networks (KANs), we introduce the KAN-based Option Pricing (KANOP) model to value American-style options, building on the conventional Least Square Monte Carlo (LSMC) algorithm. KANs, which are based on Kolmogorov-Arnold representation theorem, offer a data-efficient alternative to traditional Multi-Layer Perceptrons, requiring fewer hidden layers to achieve a higher level of performance. By leveraging the flexibility of KANs, KANOP provides a learnable alternative to the conventional set of basis functions used in the LSMC model, allowing the model to adapt to the pricing task and effectively estimate the expected continuation value. Using examples of standard American and Asian-American options, we demonstrate that KANOP produces more reliable option value estimates, both for single-dimensional cases and in more complex scenarios involving multiple input variables. The delta estimated by the KANOP model is also more accurate than that obtained using conventional basis functions, which is crucial for effective option hedging. Graphical illustrations further validate KANOP’s ability to accurately model the expected continuation value for American-style options. ...

American Call Options Pricing With Modular Neural Networks ArXiv ID: 2409.19706 “View on arXiv” Authors: Unknown Abstract An accurate valuation of American call options is critical in most financial decision making environments. However, traditional models like the Barone-Adesi Whaley (B-AW) and Binomial Option Pricing (BOP) methods fall short in handling the complexities of early exercise and market dynamics present in American options. This paper proposes a Modular Neural Network (MNN) model which aims to capture the key aspects of American options pricing. By dividing the prediction process into specialized modules, the MNN effectively models the non-linear interactions that drive American call options pricing. Experimental results indicate that the MNN model outperform both traditional models as well as a simpler Feed-forward Neural Network (FNN) across multiple stocks (AAPL, NVDA, QQQ), with significantly lower RMSE and nRMSE (by mean). These findings highlight the potential of MNNs as a powerful tool to improve the accuracy of predicting option prices. ...

High-Frequency Options Trading | With Portfolio Optimization ArXiv ID: 2408.08866 “View on arXiv” Authors: Unknown Abstract This paper explores the effectiveness of high-frequency options trading strategies enhanced by advanced portfolio optimization techniques, investigating their ability to consistently generate positive returns compared to traditional long or short positions on options. Utilizing SPY options data recorded in five-minute intervals over a one-month period, we calculate key metrics such as Option Greeks and implied volatility, applying the Binomial Tree model for American options pricing and the Newton-Raphson algorithm for implied volatility calculation. Investment universes are constructed based on criteria like implied volatility and Greeks, followed by the application of various portfolio optimization models, including Standard Mean-Variance and Robust Methods. Our research finds that while basic long-short strategies centered on implied volatility and Greeks generally underperform, more sophisticated strategies incorporating advanced Greeks, such as Vega and Rho, along with dynamic portfolio optimization, show potential in effectively navigating the complexities of the options market. The study highlights the importance of adaptability and responsiveness in dynamic portfolio strategies within the high-frequency trading environment, particularly under volatile market conditions. Future research could refine strategy parameters and explore less frequently traded options, offering new insights into high-frequency options trading and portfolio management. ...

Is the difference between deep hedging and delta hedging a statistical arbitrage? ArXiv ID: 2407.14736 “View on arXiv” Authors: Unknown Abstract The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hedging can include a speculative component aimed simply at exploiting the structure of the risk measure guiding the hedging optimisation problem. We test whether such finding remains true in a GARCH-based market model, which is an illustrative case departing from complete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation. ...

Basket Options with Volatility Skew: Calibrating a Local Volatility Model by Sample Rearrangement ArXiv ID: 2407.02901 “View on arXiv” Authors: Unknown Abstract The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear dependency structure among the assets. We describe the dynamics of the multivariate process of constituents with a copula model and propose an efficient method to extract the dependency structure from the market. The proposed method generates coherent sets of samples of the constituents process through systematic sampling rearrangement. These samples are then utilized to calibrate a local volatility model (LVM) of the basket process, which is used to price basket derivatives. We show that the method is capable of efficiently pricing basket options based on a large number of basket constituents, accomplishing the calibration process within a matter of seconds, and achieving near-perfect calibration to the index options of the market. ...