Hi Sandor,
I don't have access to the section of core reading you quote. Nevertheless;
1. Your comment is difficult to discern exactly. Some comments: A (long) call option increases when the underlying increases. A (long) put option increases when the underlying falls.
- The delta of the call option gives you information on how much the option's price will increase following a unit increase in the underlying.
- The delta of the put option gives you information on how much the option's price will increase following a unit decline in the underlying.
The intrinsic part of an option's price will move 1-1 with changes in the underlying. The time value component of the option is what generates the non-linearity between changes in an option's price and the underlying. In other words, it's the time value component that results in an option's price not moving perfectly in line with movements in the underlying.
Does this help? If it doens't, it could be worth uploading the specific part of the core reading you're looking at.
2. Let's use the following example. Stock price = 100, strike (K1) = 85, strike (K2) = 90.
It follows that the price of a call option with K1 strike will always cost more than a call option with K2 strike. The call (K1 strike) will cost at least 15 whilst the call (K2 strike) will cost at least 10.
Even in a scenario where both options had zero time value the statement must hold - otherwise there would be an easy arbitrage.
3. Could you clarify the question? The main benefit of sensitivities are to give you a feel of your exposure to changes in variables of interest.
I (and others - particularly those without access to the notes being referred to) could be more help if you provide a little more background / context to your queries
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