Option Greeks

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. ...

Derivatives Sensitivities Computation under Heston Model on GPU ArXiv ID: 2309.10477 “View on arXiv” Authors: Unknown Abstract This report investigates the computation of option Greeks for European and Asian options under the Heston stochastic volatility model on GPU. We first implemented the exact simulation method proposed by Broadie and Kaya and used it as a baseline for precision and speed. We then proposed a novel method for computing Greeks using the Milstein discretisation method on GPU. Our results show that the proposed method provides a speed-up up to 200x compared to the exact simulation implementation and that it can be used for both European and Asian options. However, the accuracy of the GPU method for estimating Rho is inferior to the CPU method. Overall, our study demonstrates the potential of GPU for computing derivatives sensitivies with numerical methods. ...