Are there any new Option pricing models?

Question

Back in the mid 90's I used the Black-Scholes Model and the Cox-Ross-Rubenstein (Binomial) Model's to price Options. That was nearly 15 years ago and I was wondering if there are any new models being used to price Options?

Answer 1

Black-Scholes itself didn't change a lot but we can now adjust it to deal with a lot more complicated factors to price more complicated contracts:

• stochastic volatility (Heston, Gatheral)
• stochastic rates (Hull)
• credit risk
• dividends

Other methods (computing intensive) have also evolved to deal with various types of contracts where BS is not very appropriate choice (e.g. Monte Carlo simulation for path-dependant options).

Answer 2

There are plenty of other models

You can also add all the exponential Lévy processes with or without time change and also other stochastic volatility models such as SABR.

I must add that there exist a paradigm different of the "risk neutral pricing" (mainly developped by Platen and Heath) called "Benchmark Pricing" and which is in a way (that I do not fully understand yet), more general than "Risk Neutral paradigm". The biggest problem being that calculation and determination of the benchmark protfolio doesn't seem easy to achieve in this "supermartingale framework".

Regards

Answer 3

Maybe you think about other model than a diffusion ?

There is an article on wilmott.com about the Korn-Kreer-Lenssen Model.

Answer 4

1. The introduction of 'volume endowed' shapes that represent support and resistance forces. Theoretical paths in , unlike in Brownian motion are either strictly monotonically increasing, flat, or monotonically decreasing and obey the equilibrium equation with an inverse relation between LHS resistance/support forces and .
2. Volatility in chart to scalar is a combination of variables such as the geometric properties of the LHS resistance/support forces, change in price, trade size, and volume.
3. The interaction of buy & sell orders within the volume is the propagator of price change.
4. The use of truncated normal distributions in contrast to a log-normal distribution.