Pricing Asian Options on Brent Futures and Estimating Their Greeks

# Greeks for Asian options on futures


# Greeks for Asian options on futures












I'm trying to get the Greeks for the PDB Option Contract (Crude Outright - Dated Brent (Platts) Average Price Option): https://www.theice.com/products/26535747/Crude-Outright-Dated-Brent-Platts-Average-Price-Options

The specifications on this contract are the followings:

Asian Option where the underlying price at end of the contract is the Average daily price between the strip and the strike price (1 month between the dates) of the Dated Brent Future (Or at least that is what I understand)

If this is in this way this contract have a combination of both, an asian option and an option on a future.

For Asian Options I know and I have used the Turnbull-Wakeman model and for Options on Futures I know the Black 76 model.

What I'm doing is to apply the same Turnbull-Wakeman model using as the spot price, the price of the Dated Brent Future (Also from ICE) instead of using the Spot Price of the Brent.

My logic is: The underlying of this asian option is the Future of Brent so use it for the inputs of the formula (spot price and volatility)

But I think I'm not doing it in the right way as I'm using a formula created for `Normal asian options' that is for options on assets not for options on derivatives.

If it helps I have the following market inputs available:

- Spot price of the Brent.

- Future/Forward price of the Brent at a big range of maturities (including the maturity of the option I'm trying to evaluate)

- The Option Price (Premium)

- The Option volatility (Computed using the Black-Scholes model (even if it is an Asian Option))

- The Option Delta (Computed using the Black-Scholes model (even if it is an Asian Option))

And the output I want is all the Greeks (Specially Delta and Vega).

As I have the Black-Scholes Delta I've compared with the Delta I get with my model and is very similar for options with far maturities and it differs more for options with maturites closer to today (If the option maturity is at the end of the month, as part of the averaged price is calculated the delta differs more but this is logic)

Also another this is, as Brent price have a regression toward the mean those models are ok to compute delta to hedge or there are better models?

Thank you,

## Answer by danp (score 0, accepted)

https://quant.stackexchange.com/a/64083

The PDB option is an Asian option which pays at the end of the averaging month the payoff max(Average-Strike,0) (call) or max(Strike - Average,0) (put), where the Average is the daily average of the nearby futures contract.

For example, for the Jan-21 APO the averaging is done over the price of the Mar-21 Brent futures contract until 28-Jan, and over the price of the Apr-21 contract until 31-Jan.

As a first approximation you can assume that the Brent futures follow the Black model (geometric Brownian motion). Then the APO can be priced for example by moment matching (Levy approximation) or the Curran method. The Greeks follow by bumping and repricing.

Hope that this helps.