MERTON_IMPLIED_VOL

MERTON_IMPLIED_VOL(faceDebtToMarketEquity,years,treasuryPct,spreadBp[,output])

TrancheData=EXTRACT(Deals,data)
AllCapital=EXTRACT(Deals,capital_structure)
Solutions=MERTON_IMPLIED_VOL(TrancheData,AllCapital)

Two tables use the reported debt/book equity ratio matched on CIK and pricing date. One input table may instead supply Face debt / market equity or Debt / book equity, Treasury yield %, Spread bp, and Years (or Settlement and Maturity as ISO dates). Date terms use actual days divided by 365.25. Each tranche retains its input columns and receives volatilities in percent or a row-level calibration status.

Extract asset, equity or debt for maturity scatterplots. spread_10y plots implied equity volatility against spread. leverage_10y plots implied asset volatility against leverage. Both include solved tranches within 31 days of ten years on the year-fraction scale. Extract slideshow for all five charts or data for the full table.

Enter total face debt divided by pricing-date equity market cap. Reported debt can proxy for face debt. Substituting book equity produces a book-leverage scenario. Years is the remaining term. Treasury yield is a semiannual bond-equivalent annual percentage and spread is the issue yield less that Treasury yield in basis points.

With face set to one, discount at the issue yield to obtain market debt. Add market equity to obtain firm assets. Fit the Merton equity call, assuming a constant risk-free rate, no payouts and a single zero-coupon liability. The observed coupon bond spread supplies a flat zero-yield spread proxy. Volatilities measure annualized instantaneous percentage returns at pricing.

MERTON_IMPLIED_VOL(0.50,10,4.428,80)
MERTON_IMPLIED_VOL(0.50,10,4.428,80,"equity")
MERTON_IMPLIED_VOL(0.50,10,4.428,80,"debt")

Default output is a one-row table. Select asset, equity or debt for a numeric result in percent (e.g., 25 means 25% per year).