Merton’s model, credit risk and volatility skews

FIGURE 3 Theoretical relationship between credit spread and at-the-money volatility.

90

# Credit spread (%)

80

Skew (bp)

70

20

60

40

60

50

80

40

100

30

20

10

0

75

100

125

150

175

200

225

ATM volatility (%)

The relationship is implied by Merton’s model for alternative values of the volatility skew when option maturity is two months and debt maturity is five years. The volatility skew is the difference between the volatility of an option with a delta of 0.25 and an option with a delta of 0.5.

FIGURE 4 Theoretical relationship between credit spread and volatility skew.

20

18

ATM (%) 40

# Credit spread (%)

16

14

12

10

8

50 60 70 80 90 100

6

4

2

0 0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

# Volatility skew (%)

Relationship is implied by Merton’s model for alternative at-the-money (ATM) volatilities when option maturity is two months and debt maturity is five years. The volatility skew is the difference between the volatility of an option with a delta of 0.25 and an option with a delta of 0.5.

# Research papers

www.journalofcreditrisk.com

19