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Description
The Black-Scholes model for pricing European call options relies on continuous delta hedging with prices distributed log-normally with a known, constant volatility. This only works in a perfect, "frictionless" market. We simulate cumulative returns for a market maker using a discrete delta hedge with different time intervals between rebalancing the portfolio. A Julia package is developed by the authors to achieve this goal, which will be open source for the benefit of the public. Using the Julia package, we estimated the distribution of cumulative returns for a delta hedged portfolio by Monte Carlo analysis. This is done using both a log-diffusion parametric model and stationary bootstrap of historical returns for simulated stock prices. With both the parametric and non-parametric models, as the time between rebalancing the portfolio decreases, the variance of the returns decreases, while the expected return is near 0. This provides empirical evidence that a Black-Scholes delta hedge is a viable hedging strategy for helping market makers to better manage and quantify their risk, even given market "imperfections".
Publication Date
12-6-2022
City
Logan, UT
Keywords
Black-Scholes model, continuous delta hedging, European call options, return variance
Disciplines
Social and Behavioral Sciences
Recommended Citation
Pound, Mitchell, "Black Scholes Delta Hedge in Imperfect Markets" (2022). Fall Student Research Symposium 2022. 57.
https://digitalcommons.usu.edu/fsrs2022/57