I have calculated all options prices, including, delta, IV, IV skew, gamma, vega, vomma, vanna, veta, charm, color etc using the Black Scholes model, I know how vomma, veta, vanna affects the vega, the gamma affects the delta. The IV affects one another 1% up and down. I have implemented them all in C# so I am ready to hear and understand the explanation you have.
If you actually understand how volatility impacts option price then then you understand why you would always sell rather than exercise early. I mean let's make this simple for you, if the option is trading above intrinsic value and you exercise, you just gave away the entire amount that the option was trading above intrinsic. Why in the world would you do that instead of simply selling it? You're essentially saying "I could sell this for $1.00 or exercise it and get $.90 so I'm going to exercise it If your question is why options trade above intrinsic, it's because the expected value of the expiration value is positive. If you look at a distribution curve and realize that you have no downside below strike, then owning the entire upper half of that probability distribution has a value of its own. That's what option buyers are paying for when they pay more than intrinsic value. If you get probability you'll more or less intuitively get that. If you actually understand the derivation of the BS formula, which is a lot different than plugging it into a C# program, it's intuitive as well.
Thanks Sig, I am afraid that I have missed some basic. Before reflecting your good answer there, I was just reading this on google: So I must ask this basic question. One who has bought an option. Does this person have 2 choises like below? - Sell the option (which means that no shares are given and results in no position at all. Simply if do a comparion, just like buying a stock and selling a stock for a profit or loss? ) - Exercise the option (which means that shares are given to the person at the strike price)
You're correct for American options, you can either sell them or exercise them. European options can only be exercised at expiration but can be bought and sold at any time. It's a bit random which options are which (it has nothing to do with if they're sold in the U.S. or Europe), but valuation is almost the same absent a big pending dividend.
Then I understand. I was not 100% sure of that you could only sell the option once you had it. I think that was the thing which confused me. Sorry for my confusion.. So with the above, then I think I understand. What you mention about "giving" away is the timevalue above the intrinsic value which makes sense? I think I then wonder. If I write/sell an option which someone buy. What happens if that person sell the option, - will I then just be in a flat position rather than giving him/her the shares and will I in this scenario keep the premium(I don't think I will keep the premium?) If I would become in a flat position, this also means that I lost money/locked in a loss against my will because the option buyer sold of the option?
When you sell an option the premium is yours forever. If the current holder ever exercises you're obligated to provide the underlying, except for cash settled options like SPX where you just end up settling in cash at expiration.
Allright... here's a quick rundown. The implied volatility controls a large part of options. And basically all of it for OTM and ATM. When IV is 0, there is only intrinsic value and for OTM and ATM that intrinsic value is zero. So, firstly you need to understand the difference between 'intrinsic value' (which is determined by difference of the strike price and current stock spot price) and 'time value' (which is basically the premium for chance of being ITM). Together they are the premium you pay to buy the option. The implied volatility is set by the market participants, usually initially that's the market makers. It changes continuously based on what the market wants. If there are more buyers, IV goes up. Sellers push IV down. IV also kinda determines the reach of the normal distribution curve, which basically determines the chance of an option becoming ITM. If an option is really far OTM, it has almost 0% chance of becoming ITM and therefore has zero time value. The ITM equivalent (same strike opposite) has also that same relation, but then 100%. If the OTM put has 0% chance, the ITM call has 100%. If the IV is really high, that chance of becoming ITM will be higher, so with IV of 20 the put has 0% and zero value. With IV of 200, it maybe has 4% chance and 0.15 value. So coming back to your example. With 30 days to go, spot at 104 and you own the 103 call... that call has a value of: intrinsic value = 1.00 time value = 1.94 total premium = 2.94 If you exercise now, you lose 1.94 in time value... so don't exercise now. That's with a vol of about 20. If IV is say 40: intrinsic value = 1.00 time value = 3.40 total premium = 4.40 If you exercise now, you lose 3.40 in time value... so don't exercise now. The 103 call might have zero time value if if spot is trading at $110 and the IV is 7 (which is ridiculously low for a stock). But even then, there's no reason to just exercise the call since it might still get a chance to be ITM, however small it is. If you want to stay long, keep it. If you want to be neutral/0 delta, look at selling 100% stock. If all that doesn't work for you. Then either exercise and sell the stock at the same time. Or, try to sell the call at intrinsic value (which usually is not the bid!). So key to understand how implied volatility works with options prices, is understanding chances of becoming ITM/probability curves.
You would still have the same position, unless you were the one he sold it to.... which is not likely. Usually he/you/we all sell/buy against market makers...