Computing European Option Greeks with Zero Dividend Yield

Summary

For European call and put options in a model that includes a continuous dividend yield, the zero-dividend case can be obtained by setting the yield parameter to zero. The response also points to a separate list of formulas, though it does not reproduce those formulas or identify the pricing model behind them.

The answer cautions that Greeks depend on the model: stochastic-volatility extensions such as Heston produce different values. It also describes finite differences as a numerical way to approximate a Greek, illustrating delta with the change in option value around the current underlying price divided by the price interval. No comparison, empirical evidence, or treatment of numerical error is provided, so the guidance is a basic model-specific shortcut rather than a full derivation.

Key ideas

• Setting dividend yield to zero in a model with a yield parameter gives its no-dividend case.
• Greeks depend on the pricing model, and extensions such as stochastic volatility change their formulas.
• Finite differences can approximate delta by measuring option-value changes across a small underlying-price interval.

Tags

# Where can I find the formulas to compute the Greeks for European Call and Put Options Assuming no annual dividend yield?


# Where can I find the formulas to compute the Greeks for European Call and Put Options Assuming no annual dividend yield?












Every formula I come across involves a $q$ (the annual dividend yield). Where Can I find the formulas to compute the greeks assuming no dividends?

## Answer by Kevin (score 1)

https://quant.stackexchange.com/a/46621

As Nap D. Lover said, here you have a list without any dividends being considered. It all depends on your model though. If you are using a stochastic volatility model or similar extensions, you get different Greeks. For the Heston model, for instance, see Chapyer 11 in here. In general however, if you have formulae including a dividend yield $q$, just use the value $q=0$ and you get the case you need. Note that it also always possible to approximate Greeks using a finite differences, e.g. $$ \Delta(t_0,S_0) \approx \frac{V_{t_0}\left(S_0+\frac{1}{2}h\right)-V_{t_0}\left(S_0-\frac{1}{2}h\right)}{h}.$$

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