本文主要從對bank risk in options prices分析，由代寫英國留學生dissertation中心策劃組提供。是英文語種、Financial economics研究方向、不需要數據處理的碩士課程dissertation Master Assignment，不需要盲審（博士或碩士生有這個需要），如有需求請聯系本站dissertation中心或者提交相關文章的代寫需求。
 

Abstract
The volatility of its share price reflects the volatility of the market value of a bank’s assets.
We present data for the volatilities of individual banks’ shares that are implied by the prices of
options on the banks’ shares. We present evidence that implied volatilities (IV’s) better forecast
actual, future volatilities of share prices than historical volatilities do. Banks’ IV’s are correlated
with marketwide volatility, with the levels of their own share prices, with their own
subordinated debt yield spreads, and with other banks’ IV’s. Bank capital reduces the response
of IV’s to market volatility. IV’s are likely to add information about bank risk that is timely,
cheap, objective, and useful.

1. Introduction
Bank supervisors, investors, depositors, and even bank borrowers are interested in
estimates of the likelihood that a bank will become insolvent. The likelihood that a
bank will become insolvent rises with its expected losses relative to its total of equity
capital and reserve for losses. The likelihood also rises as the variance of its unexpected
losses rises relative to its net capital. 1 To offset the former effect, bank
supervisors intend that a bank’s reserves for loan and lease losses rise as a bank’s
expected losses rise. To at least partially offset an increase in the variance of a bank’s
unexpected losses, bank supervisors might also intend that a bank hold more capital,
conditions at the bank warrant. How much more, then, presumably reflects, among
other things, the bank’s supervisors’ view about the expected variability of the value
of the bank’s assets.
Judgments about the likelihood of a bank (holding company) becoming insolvent
are typically based on both on-site and off-site surveillance. 2 On-site surveillance
takes place through bank examination. To assist in off-site surveillance, financial
statements and government-mandated and other reports that contain accounting
and other data are reviewed and tracked. For decades, analysts inside and outside
bank supervisory agencies have used financial statements and reports to help assess
the likelihood that a bank would become insolvent. Book values of capital, earnings,
loan charge-offs and provisions, loans disaggregated by category of borrower, and
other variables have been mainstays in these efforts.
Over the past few decades, more and more of the assets and liabilities of large US#p#分頁標題#e#
banks have come to be traded in financial markets. This enables bank supervisors
and other analysts to monitor the market prices and quantities of the assets and liabilities
of a bank. Bank supervisors in the US, for example, sometimes monitor
yield spreads on a bank’s subordinated (sub) debt for signals about its financial outlook.
They can also monitor the prices and issuance of shares of stock in a bank. In
general, we expect that the market prices of these traded, longer-term financial assets
will be more sensitive barometers of expected future values than most accounting
measures that banks report for past periods.
Empirical work that addresses the relations between market information and
banks’ current and expected future conditions focuses on the prices of subordinated
debt and equity. For example, Flannery and Sorescu (1996), Jagtiani et al. (2000),
Sironi (2000) and De Young et al. (2001) find that sub debt yields incorporate accounting
information about the bank. Sironi (2000) notes that the sub debt yields
of European banks increasingly reflect those banks’ risks over the 1990s.
Recent studies by Evanoff and Wall (2000) and by Hancock and Kwast (2001) lay
out some of the potential benefits and pitfalls of using sub debt yields to evaluate the
conditions of banks. A joint study conducted by the Board of Governors of the Federal
Reserve System and US Department of the Treasury (2000) notes that the sub
debt yield spread seemed not to bear a consistent relation to the likelihood of banks’
financial distress. In general, prior studies also conclude that yield spreads at issuance
during 1986–1987 and before then do not reflect risks, while spreads during
1988–1991 do reflect banks’ risks. The Fed–Treasury study concludes that the
spreads between yields on banks’ subordinated debt and Treasury bond yields
change with changes in liquidity, in the supply and demand for specific issues of
sub debt, and in the characteristics of specific issues. The report finds that since
the late 1980s the sub debt yield spread responds to changes in banks’ risks when
banks are in distress or in turmoil. De Young et al. (2001) present similar findings.
They conclude that sub debt yield spreads respond less to changes in presumed risk
measures at banks that are regarded as being healthier.
