Monday, 6 July 2009

One model, one model to rule them all.....

For those who still persist in believing that my books are not as interesting or as informative as Harry Potter or Lord of the Rings, I beg to differ. We, in finance, are not bothered with magic or trinkets - we have models and indeed (to coin a phrase) one model, one model to rule them all - the Black Scholes option pricing model.

Why is the Black Scholes model so crucial in modern finance? Isn't the BS model jsut a mathematical over-indulgence flashed around by academics to impress and at best a rather technical beast that answers the question: what's an option worth? Options are often seen in terms of financial options on stocks, currencies or swaps. However BS and their co-worker Robert Merton realised the wider significance of their model. What they had developed was a general approach to valuing future alternatives.

In finance, decision making is expressed in terms of current choices or future choices. Until BS published their paper in 1973 we had a model for the former where the alternatives are immediate. For very short run decisions (i.e., where the consequences are also immediate) we match of revenues against relevant costs to get the decision contribution. Where the consequences are somewhat longer term we use the net present value model which is the same thing except future revenues and costs are discounted to a present value.

Where there is the potential to delay choosing what to do, the net present value model begins to creak. Throw in uncertainty as well as risk and the NPV model can no longer cope. This is where the BS model comes in - its tells us the value we can attach to alternatives which we can choose between at some future date. Indeed, if we reduce the exercise time to zero, the BS model reduces to the net present value of the alternatives ahead of us - the so called 'intrinsic value' of the choice available to us. Where the time to choose is extended then the model brings in some key attributes of the decision the NPV model ignores: the financial benefits potentially available to us,the riskiness of those benefits, the scale of our investment and the time we have before we need to commit.

So in an important sense, the option valuation concept whether in the form of the original BS model or the 'n' variants developed over the years, is the heart of modern finance. With it we can value firms, investment projects, intangibles, and of course those nasty derivatives which nobody (i.e., politicians, journalists and, sadly, too many accountants) can understand.



ps: the attached young lady disturbed my post lunch snooze in an Alaskan estuary. The other photographers in my party had disappeared rather quickly but I, being rather slow to wake up, and up to my neck in waders with camera at water level, was somewhat surprised to see her eyeballing me from just a few short yards distance. 'Hello' she said 'have you seen any nice salmon?' 'Sadly no' I replied, but as she started to turn away I thought I would pop the obvious question: 'what do you think of the state of the financial markets'. Her reply.....you've guessed it! But anyway, here she is.

6 comments:

Anonymous said...

HI Mr RYan ,

can u plz recommend sum book on F.M like the way v r having "colin drury" for "mgt accounting"

its a complete text "with Q based on pro. level exams of ACCA/CIMA/ICAEW"

i rephrase my question is there any book which "incorporate papers of ACCA/CIMA/ICAEW FOR financial management"

Mike in Moscow said...

Indeed, although regrettably for the investors in Long Term Capital Management (founded by Scholes and Merton)things don't always behave in practice as in theory.

Anonymous said...

Yeh Mike what has LTCM got to do with the OPM??? LTCM were convergence trading on fixed income and were forced to exit trades early cos of under capitalization and Saloman exiting their support. Something also happende in RUSSIA too....

I've never thought of the OPM in the way prof bob says. He's changed the way I look at the model and at finance. Brilliant - wish prof bob taught me!!!!

Mike said...

There may be a connection in the assumption of normal distribution used in Black-Scholes and the models developed by Merton at LTCM. The Russian default of 1998to which you refer is a good example of how, in practice, the actual distributiom may have "fat tails" - as we have seen again in the current crisis. But I agree with you that several factors contributed to the demise of LTCM. I was just making the point that in practice prices do not always behave as axpected by models that assume efficient markets and normal distributions. However if I knew how to adjust the models for such imperfections I would either be making a fortune as a trader, or, like Scholes and Merton (and Black if he had lived long enough) would have a Nobel prize. Regrettably neither...

Professor Bob Ryan said...

Some very interesting comments which I will be writing about at length. Anonymous is right in that LTCM was down to a number of factors and it is certainly true that one of the elements which led to its demise was over-reliance on models that implied log-normal price processes and hence normal return distributions. Mike from Moscow is also right in that no one has successfully cracked the problem that Fama in his Foundations of Finance observed way back in the 1970's that actual equity return distributions exhibit fat tails and greater leptokurtosis than would be implied by the normality assumption. The problem of course is in modelling such distributions. Also we do not really have a good prior theory as to why 'fat tails' should occur. Having had a look at the daily return distribution on the FTSE over the last 100 days, for example, I cannot see any evidence of the fat tail phenomenon - take a look at the last 600 days and a different picture emerges. However, before jumping to conclusions there has been a lot of corporate restructuring, ungearing and other factors which may have distorted the time series. There are some methods of modelling in odd shaped distributions (Monte-Carlo and binomial type algorithms) but before going down that route in a predictive way we do need that underlying theory.

Anyway, even though B-S is not too good under stress it does teach us a huge amount about valuation.

Ps: I am looking at the issue of good P4 reading aside from the standard BPP and Kaplan manuals. The ATC manual is pretty good as well but to stand a good chance at P4 you need (a) time and (b) a good teacher and/or some good books.

Tudor said...

Didn't know Black Scholes was published over 25 years ago. That's longer than Ginger Scholes has been playing for MUFC.

Regards