Volatility Explosions: Straddles & Strangles

NIFTY 50 is an index of large Indian companies. Our options are written on its level, and NIFTY options settle in cash. You never receive the shares. A Call you buy has value at expiry if the final settlement level is above its strike. A Put you buy has value if settlement is below its strike. CE and PE are the labels you see in the option chain, and these contracts are European style. The strike is the contract’s reference level, and expiry is its last day. Premiums are quoted per index unit, so a ₹1 change in premium is ₹65 for the 65 units we assume here.

A straddle is one Call and one Put with the same underlying, strike and expiry, in equal quantity. Ours uses the 25,000 strike. A strangle spreads the strikes apart: here the 24,500 PE and the 25,500 CE, same expiry and quantity. With NIFTY at 25,000, both strangle options are out of the money (OTM), meaning neither would pay if 25,000 were the final settlement. “Long” means you buy both options. “Short” means you sell both. A pair at one shared strike is a straddle even if that strike is far from the current index level. Different expiries, unequal quantities, or buying one leg and selling the other make different positions. The figure uses hypothetical model premiums, and the next chapter explains the assumptions behind them.

To get consistent teaching prices, we use the Black–Scholes–Merton model with hypothetical inputs. NIFTY spot is 25,000, ten calendar days remain (10/365 years), IV is 30% a year on each leg, the interest rate is 6% a year compounded continuously, and the dividend yield is 1%. The model puts the 25,000 CE at ₹512.02 and the PE at ₹477.81 per unit. The unrounded total shows as ₹989.83, or ₹64,338.73 for 65 units. We treat these model values as the entry prices for the payoff study. They are not live quotes and do not show that you could fill at them. The 65-unit quantity is a teaching assumption, not a current NIFTY lot size.

At expiry, the Call is worth the amount by which final settlement is above 25,000. The Put is worth the amount by which it is below 25,000. A leg with no such amount is worth zero. Add the two values, subtract the combined premium once, and multiply by the quantity. For this straddle the result before costs is 65 × (distance of final settlement from 25,000 − combined premium). So the two expiry breakevens are 24,010.17 and 25,989.83. The figures are rounded for display, but the calculations keep full model precision.

At expiry, the winning option has to earn back what you paid for both legs. A 500-point move from the 25,000 strike leaves only 500 points of value, against a ₹989.83 purchase price. One option finishing in the money tells you about that option’s value, not about the profit on the pair. And suppose NIFTY swings widely over the ten days but finishes at 25,000. An untouched long straddle then loses its whole premium. A volatile path and a large final distance are different things.

Before expiry the picture changes, because each premium still holds time value: the part of the premium above the option’s current intrinsic value. Take a separate model snapshot one calendar day after entry. NIFTY has risen to 25,500, nine days remain, and IV on both legs falls from 30% to 18%. Repricing both options in full gives CE ₹625.13 and PE ₹94.46, a total of ₹719.59 per unit. The Call has gained, yet the pair’s model value has fallen ₹270.24 per unit, or ₹17,565.51 for 65 units. This is a change in model value before costs. It is not a loss you have realised by selling.

Keep the same spot, expiry, model inputs and 65-unit quantity. Buy the 25,500 CE at a model price of ₹301.21 and the 24,500 PE at ₹268.58 per unit. Both start out of the money. The combined debit is ₹569.79 per unit, or ₹37,036.59. You pay less than for the straddle, but you buy options that start farther from being worth anything.

At expiry, neither option is worth anything anywhere from 24,500 to 25,500, including both ends. You lose the whole debit across that band. Above 25,500 the Call begins to pay, and below 24,500 the Put does. To earn back the debit, settlement must reach 26,069.79 or 23,930.21. Those are the expiry breakevens before costs. In this comparison they are farther from the starting spot than the straddle’s, even though the strangle is cheaper.

Go back to a settlement of 26,000. The straddle’s Call is worth 1,000 points, but the strangle’s higher-strike Call is worth only 500. After the strangle’s debit, you are left with a loss of ₹4,536.59 for the assumed quantity. This is why comparing only the premium misses half the story: the strikes decide how much value the same final index level creates. The strangle’s maximum payoff loss is smaller in rupees here, but that does not make it the better structure, and it does not make profit more likely.

Before expiry the strangle also responds to spot, time and IV, and the two strikes can have different IVs. Its sensitivities change as spot moves toward or away from the strikes. We compare them after the sellers’ payoffs. As with the straddle, the gain on the upside has no ceiling in the ideal payoff, while the gain on the downside stops at an index of zero.

Now reverse the straddle and sell the 25,000 CE and 25,000 PE in equal quantities. To compare cleanly, assume the same hypothetical entry prices as the long example and zero costs. You receive ₹989.83 per unit, or ₹64,338.73 for 65 units. In real trading, buyers and sellers do not trade at one identical price, because the order book has bids, asks and changing depth. The cash you receive at entry comes with obligations that continue. It is not profit you have earned yet.

