Roundtable Discussion - The Limits of Modeling

How far can models be trusted? How can they be checked and adapted? What other factors need to be considered?

The second session of the Derivatives Hall of Fame roundtable, entitled “First Kill All the Models,” examined the limitations of modeling in general. While at least one participant branded models as something to be avoided if at all possible, all agreed that they have serious limitations and should not be trusted implicitly. Models, at best, are flawed maps of an uncertain terrain—abstractions of reality. They need to be carefully adapted to the trading environment with sound financial concepts. To be truly useful, models should try to account for investment returns as well as investment risk. And ideally, they should also try to measure the operational and credit risks that are often ignored.

POSTED — April 4, 1998 — Archives

Fischer Black: On his induction into the Fixed Income Analysts Society Hall of Fame, Dec 3 1996

I'm very pleased and honored to be here and to say a few words about Fischer on this occasion. But, both for my sake and yours, I wish that weren't necessary. I miss Fischer - I had become used, over the years, to reflexively call his extension at Goldman whenever some financial issue puzzled or confused me, and I've only slowly adjusted to not being able to do that. It would have been so much better for all of us if he could be here in person to accept his award and make a speech.

I first met Fischer in 1986, several months after I came to work in Fixed Income Research at Goldman Sachs & Co, when he and I and Bill Toy worked together on a stochastic no-arbitrage model of interest rates. When you knocked on Fischer's door and entered his office, it was quiet and unfrenzied. Fischer didn't seem to allow his work-life to be dominated by the multiplexing, interrupt-driven set of precedences that became a way of life for anyone who'd been at an investment bank for more than a few months. He made time for everyone, and was never in the prototypical frantic rush. Most often you'd find him reading or on the telephone, or sitting with his PC keyboard entering notes into Thinktank, an organizer program he loved to use. Fischer was highly organized!. If you said something he found useful, he'd write it carefuly on a fresh sheet of lined paper and and insert it into a newly labeled manila folder which eventually went into one of his many file drawers.

POSTED — September 9, 1996 — Archives

Valuing Convertible Bonds as Derivatives

Convertible bonds are derivative securities; they contain options on the underlying common stock and the strait debt of their issuer. In this paper, we describe a binomial wone-factor model for calculating their theoretical value.  The model assumes that all uncertainty in the future value of a convertible bond stems from the volatility of the underlying stock price.  It uses a credit-adjusted discount rate when calculating the present value of future cash flows, in order to account for the credit sensitivity of a convertible.

POSTED — November 11, 1994 — Archives

Outperformance Options

To me, outperformance options1 are especially interesting because of the alternating layers of complexity and simplicity you discover as you probe more deeply into their valuation.

This note describes a journey through these layers. First we describes the outperformance option’s payoff, a simple function of two underlyers. But valuing a two-underlyer options seems compli- cated; each underlyer has to be hedged. It turns out that, if you think about it the right way, a gen- eral principle lets you find the correct and simple formula for its value. Even an options novice, who understands only single-underlyer options and the Black-Scholes formula, already knows everything necessary to value it, European- or American-style. We then examine the simple for- mulat for the outperformance option value, and notice a surprising, elegant and at first puzzling relation among its two hedge ratios. Finally, we explain the origin of this result.

POSTED — January 1, 1992 — Archives

Review of Jarrow and Turnbull’s ‘Derivative Securities’ (1996)

I often interview job candidates with degrees in science or finance. I `m always glad if they show that, whatever time decay has done to their knowledge of their subject's details, they departed their studies with a clear idea of its principles and methods. But, like Keats, sometimes I've grown half in love with easeful death at hearing Ode to a Martingale recited as though it were an axiom of options theory. From this perspective, I like Derivative Securities, Profs. Jarrow & Turnbull's balanced new book, because readers will emerge with a clear understanding of the assumptions, principles and methods of "risk-neutral" derivatives valuation. Impressively, it also touches on issues important to practitioners, but commonly ignored by academics.

POSTED — September 9, 1996 — Archives

On Vasicek’s Induction Into The Derivatives Strategy Magazine Hall of Fame (2000)

I'm very pleased and very honored to be able to introduce Dr Oldrich Vasicek here today on his induction into the Derivatives Hall of Fame. Ever since I first started to learn about financial theory fifteen or so years ago, I've admired Dr Vasicek from a distance, for several reasons. The most trivial one is that my wife, like him, was raised in what was then Czechoslovakia, leaving there in 1968 for this country. Less trivially, I was inspired by the way he managed to combine the highest academic standards with real business. But there are deeper reasons too.

POSTED — September 9, 2000 — Archives

Ins and Outs of Barrier Options Part 1

Barrier options are extensions of stanard stock options. Standard calls and puts have payoffs that dependon one market level: the strike. Barrier options have payoffs that dependon two market levels: the strike and the barrier.

POSTED — December 12, 1996 — Archives

The Future of Modelling (RISK, 10-12 Dec. 1997, pp. 164-167)

What is the purpose of modelling, in any field? Clearly, it is divination whether foretelling the future, or controlling it. So my task here is to foretell the future of a field that itself tries to foretell the future. To do that, I must first locate the present: what works now, and why. My view is a parochial one; I wasn't trained as an economist, but as a natural scientist who, for the past 10 years or so, has made a living and had some fun building the models and systems used by people who trade complex, mostly derivative, securities for their living. It is interesting, though limited, work, but it is what I know about, from the bottom up.

POSTED — December 12, 1997 — Archives