Adaptive Integration - It began 1997 with a workshop for a London based trading desk of a large American bank. The problem: pricing of complex Asian convertible bonds. No sufficient solution available. At this workshop Andreas suggested the application of a new method for solving the then adequate PDEs - on the fly.
Shhh, .... UnRisk 7 Is Coming
Yes, we have schedules. And our teams publish share them with marketing and sales ... ;)
I was in Amsterdam last week and met a few Wilmotters - we "consumed" our prize as group winners of the 2012 Dutch Science Quiz. The prize was one thing, but to meet people you discussed with over years, but have never met in person is also exiting.
I was in Amsterdam last week and met a few Wilmotters - we "consumed" our prize as group winners of the 2012 Dutch Science Quiz. The prize was one thing, but to meet people you discussed with over years, but have never met in person is also exiting.
Dupire or Not Dupire? Is this a Question?
The concept of local volatility certainly has its merits, and Bruno Dupire is the name attached to local volatility. With his analytic inversion formula published in RISK (1994), he made it possible to calculate the local volatility surface easily.
But is it also a numerically sound method to identify local vol? To answer this question, we performed the following naive experiment.Let the local volatility to be identified be in fact a flat volatility of 30%. This, of course, leads also to implied volatilities (the sysnthetic market data) of 30% for all strike prices and all expiries of options. We now add some noise so that the quoted implied volatilities are in the interval (29.99%, 30.01%).
We now assume the spot price is 100 and that these implied volatilities are quoted for strike prices (50, 52, 54, ..., 146, 148, 150) and for expiries (5 weeks, 10 weeks, ... 245 weeks, 250 weeks).
See here what Dupire's formula delivers.
What happened here? Numerical differentiation of noisy data is instable, dividing by something instable close to zero even more.
Chapter 15 of "A Workout in Computational Finance" gives insight into parameter identification problems, stable methods for treating them and how Egger and Engl obtained the following smooth (almost boring) volatility surface from the same noisy data.
But is it also a numerically sound method to identify local vol? To answer this question, we performed the following naive experiment.Let the local volatility to be identified be in fact a flat volatility of 30%. This, of course, leads also to implied volatilities (the sysnthetic market data) of 30% for all strike prices and all expiries of options. We now add some noise so that the quoted implied volatilities are in the interval (29.99%, 30.01%).
We now assume the spot price is 100 and that these implied volatilities are quoted for strike prices (50, 52, 54, ..., 146, 148, 150) and for expiries (5 weeks, 10 weeks, ... 245 weeks, 250 weeks).
See here what Dupire's formula delivers.
What happened here? Numerical differentiation of noisy data is instable, dividing by something instable close to zero even more.
Chapter 15 of "A Workout in Computational Finance" gives insight into parameter identification problems, stable methods for treating them and how Egger and Engl obtained the following smooth (almost boring) volatility surface from the same noisy data.
Scenarios - Stories About Possible Futures
for todays decision. Our UnRisk FACTORY is, in its core, an untiringly working factory that does instrument group-across-scenarario-groups analytics. Fast. Accurate. Automated.
How to Avoid Functional Stupidity
A communication and promotion expert would warn me to publish two posts a day in one blog. But I do not post for maximizing visits ...
8 Reasons, Why Econophysics Research Matters
No, I am not an economist. But interested in complex system research, I read about complexity economy an especially about Brian Arthur's work - obviously, as a technology provider, "The Nature of Technology". This is also one of the reasons why I read, and refer to, frequently Mark Buchanan's "The Physics of economy" blog - this weeks post what has "econophysics" achieved?
A Short Letter From A SteelTown
Not so few of us UnRiskers are born into the fire and heat feeling of a steel town. The steel maker is voestalpine.
We've Got the Proof
OK, this was misleading. To be honest, we’ve got the proofs. We, that is Michael Aichinger and myself, and the proofs are the proofs of our book “A Workout in Computational Finance”, which should appear with Wiley Finance in July 2013.Pre-order at Amazon
The appearance date approaches quickly which makes us quite happy. We have been working on the book for almost two years, and, from our point of view, we cover a wide range of numerical techniques useful for practitioners in quantitative finance.
In the course of the next weeks, we will spotlight selected sample sections. Hence, stay tuned.
Do We Work to Get Picked?
Yes, I took quite a high ink factor explaining not only what we do, or how our offerings work, but also why we do it. And why we question ourselves quite often, whether this is right. And what would independent experts think about what we do.
Subscribe to:
Posts (Atom)