Diagonal spread

Line the three spread families up and the naming makes sense at once. Picture an option chain with strikes down the side and expiry months across the top:

• Vertical spread — move down a column. Same expiry, different strikes.
• Horizontal spread — move across a row. Same strike, different expiries.
• Diagonal spread — move diagonally. Different strike and different expiry.

A diagonal is therefore both of the other two at once: it carries a directional view (from the strike difference, like a vertical) and a time-value view (from the expiry difference, like a horizontal). The workbook's verdict is blunt — these are much more complicated in nature and in execution, and like a horizontal spread, no payoff diagram can be drawn, because the two legs expire on different dates.

All three families share the same two constraints: same option type (two calls or two puts) and same underlying.

The usual construction sells a near-month, further out-of-the-money option and buys a far-month, closer-to-the-money one. The near leg funds part of the far leg, and it decays fast; the far leg carries the directional exposure and decays slowly.

That means the position has two separate ways to make money and two separate ways to lose it. The strike gap caps how badly the short leg can hurt you at its own expiry, exactly as in a vertical spread. But the cap is not a maximum loss for the position, because the long leg is still alive and its value depends on time and volatility that have not yet resolved.

Why it is hard to execute is worth stating plainly: liquidity in currency options concentrates in the near month. A far-month leg often has to be worked, and if only one leg fills you are left with a naked short option instead of a spread — the same one-legged risk the workbook flags for arbitrageurs.

Net debit (or credit) = Far-month premium − Near-month premium

At near expiry:
  Short near leg settles at  max(Spot − Strike_near, 0)   [calls]
  Long far leg is still worth intrinsic + remaining time value

Position value = Far-leg market value
               − Near-leg settlement
               − Net debit paid

Rupee value of any quoted figure = premium × 1,000, the USDINR contract size.

USDINR spot is 83.00. A trader is mildly bullish over the next two months but expects nothing much in the next fortnight. He builds a diagonal on calls:

Both axes have moved: the strike is 0.50 apart and the expiry is 49 days apart. On 10 contracts the outlay is Rs 4,000.

Outcome 1 — USDINR drifts to 83.40 at April expiry. The short 83.50 call is out of the money and dies.

April 83.50 call : expires worthless, keep 0.15          = +0.15
June  83.00 call : 49 days left, intrinsic 0.40 + time 0.22
                   quoted 0.62; sell it: 0.62 − 0.55     = +0.07
Net                                                      = +0.22

+Rs 220 a lot, Rs 2,200 on 10 contracts — a 55% return on the Rs 4,000 committed. Both engines fired: the short leg's time value was collected in full, and the long leg gained intrinsic value.

Outcome 2 — USDINR jumps to 84.00 at April expiry.

April 83.50 call : settles at intrinsic 0.50, received 0.15  = −0.35
June  83.00 call : intrinsic 1.00 + time 0.15 = 1.15
                   sell it: 1.15 − 0.55                      = +0.60
Net                                                          = +0.25

+Rs 250 a lot. Better than Outcome 1 — but notice how little better, despite the rupee moving a full rupee further. The 0.50 strike gap stopped capturing the move above 83.50, and the June leg's time value shrank from 0.22 to 0.15 as it went deep in the money.

Outcome 3 — USDINR falls to 82.20. The short leg dies (+0.15); the June 83.00 call is now far out of the money and worth perhaps 0.10, a loss of 0.45. Net −0.30, or −Rs 300 a lot, −Rs 3,000 on 10 contracts — most, though not all, of the Rs 4,000 debit.

Chapter 5 (Strategies using Exchange Traded Currency Derivatives), section 5.3.3, defines the diagonal spread in two sentences, and both of them are examinable: it involves options on the same underlying with different expiry dates as well as different strikes, and because the legs have different maturities no payoff diagram can be drawn.

The standard question presents two option legs and asks you to name the spread. Check both axes: same expiry different strike is vertical; same strike different expiry is horizontal; both different is diagonal. The workbook's own aside that diagonals are "much more complicated in nature and in execution" also turns up as a true/false item.

• Both things must differ. If either the strike or the expiry is shared, it is not a diagonal — it is a vertical or a horizontal spread.
• No payoff chart. Same reason as the horizontal: two expiry dates, so nothing to plot on a single axis.
• Still one option type. A call plus a put is a straddle, strangle or combination, never a spread — whatever the strikes and expiries do.
• The strike gap is not a maximum loss. In a vertical spread it is; here the far leg outlives the near one, so the position is not closed out at the near expiry and the loss is not capped there.
• Execution risk is the real-world trap. A far-month currency option can be thin; a partial fill leaves a naked short option rather than a spread.
• A diagonal is not automatically "bullish" or "bearish". It carries a directional view and a time-value view, and the two can pull against each other, as Outcome 2 above shows.