25 original derivatives interview examples with explained answers on put–call parity, binomial pricing, Greeks, forwards, bond risk and simulation.
An option price is useful only alongside the assumptions that support it. Work from terminal payoffs to replication, then connect the resulting price to Greeks, interest-rate risk and simulation error. Unless stated otherwise, examples use frictionless markets, consistent borrowing and lending rates, and per-share payoffs. They are model exercises rather than market quotes or trading recommendations.
Payoff, profit, contract delivery price and current contract value are different quantities. Make the timeline and financing convention explicit before substituting numbers.
Use no-arbitrage relations only for comparable contracts. European exercise, maturity, strike and dividends matter for put–call parity and replication.
After a calculation, state what a discrete hedge, jump, cost or changed volatility assumption would alter. A correct formula can still be a poor operational approximation.
Try each question before reading its answer. These original teaching examples remain free to read on this page.
Identify the rights the contract grants and compare portfolios with matching terminal cash flows.
A European call has strike 100 and premium 7. At expiry the stock is 112. What are payoff and profit, ignoring financing and fees?
Answer: Payoff 12; profit 5 per share.
Explanation: Apply max(S − K,0), then subtract the premium. The option's payoff chart alone does not show its net profit.
A European put has strike 90. The stock expires at 82. What is its payoff per share?
Answer: 8.
Explanation: A put pays max(K − S,0). Its holder benefits from a terminal price below the strike.
A non-dividend stock is 100, strike present value is 96 and a European call costs 9. What should the matching put cost under no arbitrage?
Answer: 5.
Explanation: C − P = S − PV(K), so P = 9 − 100 + 96. Strike and maturity must match.
A stock is 100, known dividends have present value 3, PV(K) is 95 and a matching European put costs 4. Find the call price.
Answer: 6.
Explanation: Dividend-adjusted parity is C − P = S − PV(dividends) − PV(K). Ignoring dividends would overprice the call by 3.
A non-dividend stock is 80 and PV(K) is 75. What no-arbitrage lower bound applies to its European call?
Answer: At least 5.
Explanation: A call cannot be worth less than max(S − PV(K),0). This discounted-strike bound differs from immediate exercise value.
A small tree makes risk-neutral pricing and hedge construction visible without numerical machinery.
For a nonnegative underlying worth 80, what upper bound applies to a European call under standard frictionless assumptions?
Answer: 80.
Explanation: Owning the underlying dominates the call's terminal payoff. A price above the underlying would violate that dominance.
A non-dividend asset is 100 and the one-year continuously compounded risk-free rate is 5%. Find the no-arbitrage forward delivery price.
Answer: 100 exp(0.05), approximately 105.13.
Explanation: Buying and financing the asset replicates forward delivery. This is a delivery price, not the initial value of a fair forward.
A long forward has delivery price 100. The current matching fair forward price is 106, with a discount factor of 0.95. Find its value.
Answer: 5.7.
Explanation: Discount the delivery-price advantage: 0.95 × (106 − 100). An existing forward can have nonzero value.
A stock is 100 and will be 120 or 90. The one-period risk-free gross return is 1.05. Find the risk-neutral up probability.
Answer: 1/2.
Explanation: Solve 100 × 1.05 = q × 120 + (1 − q) × 90. The risk-free return lies between the down and up gross returns.
Use stock outcomes 120 and 90, current price 100, gross risk-free return 1.05 and strike 100. Price the one-period European call.
Answer: 200/21, approximately 9.52.
Explanation: Terminal call payoffs are 20 and 0. Weight with risk-neutral probability 1/2 and discount by 1.05.
Connect derivatives of the price to the exposure being hedged and check where sign claims apply.
In that binomial model, how many shares replicate the call's difference between states?
Answer: 2/3 share.
Explanation: Delta equals (20 − 0)/(120 − 90). Financing supplies the remaining level of the replicating payoff.
In frictionless Black–Scholes replication, why does the stock's physical expected return not enter the European option price?
Answer: A self-financing delta hedge removes the local stock risk.
Explanation: The remaining locally riskless portfolio must earn the risk-free rate. This depends on the model's continuous hedging assumptions.
Under dS = μS dt + σS dW with constant coefficients, what is the drift of log S?
Answer: μ − σ²/2.
Explanation: Itô's second derivative correction subtracts half the instantaneous return variance. The drift of a log return differs from price growth.
In the standard Black–Scholes model with positive time and volatility, what is the vega sign of a long European call or put?
Answer: Positive.
