Advances in Risk Management

HAYETTE GATFAOUI 121

Table 6.2Average monthly simulated values of firm’s debt

λ

β −1.5 − 1 −0.5 0 0.5 1 1.5

0.2 2.25 4.93 8.02 8.94 7.65 4.24 1.79

1 3.48 4.54 7.47 8.94 6.86 3.75 1.82

5 3.70 4.34 7.08 8.94 6.72 3.65 1.88

moneyness (ratioVt/B), volatility and time to maturity insofar as we focus
on the combined effect of these determinants. Afternsim=1000 simulations,
we compute average values of firm’s debt for various levels ofβandλ;as
in Table 6.2.
Whateverλ, the firm’s average debt is a concave function ofβwith a
maximal value atβ∗=0. When|β|<1.5, debt is a decreasing function of
λ. In contrast, when|β|>1.5, the reverse behavior takes place. Moreover,
average debt’s value is constant whateverλwhenβ=0 since debt value
is independent ofλunder the minimal martingale measure. Debt value
depends on equity, and equity does not depend onλunder the minimal
martingale measure. Indeed, equity is a function of both firm value and
idiosyncratic risk factor (see European call’s expression). However, neither
firm value nor idiosyncratic factor depends onλwhenβis zero. Finally,
realistic values of beta in Table 6.2 (for example,β∈[0, 1]) lead to interesting
conclusions. First, an increase in beta generates a decrease in debt value.
Namely, increasing systematic risk’s impact allows for reducing debt level.
Such a pattern represents the kind of phenomenon that takes place in a good
side of business cycle. Indeed, a growth business cycle trend will improve
the financial market’s trend. Hence, increasing the correlation between firm
value and market will decrease the firm’s credit risk and debt level (good
spillover effect, and benefits from the good side of the business cycle). Sec-
ond, increasing idiosyncratic risk control (highλ) reduces the firm value’s
global risk, and then decreases the debt level for a given systematic risk
level. Hence, when idiosyncratic risk is managed and stabilized around a
convenient level, the firm can concentrate on the systematic risk side that
impacts its business profile and profits. Systematic risk becomes the most
important risk dimension in this case. Conversely, when idiosyncratic risk
cannot be conveniently managed (lowλ), such a risk can highly disturb
the firm’s financial and economic equilibrium since market conditions can
strongly magnify its consequences. Specifically, the firm can undergo hard
times before any mean reversion in idiosyncratic risk occurs. The two dimen-
sions of a firm’s business risk have then to be jointly managed. Indeed, the
firmexhibitsanincreasedlevelofstructuralfinancialriskwhenidiosyncratic
risk is uncontrolled. Namely, the firm’s accounting and financial patterns
usually behave quite badly in such a situation (see Table 6.3).