Introductory Context
"The long call butterfly's payoff at expiry is a triangular spike centred at the ATM body strike. Below the lower wing: all three calls expire worthless (or the ITM call has intrinsic value exactly offset by the short calls' obligations) -- net P&L is approximately zero or the small net debit paid. At the body strike: maximum profit. Above the upper wing: all three calls are ITM, their intrinsic values cancel out, net P&L approaches zero. The butterfly earns only within the 'tent' bounded by the two wing strikes. "
Payoff Calculation at Each Strike Level
Using the Topic 16.1 example: buy 23,000 CE Rs 148, sell 2x 23,500 CE Rs 120, buy 24,000 CE Rs 40. Net debit: Rs 148 + Rs 40 - Rs 240 = wait, let me recalculate: Rs 148 (lower wing cost) + Rs 40 (upper wing cost) = Rs 188. Rs 120 x 2 = Rs 240 (body credit). Net: Rs 240 - Rs 188 = Rs 52 net credit. This is a net credit butterfly -- the body credit exceeds the wing cost.
At Nifty 22,500 at expiry (below lower wing): all three calls OTM. All expire worthless. P&L = net credit received = +Rs 52 per unit = +Rs 3,900 per lot. At Nifty 23,000 at expiry (at lower wing): lower wing (23,000 CE) expires exactly ATM (Rs 0 intrinsic). Two short calls (23,500 CE) are OTM. Upper wing (24,000 CE) is OTM. Net P&L = net credit = +Rs 52. At Nifty 23,500 at expiry (at body/maximum profit): lower wing (23,000 CE) intrinsic = Rs 500. Two short body calls intrinsic = Rs 0 each (ATM at expiry). Upper wing (24,000 CE) intrinsic = Rs 0. Net: Rs 500 - Rs 0 = Rs 500 per unit. P&L = Rs 500 + Rs 52 credit = Rs 552 per unit. Wait -- the maximum profit formula: when both short calls expire at zero and the lower wing is ITM by the wing width: P&L = wing width - net debit (for debit butterflies) OR wing width + net credit (for credit butterflies). At Rs 52 net credit: P&L = Rs 500 + Rs 52 = Rs 552 per unit = Rs 41,400 per lot.
At Nifty 24,000 at expiry (at upper wing): lower wing (23,000 CE) intrinsic = Rs 1,000. Two short body calls intrinsic = Rs 500 each = Rs 1,000 total obligation. Upper wing (24,000 CE) intrinsic = Rs 0. Net: Rs 1,000 - Rs 1,000 = Rs 0. P&L = net credit = +Rs 52. At Nifty 24,500 at expiry (above upper wing): lower wing (23,000 CE) intrinsic = Rs 1,500. Two short body intrinsic = Rs 1,000 total. Upper wing (24,000 CE) intrinsic = Rs 500. Net: Rs 1,500 - Rs 1,000 - Rs 500 = Rs 0. P&L = net credit = +Rs 52.
Long Call Butterfly Payoff Summary
Below lower wing (23,000): P&L = +Rs 52 (net credit retained, all calls OTM). At lower wing (23,000): P&L = +Rs 52. Between lower wing and body (23,000-23,500): P&L rising from Rs 52 toward Rs 552. At body/maximum profit (23,500): P&L = Rs 552 per unit = Rs 41,400 per lot. Between body and upper wing (23,500-24,000): P&L declining from Rs 552 toward Rs 52. At upper wing (24,000): P&L = +Rs 52. Above upper wing: P&L = +Rs 52. This butterfly produces a net credit -- the Rs 52 floor means a minimum profit everywhere outside the 'tent,' with maximum profit at the body strike.
The Break-even Levels
For a net credit butterfly, the break-even concept is different -- the position is always profitable (the minimum P&L is the net credit). There are no break-even levels in the traditional sense. The maximum profit point (Rs 552 at the 23,500 body) is the peak; the minimum profit (Rs 52 at or beyond the wings) is the floor. For net debit butterflies (where wing cost exceeds body credit): lower break-even = lower wing strike + net debit; upper break-even = upper wing strike - net debit. Within the break-even range, the debit butterfly is profitable; outside it, the small loss (equal to the net debit) applies.
The Call Butterfly's Risk Profile
The long call butterfly's maximum risk is the net debit paid (for debit structures) or it has no maximum loss and a minimum profit (for credit structures). In the net credit case from the example: the position has a guaranteed minimum profit of Rs 52 per unit regardless of where Nifty settles -- making this version essentially risk-free (a rare property). However, the guaranteed Rs 52 minimum profit comes from the ATM body options' large premium relative to the wing options -- a configuration that occurs mainly when ATM options are particularly expensive (high VIX environment).
For the more common net debit case: the maximum loss is the net debit paid (Rs 25 in the Topic 16.1 alternative example). The position shows a loss of Rs 25 per unit at expiry if the underlying is outside the wing strikes on either side. The maximum profit (Rs 175 per unit in that example) is earned only if the underlying is exactly at the body strike. The risk-reward ratio (Rs 175 maximum profit / Rs 25 maximum loss = 7:1) is the butterfly's primary attraction -- a very favourable risk-reward at the expense of the precision requirement.
Why the Net Credit Butterfly Exists
A net credit long call butterfly seems paradoxical: buying and selling options and receiving money? It occurs when the ATM body options are priced at a significant premium to fair value relative to the OTM wing options -- a situation that arises when the volatility skew or the term structure of volatility makes the ATM-to-OTM premium ratio unusually wide. In high-VIX environments where ATM IV is elevated relative to the wings' IV, the body credit often exceeds the wing costs. This credit butterfly is the most income-efficient butterfly configuration -- maximum profit of Rs 552 at the body with no downside risk.
The long call butterfly's payoff tent tells the trader exactly what they are betting on: the underlying settling at the specific body strike at expiry. Not a range, not a direction -- a single level. The width of the tent (500 points between the wing strikes) tells the trader how much imprecision is tolerable. A wider tent (1,000-point wings) is more forgiving but generates less credit at the body (the wings are further OTM and cheaper). A narrower tent (200-point wings) requires extreme precision but generates higher income per wing-width unit. The wing width is the precision-income trade-off made explicit.
Enter the Long Call Butterfly When the Body Strike Is at a Major Technical Target
The butterfly's maximum profit is earned when the underlying settles at the body strike at expiry. The probability of this occurring increases when the body strike coincides with a major technical level that acts as a magnet: Max Pain for the current expiry, a significant round number (24,000, 25,000), a prior high that has been resistance-turned-support, or the weekly Pivot Point. When the body strike has OI-based and technical-analysis-based gravitational pull from multiple independent sources, the butterfly's single-point precision requirement is supported by the market's structural tendency to gravitate toward that level.