arXiv subjects

Kumar Yashaswi

Publications and source records attributed to Kumar Yashaswi.

3 recordsLinked to original sources

arXiv2021

Adaptive calibration of Heston Model using PCRLB based switching Filter

Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely used for volatility estimation and option pricing. In this paper, we design a novel method to estimate parameters of Heston model under state-space representation using Bayesian filtering theory and Posterior Cramer-Rao Lower Bound (PCRLB), integrating it with Normal Maximum Likelihood Estimation (NMLE) proposed in [1]. Several Bayesian filters like Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF) are used for latent state and parameter estimation. We employ a switching strategy proposed in [2] for adaptive state estimation of the non-linear, discrete-time state-space model (SSM) like Heston model. We use a particle filter approximated PCRLB [3] based performance measure to judge the best filter at each time step. We test our proposed framework on pricing data from S&P 500 and NSE Index, estimating the underlying volatility and parameters from the index. Our proposed method is compared with the VIX measure and historical volatility for both the indexes. The results indicate an effective framework for estimating volatility adaptively with changing market dynamics.

q-fin.CP↗

arXiv2021

Posterior Cramer-Rao Lower Bound based Adaptive State Estimation for Option Price Forecasting

The use of Bayesian filtering has been widely used in mathematical finance, primarily in Stochastic Volatility models. They help in estimating unobserved latent variables from observed market data. This field saw huge developments in recent years, because of the increased computational power and increased research in the model parameter estimation and implied volatility theory. In this paper, we design a novel method to estimate underlying states (volatility and risk) from option prices using Bayesian filtering theory and Posterior Cramer-Rao Lower Bound (PCRLB), further using it for option price prediction. Several Bayesian filters like Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF) are used for latent state estimation of Black-Scholes model under a GARCH model dynamics. We employ an Average and Best case switching strategy for adaptive state estimation of a non-linear, discrete-time state space model (SSM) like Black-Scholes, using PCRLB based performance measure to judge the best filter at each time step [1]. Since estimating closed-form solution of PCRLB is non-trivial, we employ a particle filter based approximation of PCRLB based on [2]. We test our proposed framework on option data from S$\&$P 500, estimating the underlying state from the real option price, and using it to estimate theoretical price of the option and forecasting future prices. Our proposed method performs much better than the individual applied filter used for estimating the underlying state and substantially improve forecasting capabilities.

q-fin.CP↗

arXiv2021

Deep Reinforcement Learning for Portfolio Optimization using Latent Feature State Space (LFSS) Module

Dynamic Portfolio optimization is the process of distribution and rebalancing of a fund into different financial assets such as stocks, cryptocurrencies, etc, in consecutive trading periods to maximize accumulated profits or minimize risks over a time horizon. This field saw huge developments in recent years, because of the increased computational power and increased research in sequential decision making through control theory. Recently Reinforcement Learning(RL) has been an important tool in the development of sequential and dynamic portfolio optimization theory. In this paper, we design a Deep Reinforcement Learning(DRL) framework as an autonomous portfolio optimization agent consisting of a Latent Feature State Space(LFSS) Module for filtering and feature extraction of financial data which is used as a state space for deep RL model. We develop an extensive RL agent with high efficiency and performance advantages over several benchmarks and model-free RL agents used in prior work. The noisy and non-stationary behaviour of daily asset prices in the financial market is addressed through Kalman Filter. Autoencoders, ZoomSVD, and restricted Boltzmann machines were the models used and compared in the module to extract relevant time series features as state space. We simulate weekly data, with practical constraints and transaction costs, on a portfolio of S&P 500 stocks. We introduce a new benchmark based on technical indicator Kd-Index and Mean-Variance Model as compared to equal weighted portfolio used in most of the prior work. The study confirms that the proposed RL portfolio agent with state space function in the form of LFSS module gives robust results with an attractive performance profile over baseline RL agents and given benchmarks.

q-fin.PM↗