| In this dissertation, first the term structure of interest rate is determined by describing the yield curve using cubic spline interpolation. Then, the one-factor Heath, Jarrow, and Morton (HJM) model as developed by Jarrow (1996) is used to determine arbitrage free prices for Russian Government Short Term Bonds. In this model, the initial term structure is taken as given, and the forward rate, derived from observed prices, is the driving factor. After determining the stochastic evolution of bond prices, a trading strategy is developed to construct a portfolio which gives arbitrage-free prices. The computed arbitrage-free prices are compared to the observed prices. Then the Black, Derman, and Toy model is applied. This is another arbitrage-free one-factor model. The factor driving the model is the short term interest rates. With the short term rates, the evolution of the bond prices is generated. Using the same trading strategy, a portfolio which is a synthetic bond that gives the arbitrage-free price, is created. The arbitrage free price is then compared to the observed price. |
