self.instrument_values = paths
Of course, since we are dealing now with a different model, we need a different set of
elements in the market_environment object. In addition to those for the
geometric_brownian_motion class (see Table 16-1), there are three additions, as outlined
in Table 16-2: namely, the parameters of the log-normal jump component, lambda, mu, and
delta.
Table 16-2. Specific elements of market environment for jump_diffusion class
Element Type Mandatory Description
lambda
Constant
Yes
Jump intensity (probability p.a.)
mu
Constant
Yes
Expected jump size
delta
Constant
Yes
Standard deviation of jump size
For the generation of the paths, this class of course needs further random numbers because
of the jump component. Inline comments in the method generate_paths highlight the two
spots where these additional random numbers are generated. For the generation of
Poisson-distributed random numbers, see also Chapter 10.
A Use Case
In what follows, we again illustrate the use of the simulation class jump_diffusion
interactively. We make use of the market_environment object defined for the GBM object
in the previous section:
In [ 15 ]: me_jd = market_environment(‘me_jd’, dt.datetime( 2015 , 1 , 1 ))
In [ 16 ]: # add jump diffusion specific parameters
me_jd.add_constant(‘lambda’, 0.3)
me_jd.add_constant(‘mu’, -0.75)
me_jd.add_constant(‘delta’, 0.1)To this environment, we add the complete environment of the GBM simulation class,
which completes the input needed:
In [ 17 ]: me_jd.add_environment(me_gbm)Based on this market_environment object, we can instantiate the simulation class for the
jump diffusion:
In [ 18 ]: from jump_diffusion import jump_diffusion
In [ 19 ]: jd = jump_diffusion(‘jd’, me_jd)Due to the modeling approach we have implemented, the generation of instrument values
is now formally the same. The method call in this case is a bit slower, however, since we
need to simulate more numerical values due to the jump component:
In [ 20 ]: %time paths_3 = jd.get_instrument_values()
Out[20]: CPU times: user 19.7 ms, sys: 2.92 ms, total: 22.6 ms
Wall time: 21.9 ms