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080

Case 080Market making and trading scenariosHard

A stock halts at 300 on a takeover rumour with a bid of 360 in the air. You are short 500 lots of one-month 320 calls. How do you quote at the reopen, and what do you stand to lose or make?

Old Mission CapitalChicago · 2020

1The situation

You make markets in Pimpalner Foods options. Last week, with the stock at Rs 300 and implied volatility at 30%, you sold 500 lots, 50,000 shares, of the one-month 320 call at Rs 5, and you have hedged the delta. This morning trading halts at Rs 300 on a report that a larger group will bid Rs 360 a share in cash. The exchange will reopen the stock in an hour.

Your desk head thinks the deal is about 60% likely. If it is confirmed, the stock will trade near Rs 358, a small spread below the bid, and implied volatility will fall to about 12%. If the report is denied, the stock will fall to about Rs 270 and volatility will stay at 35%.

2Your task

How should you think about your quote at the reopen, and what is your profit or loss on the short calls in each outcome?

Quick check

Before any numbers: at the reopen, what is the one-month 320 call mostly a bet on?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Quote the call as a deal bet, around Rs 24, not as a volatility product, and know that a confirmed deal costs you about Rs 17 lakh. If confirmed, the stock sits near 358 and the 320 call is worth about 39.7, a loss of 34.7 a share on 50,000 shares. If denied, the stock drops to 270, the call is worth about 0.6 and you keep about Rs 2.2 lakh. At 60% odds the call is worth about 24.1; the old model at a 323 average spot would say 13.4 and be badly wrong.

Step 1Why does the old volatility stop meaning anything?

A raffle ticket is not priced by how the weather varies; it is priced by the odds of the prize. Once a cash bid is in play, Pimpalner's share price has two destinations, near 358 if the deal is confirmed and near 270 if it is denied, and almost no probability in between. The 320 call becomes a digitalAn option whose payoff is all or nothing: a fixed amount if an event happens and zero if it does not. on the deal: worth about 40 in one world and about zero in the other. Its fair value is the probability of the deal times 40, plus a sliver for the denied case, which at 60% is about 24.1. A lognormal model fed the average spot of 323 and the old 30% volatility gives 13.4, because it spreads probability smoothly across prices the stock will never visit.

The reopen is a bet on the deal: two outcomes, two very different call valuesHalt at Rs 300short 50,000 x 320 callsold at Rs 5confirmedp = 60%denied1 - p = 40%Stock to 358, vol collapses320 call worth 39.7you lose (39.7 - 5) x 50,000Stock to 270, vol stays high320 call worth 0.6you keep (5 - 0.6) x 50,000Loss Rs 17.4 lakhthe deal is the riskGain Rs 2.2 lakhpremium keptWeighted value: 0.6 x 39.7 + 0.4 x 0.6 = 24.1Black-Scholes at 30% vol and a 323 spot would say 13.4: wrong model
If the bid is confirmed the stock trades near 358, the 320 call is worth about 39.7 and the short position loses about Rs 17.4 lakh; if it is denied the stock falls to 270, the call is worth about 0.6 and the desk keeps about Rs 2.2 lakh; at 60% odds the call is worth about 24.1, nearly twice what the old volatility model would quote.
Step 2What do you quote at the reopen?

Three things decide the quote: your estimate of the odds, your position, and how little you know. Centre the market on the deal-weighted value, about 24, skew it higher because you are short 50,000 shares of the call and want to buy some back, and make it wide, perhaps 4 to 5 rupees, because anyone lifting your offer may know more about the deal than you do. The hedge changes character too: the delta of a deal-bet call is close to the deal probability, not the 0.3 you had, and the stock you hold against it will gap with the news rather than drift. A market maker who keeps quoting the pre-halt 30% volatility is handing informed traders free money.

Step 3What is the P&L in each outcome?
OutcomeStockVolatility320 call valueP&L on 50,000 short, sold at 5
Deal confirmed at 36035812%39.7-Rs 17.4 lakh
Report denied27035%0.6+Rs 2.2 lakh
Weighted at 60 / 4032324.1-Rs 9.5 lakh
On 50,000 short calls sold at Rs 5, a confirmed deal costs about Rs 17.4 lakh and a denial earns about Rs 2.2 lakh, so the position has a negative expected value of about Rs 9.5 lakh at 60% odds.

The asymmetry is the lesson. You collected Rs 5 to take a risk you priced at 30% volatility; the bid turned it into a 35 rupee loss with 60% probability against a 4.4 rupee gain with 40%. The delta hedge you hold, roughly 15,000 shares if your delta was 0.3, softens the confirmed case by about Rs 9 lakh as the stock jumps from 300 to 358, and hurts by about Rs 4.5 lakh if it falls to 270, but it does not rescue the trade. Takeover risk is the reason short call premium in a rumoured name looks generous.

Short 320 call at expiry, per share: the two reopen outcomes land on opposite ends-40-20+200240270300320360380denied: 270, keep 5confirmed: 360, lose 35halted herestrike 320stock price at expiry, Rs
The short 320 call keeps its Rs 5 premium anywhere below 320 and loses one rupee for each rupee above it, so the denied outcome at 270 lands on the flat part worth plus 5 and the confirmed outcome at 360 lands at minus 35 a share.
Step 4What would a desk head want to hear at the end?

A plan, not a lament. First, the quote is a probability, and you will update it with every print and every headline. Second, buy back a tranche of calls at the reopen even at a price that looks dear, because the position is now a single bet far larger than the premium it earned. Third, note the limit: if the deal has conditions, regulatory approval or a shareholder vote, the stock will not sit at 358 but somewhere lower, and the odds will move for weeks. A market maker's job after a halt is to stop pricing yesterday's distribution.

Where candidates lose it

The common loss is reaching for Black-Scholes at the reopen with the old volatility, or a higher one, and quoting a call worth half its deal-weighted value. The distribution has two lumps; a lognormal has none.

The second is forgetting the position. A quote is never just fair value: short 50,000 calls into a possible deal, you skew to buy and widen for the information you do not have.

What the interviewer asks next

  • The bid is confirmed but needs regulatory approval in four months. Where does the stock trade, and what is the call worth?
  • You were long the calls instead. What do you do at the reopen?
  • How would you hedge the short calls if you could trade only the stock?
  • A second bidder is rumoured at 380. How does the 320 call value change?

Asked at Old Mission Capital, Trading, Chicago, 2020 (Wall Street Oasis): Lots of questions about hypothetical scenarios to see how you think, stats, and market making/options.

← Case 079Build a two-step binomial tree for a stock at 500 with up 1.1, down 0.9 and 2% a step, and price a 520 put as European and as American. Where is early exercise optimal?Case 081 →A stock at 400 should drift to 420 to 440 over two months, not beyond. Buy the 400 call at 14, buy the 400/440 call spread at 10, or sell the 380 put at 6? Pick one.

Company names and figures are illustrative.

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