The post Pricing Financial Instruments – The Finite Difference Method appeared first on Quantitative Finance Courses.

]]>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 much all you need to know for solving 1d pde’s in finance. It pays special attention to issues such as discontinuties in the payoff and how to deal with critical pricing points such as strikes and barrier points with coordinate transformations. The chapter on discrete sampling for pricing Asian and Parisian options is very useful and is something i have implemented in practice. It works very well.

Rating 4.5/5

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]]>The post Financial Calculus appeared first on Quantitative Finance Courses.

]]>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 this difficult task! By using the binomial tree approach to pricing derivatives it introduces difficult concepts such as measure, risk neutral pricing and change of measure. Ito Calculus is explained using the derivative of \( W_t^2\) to illustrate that higher order terms are needed in the Taylor expansion in order for the differential to have the right expectation. Using the tools of the Martingale Representation theorem and the Cameron Martin Girsanov Change of Measure theorem the Black Scholes formula is derived. This is quite a feet considering that the word sigma algebra isn’t mentioned once in the book! The later part of the book is devoted to pricing interest rate derivatives. It provides a nice introduction to the Heath Jarrow Morton interest rate model framework for the forward rate curve but for a detailed approach you should probably look elsewhere. There is also a brief mention of the Libor market model (BJM) but again you should look elsewhere for more details as you could write (and some authors have!) a whole book on the subject.

Rating 4/5

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]]>The post Probability With Martingales appeared first on Quantitative Finance Courses.

]]>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 opinion is where the book really has no equal. Conditional Expectations, Martingales and their convergence theorems are masterfully taught. The exercises on this topic are fun too. It includes the famous how long will it take on average for a monkey to type ‘ABRACADABRA’!

Rating 4.5/5

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