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Let us now examine each of these in the context of risk parameters From a risk management perspective, how the value of a financial variable changes in response to market dynamics is of great interest For example, we know that the measure of an option s exposure to changes in spot is captured by delta and that changes in the risk-free rate are captured by rho To complete the list, changes in time are captured by theta, and vega captures changes in volatility Again, the value of a call option prior to expiration may be written as Oc S(1 RT) K V There is no risk parameter associated with K since it remains constant over the life of the option.

Burrows and colleagues (2000) assessed the recording policies and practices in 10 police forces They then went on to investigate, in more depth is ve of those forces, what happened when calls involving crime allegations were made to the police by members of the public, and whether they were recorded as crimes and, if not, why not They found that there was no standard practice and that the way that a crime report originates varies between forces Forces have different arrangements for dealing with telephone calls from the public, a crucial distinction being between forces which operate single tier and two-tier control rooms, ie whether all calls go to one central point or to a number of local points usually at the basic command unit level.

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Since every term shown has a positive value associated with it, any increase in S, R, or V (noting that T can only shrink in value once the option is purchased) is thus associated with an increase in Oc For a put option, Op K S(1 RT) V, so now it is only a positive change in V that can increase the value of Op To see more precisely how delta, theta, and vega evolve in relation to their underlying risk variable, consider Figure 512 As shown in Figure 512, appreciating the dynamics of option riskcharacteristics can greatly facilitate understanding of strategy development We complete this section on option risk dynamics with a pictorial of gamma risk (also known as convexity risk), which many option professionals view as being equally important to delta and vega and more important that theta or rho (see Figure 513).

Example Candidate Cases Case 1 (e1) Respiratory Pulmonary Cough Dyspnea High High Chest pain Pleural effusion Pneumococcal (DI2-1) Liver tumor (CY1) Pleural biopsy Pleurosocopy Case 2 (e2) Respiratory Pulmonary Cough Dyspnea High High Chest pain Pleural effusion Streptococci pneumonia (DI2-2) Normal (CY2) Pleural biopsy Pleurosocopy

Methods of creating crime reports varied, some forces have of cers telephoning the details to a central in-putting bureau, others have the of cer entering the details themselves on the force computerized crime-recording system Burrows and colleagues found, however, that most forces still rely on of cers preparing hand-written reports, which are subsequently put onto the crime-recording system by others, usually civilian inputers In some forces the police of cer is able to assign a crime classi cation In others this is restricted to a small number of people in a crime management unit In two forces they found that it took days for a crime report to materialise, providing opportunities for data manipulation and consequences for crime analysis based on incomplete data.

The previous chapter discussed how these risks can be hedged for mainstream options Before leaving this section let s discuss options embedded within products Options can be embedded within products as with callable bonds and convertibles By virtue of these options being embedded, they cannot be detached and traded separately However, just because they cannot be detached does not mean that they cannot be hedged..

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The guidance on the criteria to be applied to recording incidents as crimes is contained in the government s Counting Rules published by the Home Of ce (Home Of ce, 1998) This is a massive and arcane document that de es comprehension by all except those individuals steeped in its usage Most forces do not provide further guidance on what is to be recorded as a crime (HMIC, 2000) Two models of crime recording were identi ed by Burrows that were described as prima facie and evidential Forces adopting the prima facie model recorded details of the allegation without scrutiny Forces adopting the evidential model require the details to be substantiated before a crime is accepted and recorded in their statistics, creating spurious signi cant improvements in these force s clear-up rates.

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