Derivatives Pricing Question

[miggety]

Hey All, This is my first post on these boards, so here's a quick little blurb about me and then i'll dive into my question. I majored in Applied Mathematics (years ago) worked as a developer for the past 7years and then just recently got a job with an investment company. Since starting i've been trying to absorb as much as possible both on the jobs and through a pretty extensive collections of books that I've purchased over the course of the last 2 months. Pretty much every book i've purchased (Shreve, Neftci, Hull, etc.) has heavily covers derivatives pricing and i'm wondering exactly how this information is used.

Once a price for say an option is derived from either a Black-Scholes model or a Binomial Model how does this information factor into an investment decision? Is this information being used by everyday investors and in what way? Do these models spit out a fair price for a derivative and then investors use this information to find derivatives that are mispriced? Also does everyone who uses these models arrive at the same price based on similar parameters or is there some subjective component to these models that allows people using say the Binomial to arrive at completely different outcomes for the same asset?

Overall, i'm just beginning to wrap my head around these concepts but am having difficulties seeing the entire process of how the information in these derivatives pricing models are used. If anything in my question doesn't make sense, just let me know and i'll clarify, this is all really new to me.

Thanks,

 

[Yike Lu]

The typical use for pricing exotics is at IBank options trading desks. A client calls up a bank and wants some type of exotic (Asian option, barrier, etc) and the desk makes him a price which he can then choose to trade on. So the bank desk uses a model but the client may or may not, although the client probably should to at least make sure he's not getting screwed.

Once the price is made and the client makes the trade, the bank desk then hedges the Greeks, typically by transacting in the vanilla markets.

There are certainly other use cases of pricing, the major one to come to mind is options market making, but probably the most typical one is at a bank's trading desk.

 

[financeguy]

basically agree with Yike Lu
also address your point about subjectivity in model choice
normally all banks use pretty similar models to value these exotics.. in addition to the customer market, in standard exotics there are active broker markets in which banks can trade with each other.. so each bank can calibrate their models to the prices they observe in the broker market as well as the information they get from customers (which is normally limited at best, dishonest at worst).. also the less commonplace / bespoke derivatives are normally made from those standard exotics and vanillas as building blocks, so given that every bank is able to calibrate their exotic models to the prices in the market, they should come up with similar prices for the more funky stuff as well.. this is NOT always the case however and a lot of the time banks can have very different prices for complex products, usually more so for products which are difficult to calibrate to flow exotics and vanillas, so that will come down to what specific model you're using

 

[DoubleTrouble]

Also, derivative pricing is not a very interesting topic on the market. What is interesting on the market is to hedge derivatives in various models.

 

[ganigorkem]

agree with Yike Lu but to add some more, every bank, every option trading desks have different perceptions of the market even though they have the same information. Black-Scholes-Merton might not give a fair price for that option, because of the information factor. due to this, "the modelers" put in their own intuition in play, and thats where information goes in. look up implied volatility...

 

[miggety]

Thanks a lot guys, this is extremely helpful information, it really cleared up a lot of questions I had. I'm still trying to see the big picture and this will go a long way towards getting me to that point. One question I do have is concerning DoubleTrouble's reply about hedging derivatives in various models, i'm still too new to fully understand what that means. Could any of you point me to some books or sites that would cover what some of those models are or just anything related to that topic. Thanks again!

 

[marina]

Pretty much every book i've purchased (Shreve, Neftci, Hull, etc.) has heavily covers derivatives pricing and i'm wondering exactly how this information is used.

what type of derivatives you are working on? in equity derivatives, most of the retail traders don't bother about mispricing. they use it mainly for speculation. take a look at this book to know how retail traders use options
http://www.amazon.com/Options-Trading-Perception-Deception-expanded/dp/0977869172/

 

[miggety]

Hey Marina, Thanks for the link I just put that on my wishlist will definitely purchase in the next day or so! As for my job, I work for a fixed income investment firm we use credit derivatives (mainly credit default swaps) to value CLO's. I'm working as part of a team where everyone else has extensive knowlegde about this stuff, so I try to play catch up at nights and on the weekends reading whatever I can get my hands on. Technically, i don't work with options (where i'm guessing Black-Scholes and the Binomial model are used most) but since many of the books I've bought cover that, it's curiosity really that's driving me to understand it.

For me I've never really done any investing so when I come across a new concept, like options pricing, I try to think of how I would use it if I were say a managing a portfolio. If i can understand how I would use it in that context, it helps drive home the concept a little bit better for me.

 

[Yike Lu]

Black-Scholes is great for intuition, but for actual pricing it is way too simplistic. Pricing is primarily not used for managing portfolios, it's used to trade options, (i.e., to make sure you are not getting screwed on the trade).

Hedging is very important since option positions have multiple exposures (i.e. ways to lose or make money). E.g., you're long a call, stock could go up/down, vol could go up/down, and you're bleeding time value every day. Market makers and bank desks run options trading businesses not for speculation, so hedging is imperative to their business model.

 

[miggety]

Thanks Yike Lu. I'm just starting to understand the limitations of Black-Scholes. Right now I'm at a point where i'm learning a lot of these different techniques. I think right now one of my main hurdles is in the application. When are certain techniques used? How do I identify situations that call for a specific model? For example When would I use GARCH, Monte Carlo, Black-Scholes, Binomial Model, etc. and what information exactly are they giving me? How are they used together I'm sure it'll come in time but for right now, i still have a lot to learn.

 

[KaiRu]

I think you should start from FAQ in Quant Finance by P.Wilmott.
All your questions which you've mentioned above are answered in this book.

 

[miggety]

Thanks KaiRu that looks like a great resource, i just put that on my "to buy" list. Like I mentioned earlier i still have a very long way to go but the feedback i got on this thread was huge help. Much thanks to everyone.