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I. Basic math.
II. Pricing and Hedging.
1. Basics of derivative pricing I.
2. Change of numeraire.
3. Basics of derivative pricing II.
4. Market model.
5. Currency Exchange.
6. Credit risk.
A. Delta hedging in situation of predictable jump I.
B. Delta hedging in situation of predictable jump II.
C. Backward Kolmogorov's equation for jump diffusion.
D. Risk neutral valuation in predictable jump size situation.
E. Examples of credit derivative pricing.
F. Credit correlation.
G. Valuation of CDO tranches.
7. Incomplete markets.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Credit risk.


uppose a high graded institution (let us call it 'AA Bank') is approached by a low graded company (we call it 'Business') for a loan. Business is prepared to pay significant interest on the balance. However, there is a noticeable risk of default. If AA Bank issues a loan then regulatory oversight would require that AA Bank keep significant reserve capital against such transaction. This reserve capital requirement would significantly reduce the profit and still leave AA Bank exposed to the risk of loss.


Credit risk figure 1

Instead, Business may approach a low grade lending institution, we call it "BB Bank". BB Bank do not have the same problem with oversight. However, it suffers from high borrowing costs itself. Hence, if it lends to Business, then its profit would also be low against the same risk of loss.


Credit risk figure 2

The situation resolves with introduction of Credit Default Swap. AA Bank lends to Business and purchases insurance against default by Business written by BB Bank. This way AA Bank is only exposed to the simultaneous default by the BB Bank and Business and does not need to keep the reserve capital. AA Bank keeps the difference between the ingoing and outgoing coupon payments. BB Bank receives coupon in exchange for its obligations and does not need to procure any capital.


Credit risk figure 3

The described above situation is an illustration of a general tendency. Financial institutions create wealth by ignoring some risk that is perceived as almost non-existent. Initially such perception (that Business and BB Bank would not default simultaneously) is correct. However, as more people join the same activity, the total amount of notional on the market becomes so great that the presence of these contracts significantly increases the probability of the event that was initially perceived as nearly impossible. When the signs of the trouble arrive, AA Bank might move to close the position or purchase additional insurance and discover that the necessary liquidity is no longer present.

The reference for the math of the following sections is [AndersenOnLine] .




A. Delta hedging in situation of predictable jump I.
B. Delta hedging in situation of predictable jump II.
C. Backward Kolmogorov's equation for jump diffusion.
D. Risk neutral valuation in predictable jump size situation.
E. Examples of credit derivative pricing.
F. Credit correlation.
G. Valuation of CDO tranches.

Notation. Index. Contents.


















Copyright 2007