Credit claimed that this model can be used

Credit
risk nowadays has become a crucial problem in the banking sector. It defines as
a risk that relates to the default by borrowers that fail to make a required
payment to the debt holders. According to Benos and Papanastasopoulos 1 there
are two categories of approach in measuring credit risk, which are structural
and theoretical. Structural approach adopts contingency claim analysis while
theoretical approach adopts accounting ratio-based approach. However, the focus
of this paper is to review on the structural approach only. The origin of this
approach goes back to Fischer Black and Myron Scholes. Fischer Black and Myron
Scholes 2 in their seminal paper propose the Black-Scholes model (B-S model)
to value options in terms of the price of the stocks. Despite its popularity,
the B-S model is actually built with some unrealistic assumptions about the
market such as the underlying asset follow a lognormal random walk, volatility
and interest rate are constant, the options can be exercised at maturity date
only, the stock pays no dividends during the life of the option and etc, as
discussed by Willmott 3 and Teneng 4. Due to those unrealistic assumptions,
many models have been proposed to tackle these problems. The most well-known
among these are Merton model and KMV-Merton model. In 1974, Merton 4 together
with Black and Scholes enhanced the original B-S model and claimed that this
model can be used to develop a pricing theory of corporate liabilities. The analysis
of their study is also extending to include the callable bonds. The assumptions
of Black-Scholes Merton model (Merton model) are in line with the original B-S
model. KMV-Merton was introduced by the KMV Company in 1989. They enhance the
Merton’s model ideas with a little bit different in determining the risk of a
portfolio. The aim of this paper is to derive the B-S model and to review on
the study done by the academicians to the B-S model which consists of Merton
model and KMV-Merton model. The outlines of this paper are as follows: section
2 presents the derivation of B-S formula for a call option, section 3 discusses
on the modifications done to the B-S model and in chapter 4, we conclude.

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