Binomial trees are frequently used to approximate the movements in the price of a stock or other asset In each small interval of time the stock price is assumed to move up by a proportional amount u or to move down by a proportional amount d Options
Models to be Considered Constant elasticity of variance (CEV) Jump diffusion Stochastic volatility Implied volatility function (IVF) Options, Futures, and Other Derivatives
Why Interest rate Derivatives are Much more difficult to value Than Stock Options We are dealing with the whole term structure of interest rates; not a single variable The probabilistic behavior of an individual interest rate is more complicated than that of a stock price Options, Futures, and Other Derivatives, 5th edition C 2002 by John C. Hull
The Two-Factor Hul-white Model (equation 24.1, page 571) dx=0(0)+u-ax dt +o,dz1 du= -but +o,dz, where=f(r and the correlation between dz, and dz, is p The short rate reverts to a level dependent on u, and u itself is mean reverting
Credit ratings In the s&P rating system, AAA is the best rating. After that comes AA, A BBB. BB.B. and ccc The corresponding Moody's ratings are Aaa. Aa,a. Baa, Ba.b. and caa Bonds with ratings of BBB (or Baa) and above are considered to be investment grade
An alternative to the NPV Rule for Capital Investments Define stochastic processes for the key underlying variables and use risk- neutral valuation This approach (known as the real options approach) is likely to do a better job at valuing growth options, abandonment options, etc than NPV
8.1 Definition of Monetary Policy Government policy concerning money and credit conditions, especially the rate of growth in the money supply and the level of interest rates
5. 1 The Government Bond Market 5.1.1 when the government runs a deficit, it has to get the funds. There are three ways for the government to get funds
