Chase the Devil

Some people use Heston to fit one slice of a volatility surface.

Two months ago, I looked at arbitrage free interpolation using piecewise-constant density.

I am going to write a little about my experience and conclusions so far around interviewing a candidate for a software developer position or for a quant position, but it should be quite general.

I am currently reading the book “Nonlinear Option Pricing” by J.

There is a relatively new JVM based language, Xtend.

P.

The calibration of a stochastic volatility model or a volatility surface parameterization (like SVI) involves minimizing the model options volatilities against market options volatilities.

Tension splines can produce in some cases arbitrage free C2 interpolation of options, but unfortunately this is not guaranteed.

In a previous post, I have explored the arbitrage free wiggles in the volatility surface that P.

I always wondered if Bachelier was really worse than Black-Scholes in practice.

Peter Jaeckel, in a recent paper (pdf), shows that something that sounds like a reasonable arbitrage free interpolation can produce wiggles in the implied volatility slice.

In an earlier post, I have been quickly exploring adjoint differentiation in the context of analytical Black-Scholes.

Several papers show that the limit for large strikes of Heston is SVI.

With a small time expansion, it is easy to derive a reasonable initial guess, without resorting to some global minimizer.

Small time expansions for Heston can be useful during the calibration of the implied volatility surface, in order to find an initial guess for a local minimizer (for example, Levenberg-Marquardt).

The paper implied vol for any local stochastic vol model from Lorig et al. presents a very generic and simple formula to compute implied volatility expansions up to order-2 (there is actually an order-3 formula available in their Mathematica CDF file).

Last week, my work laptop died after spilling out some water on its keyboard inadvertently.

At first I did not make use of the Brownian Bridge technique in Heston QMC, because the variance process is not simulated like a Brownian Motion under the Quadratic Exponential algorithm from Andersen.

Adjoint algorithmic differentiation is particularly interesting in finance as we often encounter the case of a function that takes many input (the market data) and returns one output (the price) and we would like to also compute sensitivities (greeks) to…

Pooley et al., in Convergence Remedies for non-smooth payoffs in option pricing suggest that placing the strike on the grid for a Vanilla option is good enough: At the same time, Tavella and Randall show in their book that numerically, placing the strike…

Recently, I noticed how close are the two PDE based approaches from Andreasen-Huge and Hagan for an arbitrage free SABR.

Today, after wondering why my desktop computer became so unstable (frequent crashes under Fedora), I found out that the micro usb port of my cell phone has some kind of short circuit.

The Fortran minpack library has a good Levenberg-Marquardt minimizer, so good, that it has been ported to many programming languages.

Several months ago, I took a look at two interesting recent ways to price under SABR with no arbitrage: One way is due to Andreasen and Huge, where they find an equivalent local volatility expansion, and then use a one-step finite difference technique to…

Prices of a Future contract and a Forward contract are the same under the Black-Scholes assumptions (deterministic rates) but the price of options on Futures or options on Forwards might still differ.

Using precise vanilla option pricing engine for Heston or Schobel-Zhu, like the Cos method with enough points and a large enough truncation can still lead to spikes in the Dupire local volatility (using the variance based formula).

I always imagined local stochastic volatility to be complicated, and thought it would be very slow to calibrate.

I did some experiments fitting Heston, Schobel-Zhu, Bates and Double-Heston to a real world equity index implied volatility surface.

I recently stumbled upon an error in the various papers related to the Heston Cos method regarding the second cumulant.

A few years ago, I found an interesting open source symbolic calculus software called Xcas.

I tried today the Scala courses on coursera by the Scala creator, Martin Odersky.

My Scala habits have made me create a stupid bug related to Java enums.

A coworker pointed to me that Andersen and Piterbarg book “Interest Rate Modeling” had a chapter on Fourier integration applied to Heston.

By default, text in Fedora 19 looks ok but not great.

I recently wrote about the Cos method.

I have had some stability issues with the Ubuntu 13.04 on my home computer, not on my laptop.

I just stumbled upon Julia, a new programming language aimed at numerical computation.

Fang, in her thesis, has the idea of the COS method and applies it to Heston.

I was used to Scilab for small experiments involving linear algebra.

Joda has the concept of LocalDate LocalDateTime and DateTime.

This is a kind of following to the CUDA performance myth.

The other day I installed the latest Ubuntu 13.04 under a VirtualBox virtual machine using Windows as host.

As Bessel (sometimes called Hermite) spline interpolation is only C1, like the Harmonic spline from Fritsch-Butland, the forward presents small kinks compared to a standard cubic spline.

I discovered that suddenly emails sent to me bounced back yesterday.

It’s been a while since I do a pet project in Scala, and today, after many trials before, I decided to give another go at Jetbrain Idea for Scala development, as Eclipse with the Scala plugin tended to crash a little bit too often for my taste (resulting…

The theta finite difference scheme is a common generalization of Crank-Nicolson.

Today, a friend asked me if Scala could pass primitives (such as Double) by reference.

On my test of yield curve interpolations, focusing on parallel delta versus sequential delta, Akima is the worst of the lot.

I had explored the issue of pricing a barrier using finite difference discretization of the Black-Scholes PDE a few years ago.

At a presentation of the Thalesians, Hagan has presented a new PDE based approach to compute arbitrage free prices under SABR.