Large-Scale Financial Risk Management Services. Jan-Ming Ho Research Fellow. Background. Worldwide credit crisis and the credit rating agencies Enron’s bankruptcy in 2001 Lehman Brother’s in 2008 Synthetic CDO backed by RMBS and CDS The Credit Rating Business Protected Oligopoly
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Φ+(k, n) is a convex function of n, Θ+(k, n) is monotonic in n, and Θ+(k, i) ≥ Θ+(k, j) if i > j.
Value at Risk (VaR):
Where:
The probability of up is:
Here σ is the volatility of the underling stock price and t = one time step/ time period of σ
If K ≧ Si*Rj, the portfolio gain (v) equals
If K < Si*Rj, the portfolio gain (v) equals
The portfolio gain at time T can be computed as follows:
where P0is the initial option price; i=1,…,m; and j=1,…,n
Steps of the SSSO-Naive Algorithm
r1 = um
S1 = stock_price * r1
S1
S2
……………
un
un-1d
un
un-2d2
un-1d
un
p-quantile
…….
Sm-3
un-2d2
un-1d
…….
un
Sm-2
…….
un-2d2
un-1d
dn
…….
…….
Sm-1
un-2d2
dn
…….
…….
Sm
dn
…….
dn
un-1d
un-2d2
...
u6dn-6
u5dn-5
u4dn-4
u3dn-3
un
u2dn-2
un-1d
un
un
udn-1
un-2d2
un-1d
un-1d
dn
un-2d2
...
un-2d2
u6dn-6
...
...
u5dn-5
u6dn-6
u6dn-6
u4dn-4
u5dn-5
u5dn-5
u3dn-3
u4dn-4
u4dn-4
u2dn-2
u3dn-3
u3dn-3
udn-1
u2dn-2
u2dn-2
dn
udn-1
udn-1
dn
dn
The Steps of the SSSO Algorithm
S1
S2
S3
……………
p-quantile
Sm-3
Sm-2
Sm-1
Sm
where TCEp_SSSO Algorithm is the TCEp value calculated by the SSSO algorithm, and TCEp_benchmark is the TCEp value calculated by the Black-Scholes formula.
European convertible bond (ECB) and asset swap (CBAS)
CB ID: 23171 (TCRI rating: 4)
CB ID: 19023 (TCRI rating: 5)
CB ID: 14773 (TCRI rating: 3)
CB ID: 140201 (TCRI rating: 4)
Source: Wikipedia
Stock Price Simulation by geometric Brownian motion
(100 paths are selected randomly)
Estimating default intensity (hazard rate) using Duffie’s model
Constant payment
Constant payment
Constant payment
Constant payment
Constant payment
Lending date
Payment date 1
Payment date 2
Payment date n-1
Maturity date
principal
Partial amount of money
Constant payment
Constant payment
Constant payment
Lending date
Payment date 1
Payment date 2
Default date
Payment date n-1
Maturity date
principal
Outstanding
Constant payment
Constant payment
Constant payment
Lending date
Payment date 1
Payment date 2
Payment date n-1
Maturity date
Prepayment date
principal
Determined
Using Tsai el al(2009)
model
Not a constant!!
where Vi is the mortgage price at time i, i=0,1,2,…,n=T/Δt. PV(.) and Ei(.) denotes the present value and expectation of the information at time i under risk-neutral measure.
with initial probability
with initial probability
First expectation
Second expectation
the next year