arXiv subjects

Jay Cao

Publications and source records attributed to Jay Cao.

3 recordsLinked to original sources

arXiv2022

Gamma and Vega Hedging Using Deep Distributional Reinforcement Learning

We show how D4PG can be used in conjunction with quantile regression to develop a hedging strategy for a trader responsible for derivatives that arrive stochastically and depend on a single underlying asset. We assume that the trader makes the portfolio delta neutral at the end of each day by taking a position in the underlying asset. We focus on how trades in the options can be used to manage gamma and vega. The option trades are subject to transaction costs. We consider three different objective functions. We reach conclusions on how the optimal hedging strategy depends on the trader's objective function, the level of transaction costs, and the maturity of the options used for hedging. We also investigate the robustness of the hedging strategy to the process assumed for the underlying asset.

q-fin.CP↗

arXiv2021

Deep Learning for Exotic Option Valuation

A common approach to valuing exotic options involves choosing a model and then determining its parameters to fit the volatility surface as closely as possible. We refer to this as the model calibration approach (MCA). A disadvantage of MCA is that some information in the volatility surface is lost during the calibration process and the prices of exotic options will not in general be consistent with those of plain vanilla options. We consider an alternative approach where the structure of the user's preferred model is preserved but points on the volatility are features input to a neural network. We refer to this as the volatility feature approach (VFA) model. We conduct experiments showing that VFA can be expected to outperform MCA for the volatility surfaces encountered in practice. Once the upfront computational time has been invested in developing the neural network, the valuation of exotic options using VFA is very fast.

q-fin.CP↗

arXiv2021

Deep Hedging of Derivatives Using Reinforcement Learning

This paper shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The paper illustrates the approach by showing the difference between using delta hedging and optimal hedging for a short position in a call option when the objective is to minimize a function equal to the mean hedging cost plus a constant times the standard deviation of the hedging cost. Two situations are considered. In the first, the asset price follows a geometric Brownian motion. In the second, the asset price follows a stochastic volatility process. The paper extends the basic reinforcement learning approach in a number of ways. First, it uses two different Q-functions so that both the expected value of the cost and the expected value of the square of the cost are tracked for different state/action combinations. This approach increases the range of objective functions that can be used. Second, it uses a learning algorithm that allows for continuous state and action space. Third, it compares the accounting P&L approach (where the hedged position is valued at each step) and the cash flow approach (where cash inflows and outflows are used). We find that a hybrid approach involving the use of an accounting P&L approach that incorporates a relatively simple valuation model works well. The valuation model does not have to correspond to the process assumed for the underlying asset price.

q-fin.CP↗