11 JPMorgan Chase Quantitative Research (New Grad) Interview Questions (2026)

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STAR. QR sits between desks and engineering — communication is half the job. Pick a moment where you translated math into a decision. Show that you understand the listener's frame, not just the math.

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Specific reasons: bank-scale problem set (rates, FX, credit, equities — not just one asset class), close coupling to trading desks, the breadth of the firm's market footprint, training-by-doing rather than pure research. Avoid bashing the alternative. Show you've thought about the tradeoffs.

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Assume log-normal underlying, no arbitrage, constant volatility, risk-free rate r. Set up the replicating portfolio (delta hedge), derive the Black-Scholes PDE, solve with the boundary condition C(S,T) = max(S-K, 0). Closed form: C = S·N(d1) - K·exp(-rT)·N(d2). Be ready to state d1, d2. QR expects you to know this cold.

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W_t ~ Normal(0, t). For X ~ Normal(0, sigma^2), E[X^4] = 3·sigma^4. So E[W_t^4] = 3t^2. Derive from moment-generating function or by computing the integral. Be ready for follow-ups on higher moments and on Ito's lemma applied to f(W_t) = W_t^4.

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Markov chain on states {empty, H, HH, HHT}. Set up expected-time equations: E_0 = 1 + 0.5·E_H + 0.5·E_0, E_H = 1 + 0.5·E_HH + 0.5·E_0, E_HH = 1 + 0.5·E_HH + 0.5·0. Solve: E_HH = 2, E_H = 4, E_0 = 8. Show the technique cleanly — QR uses these chains everywhere.

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Simulate N paths under geometric Brownian motion. For each path, compute the arithmetic average of S over the path. Payoff = max(avg - K, 0) for a call. Discount by exp(-rT) and average across paths. Discuss variance reduction (control variate using geometric Asian, which has closed form). Code it in Python with numpy.

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Real-world (P-measure) is the actual probability of events. Risk-neutral (Q-measure) is a constructed probability under which discounted asset prices are martingales — used for derivative pricing. The Radon-Nikodym derivative dQ/dP encodes the market price of risk. QR uses Q for pricing, P for risk management.

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P(all red) = C(5,3)/C(10,3) = 10/120 = 1/12. By symmetry, P(all blue) = 1/12. So P(all same) = 2/12 = 1/6. Show the combinatoric reasoning. Be ready for variants (k of n same color, with replacement, etc).

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Closed-form OLS: beta = (X^T X)^{-1} X^T y. Add intercept column to X. Use np.linalg.solve for stability over inv(). Discuss when to use QR decomposition instead. Mention assumptions: linearity, homoscedasticity, no perfect multicollinearity.

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For f(t, X_t) where dX_t = mu·dt + sigma·dW_t, Ito's lemma gives df = (partial_t f + mu·partial_x f + 0.5·sigma^2·partial_xx f)·dt + sigma·partial_x f·dW_t. The extra second-order term distinguishes stochastic calculus from regular calculus — it comes from (dW_t)^2 = dt in the limit. Apply it to f = log(S_t) to derive the SDE for log-prices under GBM.

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Var(sum) = N·sigma^2 (independence makes covariances zero). State this and the corollary: std of the sum grows like sqrt(N), not N. Be ready for the follow-up: variance of the sample mean is sigma^2/N — basis for the central limit theorem.