Introductory Context
"The put butterfly is the preferred construction when the volatility skew creates a larger body credit on the put side than the call side -- which occurs regularly in Indian equity options markets due to the higher IV on OTM puts versus OTM calls. In this skew environment, the put butterfly's body credit (from two short ATM puts) may exceed the call butterfly's body credit (from two short ATM calls) by Rs 5 to Rs 15 per unit, making the put butterfly more cost-efficient for the same three-strike structure. "
Construction and Premium Comparison
For the same three strikes (23,000, 23,500, 24,000) with Nifty at 23,500: Long put butterfly: buy 24,000 PE (ITM put, upper wing), sell 2x 23,500 PE (ATM put, body), buy 23,000 PE (OTM put, lower wing). Put premiums (typical, moderate VIX): 24,000 PE Rs 135, 23,500 PE Rs 112 each, 23,000 PE Rs 52. Net put butterfly cost: (Rs 135 + Rs 52) - (Rs 112 x 2) = Rs 187 - Rs 224 = -Rs 37 net credit per unit. Per lot: Rs 37 x 75 = Rs 2,775 net credit.
Comparing to the call butterfly for the same strikes: buy 23,000 CE Rs 148, sell 2x 23,500 CE Rs 120, buy 24,000 CE Rs 40. Net call butterfly: Rs 52 net credit (from earlier calculation). In this example, the call butterfly actually produces slightly more credit (Rs 52) than the put butterfly (Rs 37). This difference reflects the specific skew conditions and VIX level -- in different market conditions, the put butterfly may be more or less expensive than the equivalent call butterfly. Always check both constructions before entry to identify the more cost-efficient version.
Long Put Butterfly vs Long Call Butterfly
Same strikes: 23,000/23,500/24,000. Call butterfly: buy 23,000 CE, sell 2x 23,500 CE, buy 24,000 CE. Net credit Rs 52 per unit. Max profit Rs 552 at body. Put butterfly: buy 24,000 PE, sell 2x 23,500 PE, buy 23,000 PE. Net credit Rs 37 per unit. Max profit Rs 537 at body. At-expiry P&L is nearly identical for both (put-call parity). Cost difference: Rs 15 per unit in favour of the call butterfly in this example. In skew-heavy environments: the put butterfly may be cheaper.
The Put Butterfly's Payoff at Expiry
At Nifty 24,500 at expiry (above upper wing): all three puts are OTM. All expire worthless. P&L = net credit received = +Rs 37 per unit. At Nifty 24,000 at expiry (at upper wing): upper wing (24,000 PE) expires exactly ATM (Rs 0 intrinsic). Two body puts (23,500 PE) are OTM. Lower wing (23,000 PE) is OTM. P&L = net credit = +Rs 37. At Nifty 23,500 at expiry (at body, maximum profit): upper wing (24,000 PE) ITM by Rs 500. Two body puts expire ATM (Rs 0 intrinsic). Lower wing (23,000 PE) OTM. Net: Rs 500 (upper wing) - Rs 0 = Rs 500. P&L = Rs 500 + Rs 37 (credit) = Rs 537 per unit = Rs 40,275 per lot.
At Nifty 23,000 at expiry (at lower wing): upper wing (24,000 PE) ITM by Rs 1,000. Two body puts each ITM by Rs 500 = Rs 1,000 total obligation. Lower wing (23,000 PE) ATM (Rs 0). Net: Rs 1,000 - Rs 1,000 = Rs 0. P&L = net credit = +Rs 37. Below 23,000 (below lower wing): upper wing (24,000 PE) intrinsic Rs X. Two body puts each intrinsic Rs X - Rs 500 total Rs 2(X-500). Lower wing (23,000 PE) intrinsic Rs X - 1,000. Net: Rs X - Rs 2(X-500) + Rs (X-1000) = Rs X - Rs 2X + Rs 1000 + Rs X - Rs 1000 = Rs 0. P&L = net credit = +Rs 37.
When to Use the Put Butterfly vs Call Butterfly
Three practical criteria determine which butterfly construction to use: (1) Net cost comparison: calculate the net debit or credit for both constructions using current market premiums. Use whichever produces the smaller net debit or larger net credit. (2) Margin consideration: if the short puts in the put butterfly require significantly more SPAN margin than the equivalent short calls, the call butterfly may be preferred even if its net debit is slightly higher. (3) Liquidity: for Nifty options, both calls and puts are highly liquid at ATM and near-ATM strikes, so liquidity is rarely the deciding factor. For individual stock options where OTM puts may be less liquid than OTM calls (or vice versa), liquidity can determine the construction.
Put-Call Parity and the Equivalence of Call and Put Butterflies
Put-call parity guarantees that a call butterfly and a put butterfly with the same three strikes and expiry will produce identical P&L at expiry (ignoring bid-ask friction and marginal premium differences). This is because any difference in the call and put premiums at each strike is accounted for by the forward price and interest rate components embedded in put-call parity. When the market is in equilibrium, the arbitrage-free pricing ensures equivalence. In practice, minor deviations from the theoretical equivalence exist due to the volatility skew, interest rates, and trading frictions -- but these are small enough that the choice between call and put butterfly is primarily a practical (cost/margin) decision rather than a fundamental structural one.
The put butterfly and call butterfly produce the same tent-shaped payoff, the same maximum profit at the body, and the same approximate zero-profit at the wings. The choice between them is a practical optimisation: which version costs less to enter, requires less margin, and has tighter bid-ask spreads? In Indian markets, this comparison is worth making for every butterfly entry -- the skew and term structure create situations where one construction consistently outperforms the other in cost efficiency.
Check Both Call and Put Butterfly Costs in Sensibull Before Every Entry
For every butterfly spread entry: build both the call butterfly and the put butterfly in Sensibull's Strategy Builder using the same three strikes. Compare the net debit/credit for each. Use the construction with the lower net debit or higher net credit. This 30-second comparison can save Rs 10 to Rs 20 per unit (Rs 750 to Rs 1,500 per lot for a 75-unit Nifty lot) by consistently selecting the more cost-efficient construction. The saved cost directly increases the maximum profit of the position.