Can DCF approach be expressed as a linear regression?
The Discounted Cash Flow approach is a pervasive concept in the banking domain. It can used in several areas such as loss estimation in credit risk, market value of assets/liabilities in the ALM and of course in security valuation. I have recently come across a research paper which show that every DCF approach can be express as a linear regression. The following mathematical proof shows the same.
= ln (1+r) + ln(T) - ln(1-alpha)
ln(MVA/CF) = -ln (1-alpha) +lnT + ln(1+r)
ln(MVA/CF)= b0+ b1*lnT +b2*ln(1+r)
Hence, MVA of asset at a point in time T, that is computed through the DCF approach, can be expressed as a linear regression of
T: Residual maturity
R: Discount rate
CF: Coupon rate
Source: Investing.com, GS 2033, 7.18%
This math can be translated into code using either SKlearn of Python or SAS. I have taken the last 30 days data of 10 year Gsec bond and fitted to the linear regression. Of course, the results can be improved further by addressing the OLS assumptions which are galore here. However, here is the MVP prototype of this concept.
PS: To further improve, you need to work on addressing the breach of OLS assumptions.