Put–call parity
Stock at 115. The 95-strike European call costs 25.2. Assuming zero rates and no dividends, what must the 95-strike put cost?
Answer and worked solution
Answer: 5.2
Put–call parity with r = 0: P = C − S + K = 25.2 − 115 + 95 = 5.2.
Options: interview questions and key results
Parity, quick pricing, deltas. The results to know for quant trading interviews, then a worked example of each of the 6 question types. Free, no sign-up.
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Key results
- Put–call parity (r = 0): C − P = S − K.
- ATM call ≈ 0.4·σ·S·√T; ATM straddle ≈ 0.8·σ·S·√T.
- One-step binomial: q = (S₀ − Sd)/(Su − Sd), price = Eq[payoff].
- Delta-hedge: hold −Δ shares per option (×100 per contract).
Worked examples (6)
Try each one before opening the solution. In the app, every type generates fresh numbers each time.
ATM rule of thumb
Use the rule of thumb C ≈ 0.4·σ·S·√T to estimate an at-the-money call: S = 50, σ = 20%, expiry 6 months.
Answer and worked solution
Answer: 2.8284
0.4 × 0.2 × 50 × √(6/12) = 2.8284. The 0.4 comes from 1/√(2π) ≈ 0.399. Traders use this constantly to sanity-check prices.
Implied vol from a straddle
A stock trades at 100. The 3-month at-the-money straddle (call + put) costs 20. Using straddle ≈ 0.8·σ·S·√T, what annualised implied volatility is the market pricing? (decimal or %)
Answer and worked solution
Answer: 0.5
σ ≈ straddle / (0.8·S·√T) = 20 / (0.8 × 100 × 0.5) ≈ 0.5. The straddle price is roughly the market's expected absolute move.
One-step binomial pricing
One-period model, zero rates: a stock at 100 goes to either 120 or 95. Price a call struck at 100.
Answer and worked solution
Answer: 4
Risk-neutral probability of the up move: q = (100 − 95)/(120 − 95) = 0.2. Call = q·(120 − 100) = 4. The real-world probability of the up move doesn't matter, because the option can be replicated with stock and cash.
Calls on dice
A contract pays max(X − 2, 0), where X is the roll of one fair die. What is its fair value?
Answer and worked solution
Answer: 5/3 ≈ 1.6667
This is a call option on a die with strike 2. Average the payoff over all 6 equally likely outcomes: 1.6667. Market-making interviews love this format.
Delta hedging
You are short 17 call contracts (100 shares each), each with delta 0.4. How many shares must you buy to be delta-neutral?
Answer and worked solution
Answer: 680
Position delta = −17 × 100 × 0.4 = −680 shares, so buy 680 shares. You'll need to rebalance as delta changes (gamma).
Other topics
Dice & coins · Cards & combinatorics · Conditional & Bayes · Expected value & games · Random walks & martingales · Markov chains & order statistics · Classic brainteasers · Number sequences · Distributions · Variance & covariance · Estimation & testing · Regression & correlation · Returns, risk & sizing · Time series
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