Transaction costs prevent firms and individuals from fully hedging all financial risks
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Peer-reviewed economic and financial literature demonstrates that nonzero transaction costs invalidate standard continuous hedging models, necessitating modified strategies to account for these market frictions.
Nonzero transaction costs invalidate the Black-Scholes (1973) arbitrage argument based on continuous trading. Leland (1985) developed a hedging strategy which modifies the Black-Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Leland claimed that the exact hedge could be achieved in the limit as the length of rebalance intervals approaches zero. Unfortunately, the main theorem (Leland 1985, P1290) is in error. Simulation results also confirm opposite findings to those in Leland (1985). Since standard delta hedging fails to exactly replicate the option in the presence of transaction costs, we study a pricing and hedging model which is similar to the delta hedging strategy with an endogenous parameter, namely the volatility, for the calculation of delta over time. With transaction costs, the optimal hedging volatility is substantially different from the stock's volatility under the criterion of minimizing the total absolute replication error weighted by the probabilities that the option is in or out of the money. This model provides a close explanation of the skewness of the implied volatilities for equity options. As a special case, option prices from our model are identical to the Black-Scholes option prices when transaction costs are ignored. Data on S&P500 index cash options from January to June 2002 are used to illustrate the model.
In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: We extend the framework developed by Davis, Panas and Zariphopoulou (1993) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whaley and Wilmott (1994). We provide a simulation analysis in order to compare the performance of the utility based hedging strategy against the asymptotic strategy and some other common strategies.
This paper investigates the use of reinforcement learning (RL) algorithms to learn adaptive hedging strategies for derivatives under realistic market conditions, incorporating permanent market impact, execution slippage, and transaction costs. Market frictions arising from trading have been explored in the optimal trade execution literature; however, their influence on derivative hedging strategies remains comparatively understudied within RL contexts. Traditional hedging methods have typically assumed frictionless markets with only transaction costs. We illustrate that the dynamic decision problem posed by hedging with frictions can be modelled effectively with RL, demonstrating efficacy across various market frictions to minimize hedging losses. The results include a comparative analysis of the performance of three RL models across simulated price paths, demonstrating their varying effectiveness and adaptability in these friction-intensive environments. We find that RL agents, specifically TD3 and SAC, can outperform traditional delta hedging strategies in both simplistic and complex, illiquid environments highlighted by 2/3rd reductions in expected hedging losses and over 50% reductions in 5th percentile conditional value at risk (CVaR). These findings demonstrate that DRL agents can serve as a valuable risk management tool for financial institutions, especially given their adaptability to different market conditions and securities.
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