Asymmetric payoff

A futures position is symmetric: a 100-point move up gains exactly what a 100-point move down loses. Plot it and you get a straight line.

An option is asymmetric. The workbook says options are "products with asymmetric risk exposure i.e., the gains when the underlying asset moves in one direction are significantly different from the losses when the underlying asset moves in the opposite direction". The buyer of a call on a stock loses at most what he paid for the option if the stock falls, but gains in proportion to the rise if the stock rises — "thereby resulting in an asymmetric payoff". Futures, by contrast, have symmetric risk exposures (symmetric payoff).

This is why options exist at all. The workbook opens Chapter 4 by noting that futures have a linear payoff with unlimited losses and profits, while some participants "desire to ride the upside but restrict the downside".

The buyer's side (Chapter 4, section 4.5): a long option has limited risk — the premium paid — and unlimited profit potential.

The seller's side is the same asymmetry reversed: a short option has unlimited downside risk but limited upside, to the extent of the premium received.

Margins follow the asymmetry. Because the buyer's loss is capped at a premium already paid, the option buyer pays no margin. The seller, whose loss is open-ended, pays margin and daily MTM.

Pricing follows it too. In section 4.9 the workbook notes that option writers, "conscious about the fact that they are at the receiving end of the asymmetric nature of options pay offs", tend to extract higher premiums from buyers when implied volatility is high — a margin of safety for them.

Futures for contrast. In section 3.6 both long and short futures positions have unlimited profit or loss potential, which "results into linear payoffs".

Long call versus long futures — both on an index at 17,500, lot size 50. The call has a strike of 17,500 and a premium of Rs 95, the figures the workbook uses in Chapter 4 (premium outlay 95 × 50 = Rs 4,750). The futures position at 17,500 is illustrative.

Read the rows in pairs around 17,500:

• Futures: +200 points gains Rs 10,000; −200 points loses Rs 10,000. Symmetric.
• Call: +400 points gains Rs 15,250; −400 points loses only Rs 4,750. Asymmetric.

The price of that asymmetry is visible too: at 17,500 the futures holder is flat while the call holder is down Rs 4,750, and the call needs the index above 17,595 (strike + premium) just to break even.

Chapter 4, section 4.6 (Distinction between futures and options contracts), defines the asymmetric payoff and contrasts it with the symmetric payoff of futures; section 4.5 tabulates the risk and return of long and short options; section 4.9 links the asymmetry to how writers price options. Chapter 3, section 3.6, establishes the linear futures payoff. Expect "which instrument has an asymmetric payoff", "who pays margin and why", and payoff table questions.

• Options are asymmetric; futures are symmetric (linear). Do not describe a futures payoff as asymmetric because it can be long or short.
• The asymmetry cuts both ways. The buyer has limited loss and unlimited gain; the writer has limited gain and unlimited loss.
• Only the option seller pays margin, precisely because his side of the asymmetry is open-ended.
• Limited loss is not no loss. The buyer can lose the entire premium, and loses it most often when the option expires out of the money.
• A put buyer's "unlimited" gain is in practice bounded: the maximum profit for a long put is when the price of the underlying falls to zero.