Risk-neutral measure

Then, by changing from the risk-neutral measure Q to the Tq—forward we obtain the moments... 

Again, we need to transform the process for the (log) bond price dynamics dXit, T) from the risk-neutral measure Q to the forward measure Tq. Thus, following section (5.1) we derive a measure transformation specially adapted to the additional innovation of the stochastic volatility. The bond price can be computed by integrating from t to 7b via... 

It is obvious that = 0 and therefore the volatility of the forward rate determines the drift as well. In other words all that is needed for the HJM methodology is the volatility of the bond prices. The short rates are easily calculated from the forward rates. Once a model for short rates is determined under the risk-neutral measure Q the bond prices are calculated from... 

Later on, we need to change the Gog) bond price proeess from the risk-neutral to the appropriate forward measure in order to compute the price of a bond option by summing over the single risk-neutral exercise probabilities. 

The assumption of complete capital markets states that, as a result of arbitrage-free pricing, there is a unique probability measure Q, which is identical to the historical probability P, under which the continuously discounted price of any asset is a Q-martingale. This probability level Q then becomes the risk-neutral probability. 

In the academic literature, the bond price given by equation (3.15) evolves as a martingale process under the risk-neutral probability measure P. This process is the province of advanced fixed-income mathematics and lies outside the scope of this book. An introduction, however, is presented in chapter 4, which can be supplemented by the readings listed in the References section. 

The price of coupon bonds can also be derived in terms of a risk-neutral probability measure of the evolution of interest rates. The formula for this derivation is (3.22). 

Perhaps most important, Chemical Risk provided the basis for a call for scientific collective action and increased public awareness. Future Nobel laureate Joshua Lederberg (1969) noted in one of his regular Science and Man columns that we [biologists] all have a basic responsibility to go beyond an emotional expression of concern to use it to energize the search for authentic scientific measures of potential hazards and for means to neutralize them. We have a great deal of taxing work ahead in trying to set up scientifically valid and politically useful criteria from laboratory studies for these elusive but all-important hazards. ... 

However, SICM remains insensitive to the electrochemical properties of a surface, as the total ion flow is recorded thus the technique is not ion specific. SICM is also insensitive to neutral species in solution. By combining the power of SICM with SECM and integrating an electrode component into the SICM probe, it is possible to have a redox signal-independent measure of the surface topography, while recording local substrate electrochemical activity. This is in much the same way the AFM probe provides an independent measure of substrate structure in SECM-AFM. However unlike AFM, the SICM tip never makes contact with the surface so there is no risk of sample mechanical deformation. 

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