Historically, there has been limited cross-product trading of credit assets such as bank loans, credit insurance and credit re-insurance, credit derivatives, industrial bonds, and convertible bonds. With the growth of credit derivatives, a legal structure has evolved enabling credit trading across asset classes.
Determining the value of a credit asset is a necessary component of trading but has been a somewhat inexact process. Because the market for credit assets is not very liquid, it is not possible to quickly ascertain the market value of a particular credit asset on a given day. Further complicating valuation are options to draw, prepay, and term-out (i.e., renew) which may be included in the terms of the loan contract. The fact that such options are recurring during the life of the loan and that borrowers seldom exercise such options in an optimal way, makes attributing a value to an option difficult.
One conventional approach for loan valuation uses a hazard rate model. This model captures the expected draw by way of a pre-calculated parameter, which is a function of the credit rating at value date.
According to the hazard rate model, the funded portion of the loan is modeled as a bond, and the unfunded portion is modeled as a modified default swap. The funded cash flow structure is identical to a bond with notional of funded amount plus the additional draw. The unfunded part is equivalent to a default swap with the reference price set at draw rate at default with notional set to be the unfunded amount less the additional draw. Consequently, the present value of the loan is the sum of the present value of the bond and that of the default swap.
Thus, the present value of the funded part is:
      PV    b    =                                          F            a                    ⁡                      [                                                            ∑                                      i                    =                    1                                    N                                ⁢                                                      B                    ⁡                                          (                                              t                        i                                            )                                                        ⁢                                                                          ⁢                                      P                    ⁡                                          (                                              t                        i                                            )                                                        ⁢                                                                          ⁢                                      C                    i                                    ⁢                  Δ                  ⁢                                                                          ⁢                                      t                    i                                                              +                                                B                  ⁡                                      (                                          t                      N                                        )                                                  ⁢                                                                  ⁢                                  P                  ⁡                                      (                                          t                      N                                        )                                                                        ]                          ÷                  R          L                    ⁢                          ⁢                        F          a                ⁡                  [                                    ∑                              i                =                1                            N                        ⁢                                          B                ⁡                                  (                                      t                    i                                    )                                            ⁢                                                          ⁢                                                                                    P                    ⁡                                          (                                              t                                                  i                          -                          1                                                                    )                                                        -                                      P                    ⁡                                          (                                              t                        i                                            )                                                                                                                    ]                      -                  ⁢                  α        s            ⁢      U      where                {ti}iN=0—cash flow date for i≧1, t0 is the value date and tN is in the maturity of the loan.        {Ci}iN=1—coupon at cash flow date ti.        B(t)—the discount function at time t.        P(t)—the survival probability at time t.        RL—loan recovery rate.        Fa—adjusted funded amount.        αs—expected (scaled) draw rate.        F—current funded amount.The coupon Ci is given byCi=ri+fi+ui+si where ri, fi, ui and si are the LIBOR rate, facility fee, utilization fee and spread paid at ti respectively.        
The adjusted funded amount is given byFa=F+αsU 
The present value of the default swap is given by,
      PV    d    =                    U        a            ⁢                        ∑                      i            =            1                    K                ⁢                              B            ⁡                          (                              t                i                            )                                ⁢                                          ⁢                      P            ⁡                          (                              t                i                            )                                ⁢                                          ⁢                      c            i                    ⁢          Δ          ⁢                                          ⁢                      t            i                                -                            α          D                ⁡                  (                      1            -                          R              L                                )                    ⁢                        U          α                ⁢                                  [                              ∑                          i              =              1                        N                    ⁢                                    B              ⁡                              (                                  t                  i                                )                                      ⁢                                                  [                                          P                ⁡                                  (                                      t                                          i                      -                      1                                                        )                                            -                              P                ⁡                                  (                                      t                    i                                    )                                                      ]                          ]            where                αD—the draw rate at default.        {ci}—premium cash flow at time ti, this is computed asci=fi+oi         where fi and oi are the facility fee and commitment fee paid at time ti.        Ua—adjusted unfunded amount and is computed asUa=U−αsU.         
The hazard rate model approach determines the draw independent of the current spread and time to maturity. Loans with a term-out option are valued by extending the maturity of the loan using a pre-calculated lookup table obtained from historical data. Furthermore, this approach does address the timing and amount of draw and prepayment options.
Because the value of an option depends on various parameters such as intrinsic value (in, at, out-of-the money), time to maturity, volatility, spread levels, fees, and other miscellaneous indicatives in the loan contract, system and techniques are needed which capture such dependencies, correctly address draw and prepayment options, and better construe term-out options.
USPTO Backgrounds
USPTO Backgrounds