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

Company a buys default protection from b to protect against default on a reference bond issued by the reference entity, C A makes periodic payments to In the event of a default by c A has the right to sell the reference bond to B for its face value

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

Valuation of Swaps The standard approach is to assume that forward rates will be realized This works for plain vanilla interest rate and plain vanilla currency swaps, but does not necessarily work for non- standard swaps

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

Term Structure models Blacks model is concerned with describing the probability distribution of a single variable at a single point in time a term structure model describes the evolution of the whole yield curve

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

Derivatives Dependent on a single Underlying Variable Consider a variable, 0, (not necessarily the price of a traded security) that follows the process d e S Imagine two derivative s dependent on e with prices f, and f2. Suppose

Models to be Considered Constant elasticity of variance (CEV) Jump diffusion Stochastic volatility Implied volatility function (IVF) Options, Futures, and Other Derivatives

Binary options Nonstandard American Lookback options options Shout options Forward start options Asian options Compound options Options to exchange Chooser options one asset for another Barrier options Options involving