Case 063Margin, clearing and risk limitsCore
A broker is short 20 lots, lot 50, of the one-month Satpura 50 22,000 straddle on 14% implied volatility. The exchange revalues the position for index moves of minus 6% to plus 6% combined with volatility up or down 4 points. Which scenario is worst, and what margin does it imply?
1The situation
Anjaneri Securities, a proprietary trading firm, is short 20 lots of the one-month Satpura 50 22,000 straddle: it has sold 1,000 index units of the 22,000 call and 1,000 of the 22,000 put. The index is at 22,000, implied volatility is 14% and the one-month rate is 7%, which prices the straddle at about 715 points, so the firm collected about Rs 7.15 lakh. (A quoted price of 600 points would imply volatility nearer 12%; at 14% the straddle is worth about 715.)
The exchange's margin model revalues every position under a grid of scenarios: index moves of minus 6%, minus 3%, zero, plus 3% and plus 6%, each combined with implied volatility down 4 points, unchanged and up 4 points. The initial margin is the worst loss across the grid. The model's current parameters and any add-on charges are set by the exchange's circulars and must be confirmed there.
2Your task
Revalue the short straddle in all fifteen scenarios, find the worst, and explain why that cell is the one a short straddle should expect to be charged on.
Quick check
Before working it: which scenario produces the largest loss for the short straddle?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The worst scenario is a 6% rise with volatility up 4 points, a loss of about Rs 8.56 lakh, so the scenario margin is about Rs 8.6 lakh on Rs 7.15 lakh of premium. A 6% fall with volatility up costs Rs 6.36 lakh. A short straddle loses on movement in either direction and on rising volatility, so the margin model charges for both at once.
Step 1How does a scenario margin decide what to charge?
Think of a landlord taking a deposit. He does not ask what the tenant will probably break; he asks what the worst plausible damage would cost and holds that much. A scenario margin model does the same: it revalues the position under a fixed set of plausible market moves and holds the worst loss as initial margin. For Anjaneri the position is short 1,000 index units of a straddle worth about 715 points, so every point the straddle gains in value is a Rs 1,000 loss for the firm.
Step 2Why is a large move with rising volatility the worst cell?
Read the grid one axis at a time. Along the middle row, the index does not move and only volatility changes: the straddle gains or loses about Rs 2.0 lakh for 4 points of volatility. Down the middle column, volatility is unchanged and the index moves: at plus or minus 6% one leg of the straddle is 1,320 points in the money, and the loss is about Rs 5.4 lakh for the fall and Rs 7.8 lakh for the rise. The worst cell stacks the two, because a short straddle is short both gamma and vega: it loses when the index travels and loses again when the market pays more for options. In equity indices a sharp fall usually comes with rising volatility, so for the downside the worst cell is also the likely pairing, not a coincidence the model invented.
Notice the asymmetry. The plus 6%, volatility up cell, at Rs 8.56 lakh, is worse than minus 6%, volatility up, at Rs 6.36 lakh. With a 7% rate the strike is discounted: deep in the money, the call at 23,320 is worth at least spot less the present value of the strike, about 1,448 points, while the put at 20,680 is worth about the present value of the strike less spot, 1,192 points. The margin is set by the plus 6% cell, but the risk a desk lives with is the minus 6% cell, because that is the one that arrives with rising volatility.
Step 3What does the margin number leave out?
Three things. The grid stops at 6%; a gap of 10% overnight would cost far more, roughly Rs 14 lakh if volatility jumped to 20%, and the margin does not pretend to cover it. The model revalues instantly, so it gives the short straddle no credit for a day of time decay, which is conservative in calm markets. And the exchange adds other charges on top of the scenario loss, such as an exposure margin and minimum charges for short options, whose current values must be read from the exchange's own circulars. A firm sizing its book on the grid's worst cell is sizing on a regulator's plausible case, not on its own worst case, and its internal limit should sit beyond it.
Where candidates lose it
Candidates pick the middle-row cell with volatility up 4 points, because a short straddle is known to be short volatility, and forget that the price moves matter far more. Fill in the whole grid before choosing; the price axis is worth about Rs 8 lakh and the volatility axis about Rs 2 lakh.
The second miss is quoting the margin as the premium received. Rs 7.15 lakh of premium is not a cushion against a Rs 8.6 lakh scenario loss; the exchange charges the loss.
What the interviewer asks next
- Anjaneri buys 20 lots of the 23,500 call and the 20,500 put as wings. Which cells change most, and roughly what happens to the margin?
- Why might the exchange raise the scenario range after a volatile week, and what does that do to a firm running near its capital?
- How would the grid change two days before expiry, with the index still at 22,000?
Company names and figures are illustrative.
