CoachA benchmark model is an independent implementation, of the same model or of an alternative, against which a model’s outputs are compared. Outcomes analysis compares a model’s outputs with the realised outcomes they predicted: backtesting of VaR and margin, P&L attribution, default rates against PDs.
Examples
Example 26.8 (Validating chapter 7’s tree)
Chapter 7’s Hull–White trinomial tree prices European swaptions; the Jamshidian closed form of the same model is the benchmark. Over 216 points (mean reversion 1%, 5%, 20%; volatility 60 and 120 basis points; expiries 1, 5, 10 years; tenors 5 and 10; strikes at the money and ; quarterly and monthly steps), with a tolerance of half a basis point of notional or 1%: with quarterly steps 54 of 108 points fail and the worst error is 15.8 basis points of notional; with monthly steps 23 fail and the worst is 3.2. The failures concentrate at short expiries, 14 of the 23 at one year (Figure 26.1): a one-year-into-five-year at-the-money payer (mean reversion 1%, volatility 60 basis points) is worth 104.81 basis points in closed form, 103.07 in the monthly tree and 98.55 in the quarterly one. The finding: the tree needs finer steps before a near exercise date, and a condition of use until it has them.