Completed PhD Internships

2010

• Implementation of General Affine Term Structure Models
  Student: Nairn McWilliams
  Supervisor: Dr Sotirios Sabanis, University of Edinburgh and Graeme Lawson, Barrie & Hibbert
  Company: Barrie & Hibbert
  
  Project Summary: Affine term structure models (ATSMs) have desirable analytic properties as described by Duffie and Kan ("A yield-factor model of interest rates", Mathematical Finance, 6(4):379-406, 1996) and further by Dai and Singleton ("Specification analysis of affine term structure models", Jour. Finance, 55(5):1943-1978, 2000).

The goal of the project was to implement ATSMs, involving fast convergent numerical methods for the underlying stochastic differential equations (SDEs). One purpose of the project is the valuation of derivatives under the risk-neutral measure, which in turn can be used for projection under real-world statistical conditions.

With this available, the next stage was the pricing of zero-coupon bonds: by considering both Monte Carlo estimation of bond prices then later implementing the analytic functions provided by Dai and Singleton (2000) and using the estimates as a benchmark.

The project concluded by concentrating on interest rate derivatives. Primarily, this involved pricing swaptions, detailed by Tanaka et al. ("Approximation of Interest Rate Derivatives' Prices by Gram-Charlier Expansion and Bond Moments", IMES 2005-E-16, 2005). This can then in turn be used to value further derivatives, such as caps, floors and bond options.

PhD Placements in 2012

The Academy is aware of a number of students with strong quantitative skills who are interested in undertaking an industry placement during 2012. Companies with an interest in PhD placements, who would like to explore what is involved, are invited to contact the Academy.

Please contact Prof Alexander McNeil, Scottish Financial Risk Academy: a.j.mcneil@hw.ac.uk