AA Credit using market cap volatility, solving for Distance to Default
(d2 in Black Scholes)
George Robertson
## [1] "SP500"
## [1] "BAMLC0A2CAA"
The input for a stochastic analysis of AA credit is the volatility of the SP500, specifically the one year realized volatility (240 N):
The SP 500 volatility is transformed via simultaneous equation into asset volatility, using the equity value for the SP500 and the debt to arrive at a market cap (Vola below) or the volatility of the market cap (debt and equity) is derived:
Vole = [N(d1) X V X Vola] / E
The asset volatility derived:
Asset Vol of the SP500 is scatterplot to AA spreads, shows deeper insight of a stochastic analysis of credit.
While the above scatter of log of SP500 levels versus log of AA spread suggests that AA spreads might even be wide and may tighten, SP500 asset vol scatter to AA spread shows the opposite.:
The asset volatility is the sigmaa, or vol of the underlying, in a standard Black Scholes formula to find the d2. We do not solve for price, just d2, as the price asymptotes along the x axis and while correct theoretical is of little use for trading and risk management.
The d2 formula is well known:
The d2 depicts in units of volatility years (Brownian scaling of time) how far the underlying credit is from default given the current asset volatility, for a certain time period (we use 5 years) and for a certain interest rate or rho (we use 3%). The d2 is often called when using a Merton formula the “distance to default”, or D2D. D2D us plotted over time and while the SP500 has sold off of late, the D2D of the SP500 has crashed and has lost 1/2 the peak value during the low sub 10% volatility period before Feb 2018 this year:
The above D2D is scatterplot against AA spread.
It is obvious that AA spread currently ( November 23 2018 ) can explode upwards, doubling towards 150 to 175. Since this is based upon volatility the characteristics of vol changes, long dated vol, it will change via regime shifts of jumps up or down should be considered. Volatility does not move in a discrete fashion like SP500 price and likewise credit spreads which we are showing are pricing volatility will move in regime shifts.
A closeup of the above larger scale scatter is given, which gives greater detail:
It is very likely that AA credit spreads, unless long dated volatility of the SP500 drops again to levels of 2017, will surge wider. This may surprise as it can happen while the SP500 is trading upwards. It is obvious an ex post Altman or Graham Dodd type of credit analysis does little to anticipate or provide prescience for key credit spread moves.
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