The problem is that it is not as simple as just trying a different pdf. For example, you have to make sure of the no-arbitrage condition when you are "playing around". Also, there are really three models (sort of) Risk: Hedge: Pricing: I am telling you, if you are asking on ET for this, you are going to get in trouble because this requires lots and lots of academic background (or at least exposure to a model that works and you understand). For example, drastically different models are used for IRs: FX: Stock Indexes: Equities: Commodities: The way you asked your question shows a lack of even this trivial understanding. In addition, being able to price a surface or even a single month requires expensive data feeds to do in realtime, assuming you have the software infrastructure already in place! Even if you try it on historical data, the historical data is expensive. It is truly hard.
Can't hide the truth from you. You are correct about my lack of understanding of finance especially derivatives. Here is my situation: I own and traded ~10 stocks since I started investing many years ago. I only started trading options on these same stocks since 2013 and have a very modest goal: I want to do better than just buy and hold these stocks. I am quite profitable trading options but I attributed that to dumb luck as I think even a monkey can make money in 2013-2015. So, starting about a year ago, I joined ET, and I played with Black Scholes to get a feel on how things behaved when the basic parameters changed and how pricing and outcome changed with those parameters. Knowing BSM is just a first order approximation, I am now trying to go beyond BSM to get to the next level of detail causes/effects. Any help you folks are willing to give is greatly appreciated. What is your advice on where I go from here? Thanks again for your response. Regards,
Well that narrows things down considerably. So you need an American Options model for equities. But I don't understand your question. If you are long/short equities, why on earth do you want to worry about the [Way OTM options] tails? What do you expect to do with them? I don't understand how you expect to use an option model to trade underlying by worrying about tails. Or maybe you are just planning to trade options directly and not the underlying? Almost all retail traders that I know just trade the underlying, and then have some sort of options bracketing that position either to roll it, earn extra money, or to limit risk. Way out of the money options are lottery tickets. MMers need to worry about them so they know how to price them to hedge [usually] with something that closer to ATM, but retail traders that don't have a HUGE time horizon should avoid them, imo.
Market makers worry about this stuff because their edge is in the precision of their model to determine fair value. Their expectation to that fair value is on the order of a few pennies assuming they aren't on the wrong side of informed order flow. As a small buy side trader, your goal should be that informed order flow and trade where a super precise model isn't necessary. There aren't many but you can always find a few.
Let me explain: I always long those equities but in the past the percentages of each sometimes changed based on my view of their performances. Since 2013, I changed my strategy, I kept my positions fixed but adjusted my positions with long/short options (sort of delta hedge). I think I need a better tool to analyze the long/short option prices as I found using BSM was often not good enough. When I went short calls/puts, for example, I got killed by big many standard deviation moves that lognormal said would never happen. I thought a model with fat-tails would give me better handles? Thanks for taking the time to answer my questions.
Your problem isn't black scholes. It's not understanding the underlying or not understanding the trading dynamics. You should know your underltings better than the market makers.
You think that is possible? He/she trades it for a living, and I a part timer. He/she sits in an office surrounded by million dollar computer systems and I am sitting in my small kitchen using a 10 year old laptop with a discounted slow dsl line. Maybe I am asking too much.