# A decent model to calculate hedges

Is there an option pricing model that wouldn't be too time consuming to set up in Python (for example) and that would provide better delta hedges than Black-Scholes? This would be mainly for equity options.

• What kind of equity options? Why are you dissatisfied with BS? What are your criteria for "better" delta hedges? May 10, 2021 at 1:46
• I trade options on the popular stocks. My main concern with BS is that it does not take into account the smile/skew, so any model that would take that into account I'm assuming is going to give a better/more stable hedge.
– Alex
May 10, 2021 at 2:00
• You can incorporate the skew in a simple ad hoc fashion by calculating the total derivative of the BS formula with respect ot the underlying, i.e. calculate $\frac{d O}{dS}=\frac{\partial O}{\partial S} + \frac{\partial O}{\partial \sigma}\frac{\partial \sigma}{\partial S}$, and you plug in some interpolation of the smile. May 10, 2021 at 6:13

You sometimes can’t have both simplicity and robustness.However,the Heston Model analytical solution shouldn’t take you too much time to code but isn’t a great one,mainly because the volatility is not a diffusion/super-diffusion.Newer and more complex models like rough volatility models are closer to the reality but their generation is still not efficient enough to allow very fast computation.But you can still try them even if the analytical closed forms are hard to code for you.You can still use a Monte-Carlo generation (rough volatility models are martingale so we remove the drift for the volatility process)

Certainly! The Black-Scholes model, while pioneering and foundational, is based on several simplifying assumptions that might not hold in the real world. One of its main assumptions is that volatility is constant, which is often not the case. Several models have been developed to address its limitations.

One such model that's relatively straightforward to implement and provides more realistic dynamics than Black-Scholes is the Binomial Option Pricing Model. This model is particularly useful for American-style options, which can be exercised before the expiration date.

Binomial Option Pricing Model: The binomial model breaks down the time to expiration into potentially very many time intervals, or steps. In each step, the stock price can move up or down. The model then computes the option value at each step, starting from the expiration date and working backward to the present.