Explanation: More volatility raises the value of convex vanilla payoffs under this model. Do not extend this sign claim to every exotic payoff.
What does positive gamma mean for a long vanilla option's delta as the stock rises?
Answer: Delta increases.
Explanation: Gamma is the derivative of delta with respect to the stock price. A fixed hedge becomes stale when the underlying moves.
Exercise rights and carry affect value; bond duration converts a small yield move into an approximate price change.
Must every option's calendar-time theta be negative?
Answer: No.
Explanation: Carry, interest rates, dividends and payoff structure can change the sign. Even a European put can have positive theta in some settings.
Should a holder optimally exercise an American call early on a non-dividend stock when interest rates are nonnegative and markets are frictionless?
Answer: No.
Explanation: Keeping the option preserves optionality and defers paying the strike. Dividends or different rate assumptions change the comparison.
What does a strike-dependent implied volatility reveal about a single constant-volatility Black–Scholes fit?
Answer: One constant volatility cannot match all those option prices.
Explanation: Implied volatility is an inverted price quote. A smile indicates a mismatch with the model's single-volatility restriction.
A default-free bond pays 100 in two years. The continuously compounded yield is 4%. Find its price.
Answer: 100 exp(−0.08), approximately 92.31.
Explanation: Discount the single cash flow over its full maturity. Match the compounding convention to the quoted yield.
A bond has modified duration 5. A parallel yield increase is 10 basis points. Approximate its percentage price change.
Answer: −0.5%.
Explanation: Use ΔP/P ≈ −Dmod Δy with Δy = 0.001. Basis points are not percentage points.
Keep covariance, simulation uncertainty and implementation assumptions visible when assessing a numerical result.
Modified duration is 5 and convexity is 30. For a yield rise of 0.01, approximate ΔP/P through second order.
Answer: −4.85%.
Explanation: Compute −5 × 0.01 + (30/2) × 0.01². Convexity corrects the linear approximation; large moves still create approximation error.
Two equally weighted assets each have volatility 20% and correlation zero. Find portfolio volatility.
Answer: Approximately 14.14%.
Explanation: Portfolio variance is 0.5² × 0.2² + 0.5² × 0.2² = 0.02. Take the square root only after combining variances.
Independent payoff simulations have sample standard deviation 12 across 10,000 draws. Estimate the standard error of their mean.
Answer: 0.12.
Explanation: Divide payoff standard deviation by √n. This measures sampling uncertainty in the mean, not dispersion of individual payoffs.
A simulated payoff X is positively correlated with control Y whose mean is known. In X − β(Y − E[Y]), what population β minimises variance?
Answer: Cov(X,Y)/Var(Y), assuming Var(Y) > 0.
Explanation: Minimise the quadratic variance expression. The centring term preserves the expected payoff when the control mean is correct.
Why can a model's continuous delta-hedging argument fail to match realised hedge P&L?
Answer: Discrete rebalancing, transaction costs, jumps and model error leave residual risk.
Explanation: Name the assumption being relaxed and its effect. A replication formula within a model is not a guarantee of actual hedging performance.
Each question has its own page with a short answer and a credit to its source. Hints and full worked solutions are in the question bank with a free account.
Our bank summary dated contains 311 Finance/Derivatives entries in the bank. Counts describe entries in our curated practice bank, including its source and classification choices. They do not measure employer interview frequency, candidate success rates or how often any one question is asked.
The public examples above were written for these guides. They illustrate the techniques and are not a reproduction or ranking of the bank's sourced questions. The dashboard's broader bank combines sourced questions, worked answers where available and references for book entries without a reproduced solution.
| Subtopic | Bank entries |
|---|---|
| Options Pricing | 57 |
| Greeks | 43 |
| Fixed Income | 32 |
| Black-Scholes | 27 |
| No-Arbitrage | 22 |
| Exotic Options | 18 |
| Volatility & Smile | 18 |
| Option Properties & Bounds | 17 |
| Hedging & Replication | 12 |
| Portfolio Theory | 11 |
| Monte Carlo | 8 |
| Binomial Trees | 8 |
| Forwards & Futures | 7 |
| Interest Rate Models | 6 |
| Risk Management | 6 |
| Markets | 5 |
| Numerical Methods | 3 |
| Finite Differences | 3 |
| Expected Value | 2 |
| Swaps | 2 |
| Time Value of Money | 2 |
| Algebra & Number Theory | 1 |
| Credit | 1 |
Bank difficulty labels: 138 easy · 126 medium · 47 hard.
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