By Robert A. Jarrow
A big paintings, scarce in new situation.
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Additional info for Over the rainbow: Developments in exotic options and complex swaps
Sample text
Model calibration is often done at the start of trading to ensure that the model's pricing will not be too far from the general market. Deal pricing the process of quoting a bid or offer price to a customer for a particular transaction structure. The number of deal pricings done daily depends on the volume of business. Book revaluation the mark-to-market of the trading book (entire portfolio of outstanding positions). Many users require this at least once a day for management reporting. Risk management the management of the net risk of trading positions.
Historical volatility function, σ2 (US Treasury rates, 1980-90) For most reasonable volatility functions, all rates will move instantaneously in the same direction. Options which depend on yield curve twists, however, can be more accurately valued with a two-factor model. In such a model, two sources of randomness drive the evolution. Equation (2) replaces equation (1): Under a two-factor model, the term structure is subject to two different kinds of random shocks, each characterised by its own volatility function.
In general, a one-factor model offers speed but a multi-factor model is better at hedging yield curve risk. Both features are of great practical importance but we cannot have both. There is generally a trade-off: more robust management of yield curve risk must be bought by sacrificing speed. This trade-off is analogous to that between risk and return in portfolio management. Just as it is absurd to say that there is one point on the risk/return trade-off curve (efficient frontier) that is best for all investors, it is equally absurd to say that a one-factor model is always better than a two-factor model or vice versa.