Modern Option Pricing Models and Their Extensions

# Are there any new Option pricing models?


# Are there any new Option pricing models?












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 by Andrey Taptunov (score 26, accepted)

https://quant.stackexchange.com/a/88

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 by TheBridge (score 8)

https://quant.stackexchange.com/a/91

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 by allced (score 4)

https://quant.stackexchange.com/a/129

Maybe you think about other model than a diffusion ?

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

## Answer by JohnAndrews (score 4)

https://quant.stackexchange.com/a/8347

One I like is the Artificial Neural Network model with inputs the same as for the Black-Scholes model (hence Spot, Strike, Rate, Time to expiration, Dividend).

This is a modification of the Andreou et. al. (2008) framework who use hybrid artificial neural networks that incorporate information from the parametric models. Moreover, $Call = f(Call_{cs}, Call_{bs})$ where $f(.)$ is the hybrid network that links information from the parametric models with the prices $Call_{cs}$ (Corrado and Su, 1997) and $Call_{bs}$ (Black Scholes, 1973).

In the case I proposed, one can use the same hybrid networks $f(.)$ to incorporate information from the Black-Scholes inputs (Spot, Strike, Rate, Time to expiration, Dividend). Hence, $Call = f(Spot, Strike, Rf, T, Div)$.

This would allow for complex nonlinear relations. However, the approach may be sensitive to overfitting or other calibration issues.

## Answer by vonjd (score 3)

https://quant.stackexchange.com/a/8644

Option pricing is done under the risk-neutral measure, i.e. the drift term is the risk-free interest rate. Therefore the only degree of freedom to drive the underlying is the volatility. That is why volatility modelling for all (new) option pricing models is so crucial. You can find a good, concise and current overview here:

A Short Note on Volatility Models by Didier Kouokap Youmbi

Abstract:

> This document is a short summary regarding the evolution of the volatility models from Black and Scholes to the Local-Stochastic Volatility models. We show advantages as drawbacks linked to each model, and how the community has moved from one model to another in order to overcome drawbacks.

## Answer by berkorbay (score 3)

https://quant.stackexchange.com/a/11464

There is a whole family of GARCH option pricing models; ones with complex distributions, leverage effects, skewness parameters etc. For an example see Christoffersen and Jacobs (2004).

Some example GARCH models:

- NGARCH

- EGARCH

- TGARCH

Some distributions that can be used:

- Hyperbolic

- Normal Inverse Gaussian

- Variance Gamma

- and the generalized form Generalized Hyperbolic

## Answer by myoptionexpr (score 2)

https://quant.stackexchange.com/a/8034

- 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 .

- 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.

- The interaction of buy & sell orders within the volume is the propagator of price change.

- The use of truncated normal distributions in contrast to a log-normal distribution.

## Answer by Thomas Baert (score 2)

https://quant.stackexchange.com/a/24473

To the best of my knowledge, progress has been made in making pricing models more accurate, accounting for additional variables (stochastic vol. & GARCH, local vol., jumps, etc), but the option pricing equations fundamentally involve the same GBM framework, albeit they are much more complicated.

Off the top of my head, the only example I can think of something completely original is http://papers.ssrn.com/abstract=2412761 Here, option prices grow at $t^{1/4}$ instead of $t^{1/2}$

## Answer by user1157 (score 1)

https://quant.stackexchange.com/a/11469

There seems to be a tendency to include ever more risk factors into the models. CVA is a good example: based on credit default swaps it is possible to calibrate model parameters and include the risk of default into a Monte Carlo pricer.

The book Counterparty Credit Risk: The new challenge for global financial markets (Amazon) discusses counter party risk in detail.

For the implementation perspective: Mathworks has a nice practical discussion of counterparty credit risk and CVA including example code.