The first section covers the foundations of probability in measure theoretic terms. i.e events in probability as measurable sets, random variables as measurable functions, expectation as integration with respect to the probability measure etc. My only criticism is Chapter 8 on product measure could do with more explanation and examples. The second section in my […]

## Recent Articles

## Stamp Duty Changes Calculator (Autumn Statement 2014)

My wife and I are enjoying our first property we bought back in June 2014. I can tell you we weren’t very happy about the 4% tax rate we had to pay on the whole of the purchase price considering it was not much above the 4% threshold. Stamp duty being a slab tax […]

## Pricing Financial Instruments – The Finite Difference Method

This book explains how to price derivatives with the finite difference technique. It is aimed at practitioners full of many different examples, such as pricing convertible bonds, American options, Barrier options and Parisian options. It also has a nice introduction to stability analysis using the matrix approach and the fourier approach. The book covers pretty […]

## Financial Calculus

Financial Calculus is rather an old book now, first being published in 1996. Despite its age it has (as far as i know) a unique place in the literature in that it attempts to teach continuous time stochastic calculus, without requiring a knowledge of (nor teaching) measure theoretic probability. It does in fact succeed to do […]

## What is Quantitative Finance?

Quantitative Finance is an academic discipline that combines areas of mathematics, computer science, numerical analysis and economics. Arguably, the first major contribution to the subject was by Louis Bachelier with the publication of his PhD thesis, The Theory of Speculation, in 1900, the first time the stochastic process, now called Brownian motion, was used to […]

## FRM Practice Questions

Try your hand at some FRM practice questions (click the link below for the test). FRM Part 1 Practice Test – 10 questions in 24 minutes This is a random selection of questions from our database. I am continually adding more questions so feel free to try the sample FRM exam again in future. Please […]

## Futures Delta and Forward Delta

The delta of a futures contract is not the same as the delta of a forward contract. This is often a point of confusion for students. The difference between a forward contract and a futures contract is that a forward contract is an OTC contract settled at maturity and a futures contract is settled daily using […]

## What is the FRM Pass Rate?

On a number of forums I have seen people stating it is a very hard exam because the probability of passing both exams is low. The FRM pass rates are shown below. I have split the results in to two parts. The first table shows the pass rates when the exam was just one paper. […]

## ABRACADABRA: Part 3 (Comment)

A colleague of mine asked me what if we wanted to know the expected time for the monkey to type the sequence of letters ABCDEFGHIJK and not ABRACADABRA what would the result be. Trudging through the mathematics gives \( \mathbb E[T] =26^{11} \). Why is the expected time for the monkey to type ABRACADABRA longer […]

## ABRACADABRA: Part 2

To answer the question what is the expected time for a monkey to type ABRACADABRA, assuming he types the letters of the alphabet randomly at times 1,2,3,… rigorously we will need to use a theorem from discrete martingale theory, Doob’s Optional Stopping Theorem. This theorem states sufficient conditions for a stopped martingale to have the […]

## ABRACADABRA: Part 1

Since I have just reviewed ‘Probability with Martingales’ I thought it would be nice to add one of the most famous puzzles in the book to the puzzles page. If at each of times 1,2,3,.. a monkey types a capital letter at random. What is the expected time for the monkey to first produce the letters […]

## Connect

Connect with us on the following social media platforms.