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
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
Weather derivatives: Definitions Heating degree days (HDD): For each day this is max(o, 65-4)where a is the average of the highest and lowest temperature in°F Cooling Degree Days(CDD): For each day this is max( o, A-65)
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
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
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
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
Standard approach to Estimating Volatility Define on as the volatility per day between day n-1 and day n, as estimated at end of day Define S: as the value of market variable at end of day i
