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# Can the Delta be used to calculate the option premium given a certain target?

2018-10-19 05:01:00

I’m struggling for a while now with a question about options, namely 'which is the best option to buy?'. I have various books on options, but I’m not an mathematician and don’t have (yet) any extensive hands-on experience with options.

According to Cohen (Options Made Easy, 2nd Edition), the Delta of an option is the “change in option price relative to the change in underlying asset price”. He goes on to give an example of an option with an Delta of 0.5 which moves \$1, in which case the premium of the option will increase with 0.50 (call) or decrease with 0.50 (put).

Even though Delta’s of options are changing with each change to the various components which make up an option premium, I’m wondering if a Delta can be used to determine the premium of an option given a certain target.

For example, let’s say stock XYZ trades at 50 dollar and we have an price target of +10% (so the share price of XYZ increases to 55 dollar; +\$5). Let’s say an option’s current premium is 2.

• In a simple world yes, but not in the real world. Option pricing isn't that simplistic in real life. Generally option pricing uses a Monte Carlo simulation of the Black Scholes formula/binomial and then plot them nomally to decide the optimum price of the option. Primarily multiple scenarios are generated and under that specific scenario the option is priced and then a price is derived for the option in real life, using the prices which were predicted in the scenarios.

So you don't generate a single price for an option, because you have to look into the future to see how the price of the option would behave, under the real elements of the market. So what you price is an assumption that this is the most likely value under my scenarios, which I predicted into the future. Because of the market, if you price an option higher/lower than another competitor you introduce an option for arbitrage by others. So you try to be as close to the real value of the option, which your competitor als

2018-10-19 05:35:21
• One thing I would like to clear up here is that Black Scholes is just a model that makes some assumptions about the dynamics of the underlying + a few other things and with some rather complicated math, out pops the Black Scholes formula. Black Scholes gives you the "real" price under the assumptions of the model. Your definition of what a "real" price entails will depend on what assumptions you make. With that being said, Black Scholes is popular for pricing European options because of the simplicity and speed of using an analytic formula as opposed to having a more complex model that can only be evaluated using a numerical method, as DumbCoder mentioned (should note that, for many other types of derivative contracts, e.g. American or Bermudan style exercise, the Black Scholes analytic formula is not appropriate). The other important thing to note here is that the market does not necessarily need to agree with the assumptions made in the Black Scholes model (and they most certainly

2018-10-19 06:20:15