Average Price Option Strip Case Study

Value Average Price Option Strips Here

Problem: An oil-consuming client needs to buy oil in the future and needs to protect against a future rise in the price of oil, whilst still being able to benefit from a future drop.

Solution: The client asks a bank to enter an Average Price Option Strip, in which the bank pays periodically to the client any rise of the price of oil F over an Exercise Price (aka Strike) K. For each period, the price of oil F is the average of daily observations of the Front Future Contract's price during the period's duration (a month in general). The pay-off for each period is therefore:

“If F > K then the bank pays FK, otherwise the bank pays zero.”

The client receiving such a pay-off is said to be long a strip of Call Options. The Premium due by the client for the strip can be either paid upfront or paid over the duration of the Options Strip under the form of a fixed coupon C per period, so that, at each period, the net cash flow is:

If F > K then the bank pays FK. The client always pays C.”

Variations on the problem and on the solution: The client may be an oil producer instead of an oil consumer and therefore in need to protect against a drop in the price of oil, whilst still being able to benefit from a rise. The client may then buy Put Options and the pay-off at each period is:

“If F < K then the bank pays KF, otherwise the bank pays zero.”

The client may be an non-oil-based energy producer, whose net revenue is positively correlated with the price of oil. In that latter case, the client may opt for selling Call options to monetise future profits now. In this case, the pay-off at each period is:

If F > K then the client pays FK, otherwise the client pays zero.”

The Premium for the calls sold by the client can be used to subsidise preferential terms on a loan taken by the client, or else to boost the coupon served by a fixed rate investment taken by the client.

The client may also be an investor holding the view that the price of oil will rise over a level H in the future and will not drop below a level L. The client may therefore elect to subsidise her purchase of Call Options with the sale of Put Options. The resulting position is called a Risk Reversal, in which the pay-off at each period is:

“If F > H, then the bank pays F H
If F < L, then the client pays L F
Otherwise, no cash flow takes place.”

The client holding the reverse view can sell (aka 'short') the Risk Reversal rather than buying it. The levels H and L may be chosen so that the Premiums of the Call Options purchased and the Premiums of the Put options sold cancel out, to form a self-financing structure.

Example Term Sheet And Valuation:

Deal : a monthly sequence of Options (Calls or Puts) on the arithmetic average of daily observations of the front Futures contract in the underlying commodity (i.e., oil in our example).

Daily Observations are made on each business day of the period month. Each period is cash-settled in the numeraire currency (i.e., the USD in our example) on the business day immediately following the last business day of the period month.

Terms :

Currency Pair WTIUSD (US Dollar per Barrel of Cushing WTI Crude)
Effective Date Fri 01/Jul 11
Termination Date Sun 01/Jul 12
Strike At-The-Money Options
Value of the Strip USD 103.64
Value of a USD 1.00 Annuity USD 11.97578070365786
Swap's Breakeven Coupon USD 101.53027259792063
Valuation Date Mon 6 Jun 11

Schedule Table :

Maturity Date Settlement Date Expected Average Payoff Type Strike Volatility of Average Option PV
Fri 29 Jul 11 Mon 1 Aug 11 99.78 CALL 99.78 23.99% USD 3.64
Wed 31 Aug 11 Thu 1 Sep 11 100.25 CALL 100.25 26.89% USD 5.21
Fri 30 Sep 11 Mon 3 Oct 11 100.71 CALL 100.71 27.62% USD 6.24
Mon 31 Oct 11 Tue 1 Nov 11 101.08 CALL 101.08 28.23% USD 7.21
Wed 30 Nov 11 Thu 1 Dec 11 101.38 CALL 101.38 28.52% USD 8.01
Thu 29 Dec 11 Tue 3 Jan 12 101.61 CALL 101.61 28.77% USD 8.73
Tue 31 Jan 12 Wed 1 Feb 12 101.82 CALL 101.82 29.04% USD 9.5
Wed 29 Feb 12 Thu 1 Mar 12 102 CALL 102 29.06% USD 10.08
Fri 30 Mar 12 Mon 2 Apr 12 102.2 CALL 102.2 28.87% USD 10.57
Mon 30 Apr 12 Tue 1 May 12 102.37 CALL 102.37 28.64% USD 11.04
Thu 31 May 12 Fri 1 Jun 12 102.55 CALL 102.55 28.39% USD 11.46
Fri 29 Jun 12 Mon 2 Jul 12 102.63 CALL 102.63 28.49% USD 11.95

Valuation Notes:

the Value of a USD 1.00 Annuity can be used to determine the coupon payable at each period to spread the premium over the life of the deal. The periodic coupon is just the Value of the Strip divided by the Value of a USD 1.00 Annuity.

In the specific case of oil, averaging observations made over a month span two successive Future contracts, since the last trading day for oil futures contract is around the 16th of each month. Successive contract prices are well correlated for far out contracts, but not for upcoming ones (in one or two months). This has pricing / position management implications that must be considered by oil options market makers and traders.

the log-normal volatility of the average is implied from the Asian option's price.

© Reference Derivatives 2011

Alexandre Pelletier,
4 Oct 2011, 05:57