At expiry, the short result is the credit minus the two intrinsic values, times 65. With identical prices and zero costs, it is exactly the long result with the sign flipped. The maximum profit is the whole ₹64,338.73 credit, and it arrives only at a final settlement of exactly 25,000. The same breakevens, 24,010.17 and 25,989.83, now surround a profit zone. At 26,000 the short straddle loses ₹661.27, and as settlement climbs further the uncovered Call obligation keeps growing.

Now sell the lower 24,500 PE and the higher 25,500 CE instead, again in equal 65-unit quantities and at the same hypothetical model prices. The combined credit is ₹569.79 per unit, or ₹37,036.59. At expiry both options are worth zero across the whole range from 24,500 to 25,500. So the seller’s maximum profit before costs is the full credit across that range. This is the flat top in the short comparison. The short straddle reaches its maximum at one level only.

Outside the two strikes, one obligation starts to eat into the credit. You can still make a smaller profit until settlement reaches the breakeven at 23,930.21 or 26,069.79. So the range between the breakevens is wider than the flat top. At 26,000 the 25,500 Call owes 500 points and the pair keeps ₹4,536.59 before costs. At 27,000 that Call owes 1,500 points and the short pair loses ₹60,463.41. A calm centre and distant breakevens do not put a ceiling on a large move.

The uncovered Call again makes the upside loss unlimited. The Put loss is finite, since the index stops at zero, but it can far exceed the credit and the collateral you post. To close early you also need funding and a repurchase that actually fills. A wide centre does not give a probability of profit. For that you would need a stated price distribution, an observation period, entry prices and cost assumptions.

Buy protective options beyond both short strikes and the position becomes an iron condor with defined terminal wings, depending on its exact strikes and quantities. They cost money and change the result. The next lesson studies that. A stop order is a different tool. It requests an exit when a condition is met, but a gap, a missing price or an unfilled remainder can leave you exposed.

The Greeks are local sensitivities of the model at one snapshot. Add each leg’s signed exposure to read the pair, and selling flips the signs. Delta is how much the premium changes for a small move in spot. At our entry inputs, the two long-straddle legs together have a Delta of about +0.04179. So the pair’s model premium rises about ₹0.04179 for a one-point rise in spot, with other inputs fixed. That is roughly neutral, but not exactly zero. Gamma is how fast Delta changes. With positive Gamma, the long pair’s Delta gets more positive as spot rises and more negative as spot falls. The short pair does the opposite.

Both bought legs have positive Vega in this ordinary model setting: raise their IV and their values rise, with other inputs fixed. Sold legs have negative Vega. Theta is the change as time passes, with the other inputs held still. At entry the long pairs have negative Theta per calendar day and the short pairs positive Theta. For 65 units, the long straddle’s entry Vega is about +₹2,142.55 per annual-IV percentage point, and its Theta is about −₹3,212.55 per calendar day. These are sensitivities, not promises about tomorrow’s quotes.

A long pair can lose because the final move is too small, because the move comes after expiry, or because its resale value falls as spot, time and IV change together. A short pair can lose from a large move or from rising option values, and it can need a lot of funding. Neither case is explained by the headline or by one winning leg. Follow the combined position, its time horizon and the cash you need to hold or settle it.

An order for two legs is not necessarily a finished pair. Say each leg asks for two assumed 65-unit lots: 130 Calls and 130 Puts. If all 130 Calls fill but only 65 Puts do, you hold one 65-unit straddle plus one stand-alone 65-unit Call. The Put order still waiting is not a contract you own. If you were selling, that extra short Call is uncovered unless another position protects it. A closing order can also leave part of the position open. Reconcile the filled quantities instead of trusting the basket’s label.

A useful study starts before you know the outcome. Write a question such as: “If NIFTY rises but uncertainty around the event falls, what happens to the combined value of this Call and Put?” Keep that note, and a competing explanation, instead of rewriting your reasoning after you see the result. A paper study trains observation and accounting. It does not show that a live position would fill, or give the same result.

The ledger uses our 25,000 straddle and 65 assumed units, with a separate fictional record of fills. The paper entry prices are CE ₹512.00 and PE ₹477.80, slightly different from the full-precision model marks used in the payoff figures. At a later observation before expiry, assume both closing sales fill completely, at CE ₹550 and PE ₹200. These closing prices are made up for the ledger. They do not come from the earlier 18% IV scenario. No real trade, quote capture or dated exchange listing is claimed. The entry payment is ₹64,337, the closing receipt is ₹48,750, and the gross paper loss is ₹15,587. An arbitrary ₹200 of total charges across the four trades gives a net paper loss of ₹15,787. The ₹200 is an accounting illustration, not a current tariff or tax estimate.