The Fed–Treasury study also notes that sub debt yield spreads differ importantly
from the KMV estimates of the expected default frequencies (EDFs) over
the 1995–2000 period. More recently, Gropp et al. (2001) reported that yield spreads
and equity-based distance-to-default measures both help to explain a bank’s financial
fragility. They concluded that regulators should use both of these market-based
signals.#p#分頁標題#e#
The correlations between yield spreads and many proxy measures for bank volatility
or probability of failure perhaps should not be expected to be very high. It may well
be that the relations between yield spreads and many proxy measures will be nonlinear.
The relations might also be altered, as suggested above, by changes in liquidity
and other idiosyncratic factors. Other more systematic factors, like changes in expected
tax impacts and changes in the prices of various risks, may also be expected
to shift yield spreads by important amounts, quite apart from any changes in the condition
or outlook for a bank. Indeed, it may well be that such shifts in yield spreads
would occur particularly, but not only, during times when information from market
prices would have been most helpful to bank analysts. For example, the financial turmoil
of the late 1990s might well have shifted yield spreads on banks’ sub debt by far
larger amounts than would be warranted by the shifts in banks’ riskiness.
A good case can be made that no single proxy should be expected to perfectly signal
banks’ volatility or risk of failure. Any measure might dominate others as indicators
of specific aspects of bank conditions. Consider signals about the variability of
the market value of a bank’s assets and equity. The standard deviation, or volatility,
of equity share returns is typically thought of as a measure of the firm’s equity risk.
As such, the market’s implied assessment of the second moment of the distribution
of share returns is likely to provide a ready supplement to the levels of share prices.
Implied volatilities (IV’s) may better signal volatility of the market value of bank equity
and assets, quite apart from the probability that a bank will fail, which will be
affected by a bank’s capital and other factors. Because they are affected so much less
by capital and other factors, IV’s may be one of the few proxy measures that would
signal, following a run of unusually good luck that increased the bank’s net worth,
that a bank remains volatile. In that regard, IV’s might be of special interest to a
bank supervisor seeking to require more capital in the face of increases in the volatility
of the value of a bank’s assets.
Here we analyze the movements of the expected volatilities of banks’ share prices
that are implied by the transactions prices for their exchange-listed options.We compare
IV to other commonly used measures of bank risk including the historical volatility
(HV) of bank share prices. We show how the IV’s move through time, how
they differ across banks, and how they co-vary across banks through time. We then
show that IV’s have lower root-mean-squared-error (RMSE) forecasts of banks’ future#p#分頁標題#e#
share price volatility than HV’s do and significantly improve forecasts based on
HV’s.
We also estimate how much individual banks’ IV’s co-vary with the volatility of a
broad index of share prices and present evidence that this covariance changes as a

function of a bank’s condition. More specifically, we show that the covariance depends
systematically on the leverage (or capital ratio) of a bank.
We find that the correlations between various proxy measures of bank volatility
and of probability of failure are appreciably above zero and below one. Our results
suggest that a bank’s IV moves partly sympathetically and partly independently of
movements in shares prices as well as in its sub debt yields. This suggests that data
for IV’s are likely to have different noise and thus different signals than those that are
readily extracted from share prices and sub debt yield spreads. At the same time, any
measure of IV’s is also subject to difficulties. In our case, we use time-varying measures
of IV that are derived from the constant-volatility, Black–Scholes option pricing
framework. Although the procedure for deriving estimates of IV’s seeks to
reduce the effects of the volatility of volatility on the estimates, estimation errors
likely remain.
Below we indicate how a regression framework can help choose the combination
of HV’s and IV’s that best forecasts actual, future bank share price volatility. If bank
analysts are willing to construct a measure that quantifies or at least categorizes,
however precisely, the risk of bank failure, then regression or various categorical
methods such as factor analysis can be used to identify the signals offered by the various
proxies for bank risk of failure. We suggest that such indicators of bank risk be
constructed and if the ensuing tests point to its signaling