79. Credit Risk Models. Модели кредитного риска.

Merton model

This model assumes that a company has a certain amount of zero-coupon debt that will become due at a future time T. The company defaults if the value of its assets is less than the promised debt repayment at time T.

Event	Assets	Debt	Share
No default	V(T)≥D	D	V(T) – D
Default	V(T)<D	V(T)	0

Where V(T) – company’s value at time T; D – debt. The equity of the company is pay-off of a long European call option on the assets of the company with maturity T and a strike price equal to the face value of the debt, while debt of the company is zero-coupon bond with nominal value equal to its face value at time T and pay-off of a short European put option on the assets of the company with maturity T and a strike price equal to the face value of the debt. The model can be used to estimate either risk-neutral probability that company will default or the credit spread on the debt.

The Merton model has been shown to be empirically accurate for non-financial firms.

Merton's model has been extended in a number of ways.

По сути: если все активы компании на момент выплаты долга меньше, чем сам долг в момент его выплаты => дефолт. Принимая это, можно представить чистые активы (стоимость компании) как в случае дефолта, так и не в случае дефолта таким образом: чистый доход по длинной позиции европейского опциона колл на активы компании со страйком равным долгу, где долг = безкупонной облигации, и чистой выплате по короткой позиции европейского опциона пут на активы компании со страйком равным долгу, где долг = безкупонной облигации. То есть в зависимости от того, есть ли дефолт или нет, мы реализуем тот или иной опцион. Это чисто синтетическая теория! Не нужно воспринимать буквально!

Cox model.

That is an extension of Merton’s model. The model assumes that a default occurs whenever the value of the assets fall below a barrier level. It also assumes that bondholders can demand liquidation of the company due to bond contract terms.

Thus, in case at some particular point of time, company’s value < debt => default. Consequently, share price equals to barrier down-and-out call on assets with strike price = nominal value of debt, barrier level = level of barrier to default, maturity = T. Thus, D=V(T)-Share Price*№ of shares.

Risk-management

79. Translation Exposure. Трансляционная экспозиция.

Translation exposure measures accounting-derived changes in owner’s equity as a result of translating foreign currency financial statements into a single reporting currency. It is a risk that a company's equities, assets, liabilities or income will change in value as a result of exchange rate changes. This occurs when a firm denominates a portion of its equities, assets, liabilities or income in a foreign currency. 

A firm's translation exposure is the extent to which its financial reporting is affected by exchange rate movements. As all firms generally must prepare consolidated financial statements for reporting purposes, the consolidation process for multinationals entails translating foreign assets and liabilities or the financial statements of foreign subsidiaries from foreign to domestic currency. While translation exposure may not affect a firm's cash flows, it could have a significant impact on a firm's reported earnings and therefore its stock price. Translation exposure is distinguished from transaction risk as a result of income and losses from various types of risk having different accounting treatments. Translation gives special consideration to assets and liabilities with regards to foreign exchange risk, whereas exposures to revenues and expenses can often be managed ex ante by managing transactional exposures when cash flows take place.

Two basic methods for the translation of foreign subsidiary financial statements:

The current rate method: All financial statement items are translated at the “current” exchange rate. Unrealized translation gains or losses are recorded in a separate equity account on the parent’s consolidated balance sheet called the “Cumulative Translation Adjustment (CTA)” account.

The temporal method: Specific assets and liabilities are translated at exchange rates consistent with the timing of the item’s creation. Unrealized translation gains or losses are recorded within the income statement, not to equity reserves, thereby affecting net income.

Methods of hedging:

Balance Sheet Hedge: It requires an equal amount of exposed foreign currency assets and liabilities on a firm’s consolidated balance sheet. A change in exchange rates will change the value of exposed assets but offset that with an opposite change in liabilities. This is termed the monetary balance.

Funds Adjustment: Altering either the amounts or the currencies or both of the planned cash flows of the parent and/or subsidiary.

Forward Market Hedge: Uncovered or open hedge. Not a hedge but an attempt to gain by forward speculation a sum equal to the book loss in translation. Success depends on precise prediction of future exchange rates. Such a hedge will increase the tax burden.