Best Options Formula
- Thread starter aphexcoil
- Start date
"Best" is kind of subjective. If you are asking which one is the most accurate, I would think it's the cox/rubenstein model, but it's difficult to work with. If you are asking for the easiest one to work with, I would say Black Scholes. When you consider the difference in accuracy between the 2 models, and the amount of effort both require, most retail traders work with Black Scholes. Check me on this because I'm not absolutely sure.
Best for what kind of options? equity? fx? futures? But in general, the main two impovements are
1. Using a yield curve, not constant rate as an interest rate. It is probably most reasonable to use LIBOR rather then treasury, but I am biased there.
2. Using a local vol model (Dupre/Derman-Kani) Local volatility is basically the concept of forward volatility (which is dependent on t only) extended to also depend on the price of the underlying S.
Alternatively, using some sort of stochastic vol model (Lebner, Levin-Chin, SABR) but they are too complex to discuss here.
If we are talking equity, for Europeans, it is still old and trusted BS with some minor adjustments. For Americans - most people are using numerical methods for American: binomial, trinomial, finite grid etc. To much stuff to go into detail. What exactly do you want to price and hedge?
1. Using a yield curve, not constant rate as an interest rate. It is probably most reasonable to use LIBOR rather then treasury, but I am biased there.
2. Using a local vol model (Dupre/Derman-Kani) Local volatility is basically the concept of forward volatility (which is dependent on t only) extended to also depend on the price of the underlying S.
Alternatively, using some sort of stochastic vol model (Lebner, Levin-Chin, SABR) but they are too complex to discuss here.
If we are talking equity, for Europeans, it is still old and trusted BS with some minor adjustments. For Americans - most people are using numerical methods for American: binomial, trinomial, finite grid etc. To much stuff to go into detail. What exactly do you want to price and hedge?
My main objective right now is to look at an option (Let's take MSFT 2005 $30 CALL) and be able to:
a) Compute what the implied volatility is
b) Compute the Delta
c) Compute the Gamma
I'd like to do it for a few option models, not just the BS but some of the other ones. I'm mainly concerned with American style options at this point.
Thanks.
a) Compute what the implied volatility is
Ok, implied vol tracks back to the issue of using either local volatility models or stochastic vol models. For the local vol model, Derman/Kani paper has all the answers, but it is not trivial to implement. In terms of stochastic vols i recommend using SABR - it produces very stable hedges and very pretty fits into the actual vol skew.
b) Compute the greeks
Well, since you are mainly interested in americans, I would use a good bi- or tri-nomial tree model - they allow you to account for all sorts of little things, for example dividends are easily modeled by "shifting" the tree (read - adding dividend amount to the nodes after/at the dividend point). They are not trivial to implement, but as soon as you have a tree pricer working, any exotic options (with exception of some path dependent ones, like asians) can be priced with it. Alternatively, you can use PDE appoach to american option pricing, but that is even more involved and tricky.
Ok, implied vol tracks back to the issue of using either local volatility models or stochastic vol models. For the local vol model, Derman/Kani paper has all the answers, but it is not trivial to implement. In terms of stochastic vols i recommend using SABR - it produces very stable hedges and very pretty fits into the actual vol skew.
b) Compute the greeks
Well, since you are mainly interested in americans, I would use a good bi- or tri-nomial tree model - they allow you to account for all sorts of little things, for example dividends are easily modeled by "shifting" the tree (read - adding dividend amount to the nodes after/at the dividend point). They are not trivial to implement, but as soon as you have a tree pricer working, any exotic options (with exception of some path dependent ones, like asians) can be priced with it. Alternatively, you can use PDE appoach to american option pricing, but that is even more involved and tricky.