Option-adjusted duration

There are valuation models that can be used to value bonds with embedded options. These models take into account how changes in yield will affect the expected cash flows. Thus, when V and V+ are the values produced from these valuation models, the resulting duration takes into account both the discounting at different interest rates and how the expected cash flows may change. When duration is calculated in this manner, it is referred to as effective duration or option-adjusted duration or OAS duration. Below we explain how effective duration is calculated based on the lattice model and the Monte Carlo model. 

The modified duration and convexity methods we have described are only suitable for use in the analysis of conventional fixed-income instruments with known fixed cash flows and maturity dates. They are not satisfactory for use with bonds that contain embedded options such as callable bonds or instruments with unknown final redemption dates such as mortgage-backed bonds. For these and other bonds that exhibit uncertainties in their cash flow pattern and redemption date, so-called option-adjusted measures are used. The most common of these is option-adjusted spread (OAS) and option-adjusted duration (OAD). The techniques were developed to allow for the uncertain cash flow structure of non-vanilla fixed-income instruments, and model the effect of the option element of such bonds. 

Finally, the option-adjusted spread (OAS) is the constant spread that, when added to all the rates on the interest rate tree, will make the theoretical value equal to the market price. Spread duration based on OAS can be interpreted as the approximate percentage change in price of a nongovernment for a 100 basis point change in the OAS, holding the government rate constant. 

Option-adjusted spread analysis uses simulated interest rate paths as part of its calculation of bond yield and convexity. Therefore an OAS model is a stochastic model. The OAS refers to the yield spread between a callable or mortgage-backed bond and a government benchmark bond. The government bond chosen ideally will have similar coupon and duration values. 

For syringe applications, programmable time/pressure controllers are used to produce beads and dots. An adjustable vacuum also can be used to control drips between dispense cycles. Pressure options relate to material viscosity with zero to one bar specified for low-viscosity applications, for example. Shot duration can typically be controlled between 0.01 and 99.99 s. 

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