## Trading Latin American options

#3

### Trade implications

If the market is overpricing the peso’s volatility compared with the real’s, this may be a second reason for trading the spread between futures prices by going long the March 2015 Brazilian real and short the Mexican peso. The opposite situation prevailed on Jan. 27, 2015, with the real’s cumulative percentage price change from Jan. 1, showing a 200-basis point difference over the peso. The currency prices on Tuesday, Jan. 27, were $0.06858 for MXN and $0.3888 for BRL. By Friday, Jan. 30, both futures had declined, $0.0666 for MXN and $0.3726 for BRL. Shrinking the distance between the cumulative percentage price changes reflects a difference between -2.89% for the Mexican peso and -4.16% for the Brazilian real over a period of three days.

“Mexican peso call options” (below) shows the March 2016 call price model on Feb. 6, 2015. This is the LLP model that shows call prices predicted by a regression analysis. The price equation predicts call option prices from the lowest prices (with highest strike prices) to the highest (with lower strikes) along a parabolic curve.

The curve shows the natural logarithm of call price-to-strike price for each corresponding futures price-to-strike price, thus the LLP price curve is Log-Log Parabola. Normally the call price curve is shown as the antilog curve—with option prices sloping up as the underlying asset price increases—until at some point the slope of the price curve is 1.00. This is where the call price equals the intrinsic value (the underlying asset price less the strike price).

With longer times to expiration, the LLP price curve is restricted to an underlying-to-strike price less than 1.00. The reason is that the curve, as a parabola, insists on increasing when it should be bending toward the intrinsic value. However, looking at a March expiration date (while computing a price curve in January or February with only 30 or so days remaining) improves the odds of the regression going all the way to a slope equal to 1.00.

On the exhibit showing Mexican peso call options, the call price for strike price 0.0660 is computed by the regression equation. Otherwise, the call prices are market prices with predicted premiums close to the actual market prices. Because of the near expiration, the model is able to show a maximum delta approximately equal to 1.00, from which point each option price should be equal to the intrinsic value.

The option pricing model has another advantage—computing the upper and lower breakeven price for each strike price. For example, with the March 2015 futures price at $0.06723, breakeven prices for the $0.0670 strike price are $0.0686 and $0.0657. These are prices for the peso at expiration that would result in zero gain or loss from a delta trade on Feb. 6, hedging the March futures with the number of calls indicated by the delta ratio at the 0.0670 strike. Delta is shown as 0.549, so approximately 1.82 calls would be used to hedge each March futures contract.

Settling the trade

Completing the peso delta trade on Feb. 6, 1.82 March 0.0670 calls are sold for each long futures. The beginning futures price is $0.06723 and the options price is $0.00084. Multiplied by $500,000 per options point, the premium per call option is $420. Thus, 1.82 calls are sold for a total of $764.40 against the price of the March 2015 0.0670 futures. If the peso price is either 0.0686 or 0.0657 at expiration, there will be no gain or loss on the trade. A closing price at the March expiration between the breakeven prices will result in a profit, while a price beyond breakeven will cause a losing trade.

Upper and lower breakeven prices provide the basic framework for pricing options because the price curve for a specific strike price will be tangent to a sloped line starting on the horizontal (zero price) axis (the upper breakeven price), and extending to a point on the intrinsic value line that is exactly above the lower breakeven price.

On Feb. 11, the delta trade described above had the following results: The March futures price was 0.06608, down from 0.06723 on Feb. 6, and the 0.0670 strike was 0.00046, a decrease from 0.00084 at the beginning of the trade. The trade is still within the breakeven prices- although the $764.40 proceeds from sale of March calls is temporarily reduced by the loss on the long futures, (0.06723 - 0.06608) x $500,000 = $575.