Chapter 5: Models and Equations 295
where the expectation is with respect to the risk-neutral
process(es). The ‘present value’ here is calculated path-
wise. If performing a simulation for valuation purposes
you must discount cashflows for each path using the
relevant discount factor for that path.
Credit
Credit risk models come in two main varieties, the struc-
tural and the reduced form.
Structural models
Structural models try to model the behaviour of the firm
so as to represent the default or bankruptcy of a com-
pany in as realistic a way as possible. The classical work
in this area was by Robert Merton who showed how to
think of a company’s value as being a call option on its
assets. The strike of the option being the outstanding
debt.
Merton assumes that the assets of the companyAfollow
a random walk
dA=μAdt+σAdX.
IfVis the current value of the outstanding debt, allow-
ing for risk of default, then the value of the equity
equals assets less liabilities:
S=A−V.
HereSis the value of the equity. At maturity of this
debt
S(A,T)=max(A−D,0) and V(A,T)=min(D,A),
