Option and Swap Valuation on Bloomberg

Option and Swap Valuation on Bloomberg Chris Lamoureux, PhD Head of Finance Estes/Neill Professor of Finance University of Arizona

Philosophical Approach Market makers (as opposed to long-term traders), are especially concerned that the “model” that they use to price derivative securities be exactly calibrated to market data. Black-Derman-Toy is a widely-used model that does this calibration by matching the forward rates and the “volatility” curve. Derivatives

Philosophical Approach –2 Fitting today’s yield curve exactly is achieved at the cost of dynamic inconsistency. This means that the “model” is inherently wrong as a way to characterize the dynamics of interest rates. Nevertheless, market makers are concerned about hedging and measuring risk exposure as opposed to profiting by taking on risk (or “predicting” future movements in underlying fundamentals). Derivatives

Bloomberg Bloomberg allows users to apply several calibration models to value a variety of derivative securities. I obtained the following screen by first selecting the underlying security: 912828DM9 <GOVT> <GO> Then get option valuation for this security: OV <GOVT> <GO> Derivatives

Resultant Screen Derivatives

Screen Interpretation The preceding screen is for at-the-money 90-Day call and put options on the 4% 2/15/15 T-Note. This screen uses Black’s model to value the options. Assumptions include a constant interest rate (oddly!), the note’s price follows a geometric Brownian Motion (so that its value on option expiration is lognormally distributed), with mean equal to its forward price, and constant (proportional) variance. Derivatives

Screen --2 We get the model prices for both options. Also the implied volatility of the note price: • (Price I.Vol) (5.973) The usual way volatility is expressed is on yields: • Yield Vol (%) (17.732) Note that the risk free rate (assumed constant) is 2.80% (Repo). The forward price is 98-05 3/8. (Also note that since these options are at-the-money, all of their value is “time value” (i.e., intrinsic value is 0).) Derivatives

OV 2 Derivatives

BDT Screen The preceding screen looks at the same option, but uses the BDT model to value and measure risk exposures. Note that for BDT, we input the entire yield curve and volatility curve. The only additional information on this screen is the Z-Spread, which is the yield differential between the model and the market price for the T-Note. Note that the prices of both options are lower under BDT than Black, since the vol is low at the short end. Derivatives

Caps, Floors, Collars Calculator Bloomberg has calculators for swaps, swaptions, collars, floors, and caps. You can get there from the <CRNCY> screen (US$). The next 3 screens are for Cap valuation. Derivatives

Cap Screen 1 Derivatives

Swaptions A swaption is an option to enter a swap. The next screen uses BDT to evaluate a swaption which gives its owner the option to receive fixed and play floating on $10 million notional principal, with quarterly tenor. The option expires in 1 year and is on a 5-Year swap. Derivatives

Swaption Screen Derivatives

Option and Swap Valuation on Bloomberg