Delta hedging is the most important parameter for hedging and it plays a crucial role in the management of portfolios of options. Option traders try to adjust delta to close to zero at least once a day by trading the underlying asset to acquire neutral hedging. Even though the Black-Scholes model assumes that volatility is constant, market participants calculate a practitioner Black-Scholes vega to measure and manage their volatility exposure.
According to Black-Scholes-Merton model, it assumes that the volatility is constant across option’s maturity. The Black-Scholes delta is calculated by the partial derivative of the option price with respect to the underlying asset price by keeping other things constant. However, in reality option prices vary across time implying that the Black-Scholes assumption was violated. As known from Black (1976) and Christie (1982) and many researchers, there is a negative relation between an equity price and its volatility in a sense that the underlying asset price moves up when the implied volatility moves down and vice versa. With Black-Scholes model, it does not take this negative relation into account. The BSM model will consequently not provide the position in the underlying asset with a minimal variance of hedger’s position. As a negative relation between an equity price and its volatility, many researchers try to reduce the limitation of Black-Scholes model to provide more accuracy on pricing model by incorporating the inverse relation into the option pricing model and try to provide the position that gives the minimum variance of the hedger’s position.
To calculate minimum variance delta, it is essential to use the model to determine the expected change in the option price resulting from changes in the underlying asset and expected change in its volatility. Switching from the practitioner Black-Scholes to minimum variance delta is desirable. There are two advantages. First, it lowers the variance of daily changes in the value of the hedged position. Second, it lowers the residual vega exposure because part of its exposure is dealt with the position that is taken in the underlying asset.
Main objectives are to test whether the results presenting in optimal delta hedging for options from Hull-White minimum variance hold true in terms of liquidity issue on THAI dataset compared to different approaches. By looking at Gain from these approaches -Hull-White minimum variance, and stochastic local volatility with respect to Black-Scholes. On liquidity issue with THAI dataset, we form the research hypothesis whether that Gain resulting from Hull-White minimum variance will be more pronouncing compared to Gain from stochastic volatility model.
We answer the research question that Gain from Hull-White methodology is more pronouncing than Gain from Stochastic volatility model for SET50 option dataset from 2016-2018.
Even though the Black–Scholes–Merton model assumes volatility is constant, market participants usually calculate a practitioner Black–Scholes vega to measure and manage their volatility exposure. It implies that market participants should under-hedge equity call options and over-hedge equity put options relative to the practitioner Black-Scholes delta.
From Hull-White Methodology, we find out that the maximum gain from Call option is on delta Black-Scholes at 0.1 which is for out-of-the-money around 22%. The maximum gain from Put option is on delta Black-Scholes at -0.7 which is for in-the-money around 16%.
From SABR Methodology, we find out that the maximum gain from Call option is on delta Black-Scholes at 0.1 which is for out-of-the-money around 12%. The maximum gain from Put option is on delta Black-Scholes at -0.9 which is for in-the-money around 11%.