9 papers
Implying Volatility: How Fast Can We Go?
Fabien Le Floc'h, Jherek Healy
FlashIV is a low-latency Black--Scholes implied-volatility solver for production use. It normalises each input to an out-of-the-money price and solves a tail-stable erfcx/log-price…
Counterexamples for FX Options Interpolations -- Part II
Jherek Healy
This follow-up article analyzes the impact of foreign exchange option interpolation on the vanilla option implied volatilities. In particular different exact interpolations of brok…
Counterexamples for FX Options Interpolations -- Part I
Jherek Healy
This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is…
Heston vol-of-vol and the VVIX
Jherek Healy
The Heston stochastic volatility model is arguably, the most popular stochastic volatility model used to price and risk manage exotic derivatives. In spite of this, it is not neces…
Inserting or Stretching Points in Finite Difference Discretizations
Jherek Healy
Partial differential equations sometimes have critical points where the solution or some of its derivatives are discontinuous. The simplest example is a discontinuity in the initia…
Accurate and consistent calculation of the mean and variance in Monte-Carlo simulations
Jherek Healy
In parallelized Monte-Carlo simulations, the order of summation is not always the same. When the mean is calculated in running fashion, this may create an artificial randomness in…
Pricing American options under negative rates
Jherek Healy
This paper starts by defining the criteria where the early-exercise of an American option is never optimal, under positive, or negative rates. It follows with a short analysis of t…
The Pricing of Vanilla Options with Cash Dividends as a Classic Vanilla Basket Option Problem
Jherek Healy
In the standard Black-Scholes-Merton framework, dividends are represented as a continuous dividend yield and the pricing of Vanilla options on a stock is achieved through the well-…
Equivalence between forward rate interpolations and discount factor interpolations for the yield curve construction
Jherek Healy
The traditional way of building a yield curve is to choose an interpolation on discount factors, implied by the market tradable instruments. Since then, constructions based on spec…