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Timetable (DQFW06)

Industry Event: Modelling Philosophy

Friday 22nd April 2005

Friday 22nd April 2005
10:00 to 11:00 D Madan ([Maryland])
On modelling for equity derivatives

I will speak on the modelling issues in Equity Derivatives with emphasis on the recent development of the Local Levy Process.

INI 1 ,
11:00 to 11:30 Coffee
11:30 to 12:30 J Walton ([BNP Paribas])
The black art of FX modelling

The FX market place is the largest but least studied area of mathematical finance, primarily as the vast majority of trades are over-the-counter, but also because of the arcanery of FX quoting conventions. After demystifying the FX market it will be apparent that there is a rich source of option pricing information which can be used for model fitting. This talk will describe some of the in vogue approaches to solving the pricing problem for vanilla and exotics options and discuss some of the real-world issues facing FX quants. Additionally the future directions of FX modelling are pondered.

INI 1 ,
12:30 to 13:30 Lunch
13:30 to 14:30 M Dempster (University of Cambridge)
Modelling incomplete markets for long term asset liability management

After evaluating the strengths and weaknesses of alternative models for real world probabilities in real (incomplete) markets with unpriced uncertainties, this talk will report on current progress of the structural economic/capital market approach to asset class returns pioneered by Wilkie (1986) for this situation. This flexible approach is a natural complement to the use of dynamic stochastic programming (DSP) techniques for solving long term asset liability problems for pension, insurance and hedge fund management. A brief overview of DSP techniques will be followed by some illustrative real world case studies.

INI 1 ,
14:30 to 15:30 P Karasinski ([HSBC])
Mindless fitting?

We are required to mark-to-market non-plain (exotic) products in a way that is consistent with the observed market prices of liquid vanilla products. This means that for each exotic we must have a one-to-one mapping between vanilla prices and the exotic's price. Such mapping is called the mark-to-market model as it produces mark-to-market price and risk exposure for each exotic. Risk management policies (risk limits, desire to minimise volatility of the mark-to-market P&L) typically compel traders to hedge exotics with vanillas such that the combined risk exposure, measured by the mark-to-market model, is close to zero.

In the traditional approach we set the exotics price equal to its' value given by a valuation model that assumes a certain stochastic evolution of the relevant risk factors. In order to fit vanilla prices practitioners use, are forced to use, over-parameterised models (models with local volatility surfaces is one example) whose resulting risk factor dynamics could be counter-intuitive. Does this make a good model, i.e., does hedging to such model’s risk exposure result in realised replication cost (derivative’s actual “manufacturing cost”) that is close to the initial exotic’s price the model produces? We cannot be sure of that!!!

What are the alternatives? Can we start with a price of an exotic produced by a standard derivatives valuation model, with risk factors dynamics that makes sense (who is to judge?), and somehow, externally, adjust this price to reflect the difference between market and model prices of relevant vanilla options? Would the resulting mapping produce a hedging model that is better than the one based on the above traditional approach?

In this presentation we provide an example of such an alternative mapping based on “external price adjustors”. We show how external price adjustors modifiy the risk exposure produced by the underlying derivatives pricing model. It is likely that the simple external-adjustors method is used by some practitioners (see Pat Hagan’s paper in Wilmott Magazine entitled “Adjusters: Turning Good Prices into Great Prices”).

This work is an extension of earlier joint work with Thierry Bollier and Craig Fithian (“Marking-to-Market Non-Plain Products”, Citigroup, June 2000).

INI 1
15:30 to 16:00 Tea
16:00 to 17:00 P Carr ([Bloomberg])
Meta modelling

We model the process by which we choose the process for the model. In particular, we model the options for modelling options.

INI 1
17:00 to 18:00 Wine and beer reception
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons