Narrow Results

In this chapter, we investigate how different measures of volatility influence bank’s capital structure beside mandatory capital requirements. We study the relationship between four volatility risk measures (volatility skew and spread, variance risk premia, and realized volatility) and bank’s market leverage and we analyze if banks adjust their capital needs in response to significant increase of risk premia discounting from traders. Among the four volatility measures, volatility skew (defined as the difference between OTM put and ATM call implied volatility and representing the perceived tail risk by traders) affects bank’s leverage the most. As volatility skew increases — hence OTM put became more expensive than ATM call — banks deleverage their assets structure. One plausible explanation relates to the higher costs of equity issuance that a bank will face during a period of distress. As the possibility to incur in expensive equity issuance increases the bank prefers to deleverage its balance sheet and create a capital buffer.

This paper investigates the significance of using a variable default boundary when pricing European Black-Scholes options that are subjected to credit risks. We apply numerical method and combine Klein [1] and Johnson and Stulz [2] to link the payout ratio proportionally to the assets of the option writer. We also link the payout ratio to the value of the assets of the writer. Numerical examples compare our results with Klein [1] and Johnson and Stulz [2] based on alternative assumptions, and illustrate when the application of variable default boundary becomes important.

The following sections are included:

• INTRODUCTION
• COMPUTING THE MODEL-FREE VOLATILITY
• CHOICE OF INDEX OPTION AND DATA
• INFORMATION IN MODEL-FREE VOLATILITY
• ANALYSES OF THE VOLATILITY TERM STRUCTURE
• PROBLEM SET
• FURTHER RECOMMENDED READINGS