UNIVDRV - Universal Derivatives Add-in
UNIVDRV - Universal Derivatives Add-in comprises three integrated algorithm libraries :
UNIVDRV was developed by MBRM as a result of MBRMís Research and Development on some common problems encountered with the pricing and hedging of European and American style options, e.g. options with :
Standard methodology for option pricing, when the above situations are encountered, can result in pricing functions with poor stability and/or pricing/hedging biases. This is due to two main reasons:
Apart from handling all the above option characteristics, UNIVDRV is capable of :
UNIVDRV is implemented as function calls in a Dynamic Link Library (DLL), thus assisting in the ease of use and integration into the user's analytical environment. It can therefore be called from Excel, Access, Visual Basic, C, C++, Fortran etc. This object-orientated building-block approach provides unequalled speed, cost-effectiveness and flexibility. The software can be linked with most real-time feeds to provide a dynamic analytical environment.
1.2. The three models contained in UNIVDRV
Although UNIVDRV is an integrated package, the algorithms (theoretical models) may be grouped into three categories:
UNIVFDIF calculates the option price and the full set of sensitivities of European, American style and Bermudan variable strike exotic options (including discrete windowed and double barriers) on bonds, commodities, currencies, energy, futures and shares (with discrete dividend payments).
Exotic options with discrete monitoring of the underlying are valued accurately with the ability to specify the window (i.e. the time of the first and last sampling point/price check) and the number of sampling points/price checks inside the window.
Another interesting feature of the model is the way it handles windowed boundaries, term structures and discrete dividends thousands of times more efficiently than Monte Carlo, especially in calculating the sensitivities.
The implemented finite difference model has exceptional stability and flexibility. It is very effective in pricing/hedging discrete exotic options regardless of the frequency of monitoring of the underlying, from a single price-check to almost continuous monitoring.
The level of accuracy required is a parameter of the pricing function. Usually the three or four most significant digits of the option price are obtained almost instantaneously. Delta, Gamma, Fugit and Theta are calculated with the same accuracy as the option price.
These are the options that UNIVFDIF can handle:
As previously mentioned, for every option the user may also define:
This implements the latest research papers, combined with MBRMís internal R&D, on the analytical pricing of exotic options (i.e. with formulas or special algorithms).
These are the options that the Analytical extension to UNIVEXOT can handle:
Monte Carlo pricing of a range of Exotic options of European style handling the term structures of volatilities and interest rates, discrete dividends, windows. UNIVGARCH can assume that the underlying follows either the usual Geometric Brownian Motion or a GARCH process.
The non-uniform time stepping of the Monte Carlo simulator (the same principle as the finite difference) allows the most flexible and efficient handling of term structures, windows and discrete dividends; while variance reduction techniques further increase the speed/accuracy ratio.
GARCH Option Pricing allows risk-neutral option pricing. With its fat-tailed and asymmetric return distribution it is successful in correcting well known biases of the Black-Scholes formula when the option is out-the-money or short-to-maturity. It is particularly effective in measuring the impact of abnormal returns, sudden changes of volatility, and in anticipating changes of option price on a daily basis, especially in frequently changing markets or when assets do not follow a perfect log-normal distribution.
UNIVGARCH implements many other useful functions for the pricing and hedging of options. E.g. a simulator that shows Monte Carlo simulations of prices or volatilities from the same inputs (and with the same flexibility) as the pricing function. Also implemented is an "estimator" function to imply the GARCH volatility parameters from historical prices using an optimised proprietary algorithm, and a function to calculate the expected forward volatility over a short (or long) time horizon.
These are the options that UNIVGARCH can handle:
1.3. Confidence in the result
All the above pricing/hedging models are accessible through the same function by simply changing the model number, enabling immediate comparisons between random walk, GARCH, analytical and finite difference pricing of the same option. This enables the user to choose the model with the speed/accuracy ratio that best suits his needs and also boosts confidence in the result.
The following graph shows the implied spot-forward local volatility surface for all the European options on the FTSE-100 on the 30th of September 1998.
Gaps in the volatility grid due to missing options are filled in with a special algorithm and the user has the option to smooth the surface with an MBRM proprietary filter.
The user also has the option to display a forward-forward local volatility surface.
The software has the remarkable ability of the to fit both calls and puts at the same time, even if they appear to have different implied volatilities for the same strike & maturity date. This is achieved by the simultaneous fitting of both an implicit underlying and an implicit interest rate for each maturity, as shown in the following table:
(the user has the option to disable this "implicit" fitting of the underlying and the interest rates).
When choosing between the Garch and Black-Scholes models, two main facts should be considered. The GARCH process is a more parametric, accurate and flexible description of the time behaviour of real assets and, consequently, Garch is effective in correcting known pricing biases of the Black-Scholes formula. On the other hand, historical estimations of the properties of real assets have often been proven to have inferior predictive power than implied estimations from quoted option prices.
There is not, unfortunately, an analytical expression for the distribution of the return on an asset that follows a standard GARCH process. However, as shown via simulation, such Garch distributions can be skewed and leptokurtic. Therefore, Garch is able to fit the real world asset price behaviour (which do show skewness and leptokurtosis) better than a standard Black-Scholes formula.
The Black-Scholes model (when using a single volatility for all options) is known to frequently under-price both out-the-money and short-to-maturity options.
Moreover, GARCH can reproduce the term structure of implied volatilities (the "smile family"). Consider a set of options with different strike prices, then price each of them with Garch, and then use Black-Scholes to imply a volatility from each Garch price. The plot volatility vs. strike exhibits the characteristic U-shaped curve that one commonly observes with real options.
We do recommend Black-Scholes or Finite Difference (UNIVDRV) model (as opposed to a historically estimated Garch) when there is a liquid and efficient options market whose quoted option prices can be used to imply a local volatility surface.
The use of GARCH with historically estimated parameters in option pricing is recommended :
Cost Saving Bundle
|UNIVDRV - Universal Derivatives Add-in is an inclusive package of :|
|UNIVEXOT+ - Universal Analytical Exotics Add-in|
|UNIVFDIF - Universal Finite Difference Add-in|
|UNIVGARCH - Universal Garch Add-in|
Why not consider MBRM Comprehensive Combined Package : An inclusive package of our main software packages (This would be a massive saving on the individual selling price of these packages)