LESS THAN ZERO It’s possible to use the CME implied volatility and replicate the CME data for put option premiums and deltas using Black Scholes, by using a zero price less than zero.
This was achieved by adjusting the Futures Price and Strike Price upwards by an amount equal and opposite to the amount that the new zero was below $0/bbl.
For example, if the new zero were -$40/bbl, like the 20 April contract low price for May futures, then a $1 Put basis a $12.25/bbl futures market becomes a $41 Strike Put basis an underlying futures market at $52.25/bbl.
We solved for the “new zero” until our put premiums and delta’s matched the CME figures basis the CME implied volatilities, and the results suggested an implied zero floor price of around -$100/bbl:
OPTION RESULTS: Using -$100/bbl as the “new zero”, makes the underlying future $112.25 ($100 + $12.25) and the $0.50 Put strike = $100.50
Table 3
Basis the same implied volatility and expiry date, this gives a Put offer of $1.75/bbl and a delta of –ve 19%, which is pretty close to the CME figures.
Replicating across the CME Put Strikes shown, using a new zero of -$100 and Black Scholes gave the best fit for the premiums and deltas on the CME Screen:
The table on the left ( Table 3) shows the data from the CME screenshot; the Black Scholes data using a zero of zero; and the Black Scholes data using a “zero of -$100/ bbl”.
Source: CME Chart 3: Put Premiums (y-axis) by Strike (x-axis)
Chart 3 shows the Put Premiums using “new zeros” of -$80, -$100 and -$120/bbl, against the premiums on the CME screen, with a floor price of -$100 showing the best fit for low strike puts.
April’s extraordinary WTI action resulted after storage issues surprised derivative investors, used to trading one of the most liquid commodity markets.
Investor longs have spread their concentrated front month positions along the curve, owners of surplus storage are likely to have been big winners and, with June’s contract rolling off without drama, the market seems back to normal.
Expensive, but valuable lessons learned. Source: CME / Reuters / ADMISI
Rohan Ziegelaar E:
metals.desk@
admisi.com T: +44(0) 20 7716 8081
27 | ADMISI - The Ghost In The Machine | Q2 Edition
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