Quant firm interview prep

Akuna Capital interview questions

Q: How many Akuna Capital interview questions are on QuantGrind?

200 questions are tagged to Akuna Capital across our 2,516-problem set, concentrated in options, probability, and combinatorics. 15 are free to preview on this page; the full set unlocks with a membership, each with hints, the accepted answer, and a worked solution.

Q: How hard is the Akuna Capital quant interview?

Expect a phone screen heavy on mental math and probability, then an onsite or final round mixing brainteasers, market-making games, and topic depth. The bar is less about exotic tricks and more about speed, accuracy, and explaining your thinking clearly under time pressure.

Q: How should I prepare for the Akuna Capital quant interview?

Practice timed, out loud, and without a calculator. Rebuild each answer from first principles rather than recognizing it, and review the ones you got slowly — interview signal comes from how fast and cleanly you reason, not whether you've seen the exact prompt before.

Representative quant-interview questions tagged to Akuna Capital, concentrated in options, probability, and combinatorics. Preview a free set below, then drill the full bank with hints and worked solutions.

200 Akuna Capital questions · 15 free to preview · 2,516 problems total

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15 practice questions

Put-call gamma parity

FreeOptionsWarmupAkunaCitadelSIG

A European call and a European put are written on the same underlying with the same strike $K$ and the same expiry. The call option has a gamma of $0.02$ . What is the gamma of the put option?

Solution

For European options on the same underlying asset with the same strike $K$ and time to expiry $T$ , put-call parity gives:

C - P = S - K e^{-rT}

where $C$ is the call price, $P$ the put price, $S$ the spot price, and $r$ the risk-free rate. Gamma is the second derivative of the option price with respect to $S$ :

\Gamma = \frac{\partial^2 V}{\partial S^2}

Differentiating put-call parity twice with respect to $S$ :

\frac{\partial^2 C}{\partial S^2} - \frac{\partial^2 P}{\partial S^2} = \frac{\partial^2}{\partial S^2}\left(S - K e^{-rT}\right) = 0

because $S$ is linear in $S$ (second derivative zero) and $K e^{-rT}$ is constant. Hence:

\Gamma_C - \Gamma_P = 0 \quad \Rightarrow \quad \Gamma_C = \Gamma_P

Given $\Gamma_C = 0.02$ , the put gamma is also $0.02$ .

Butterfly spread

FreeOptionsEasyAkunaCitadelSIG

Three call options are available with the following strikes and prices:

Strike 1000, price 4
Strike 1010, price 3.5
Strike 1020, price 2.75

An arbitrage exists. Using one contract at each of the outer strikes and two contracts at the middle strike, what is the guaranteed profit (in dollars)?

Solution

The three calls have equally spaced strikes ( $\Delta K = 10$ ) and prices $C_1=4$ , $C_2=3.5$ , $C_3=2.75$ . A no-arbitrage condition for call options is that the price as a function of strike must be convex: $C_1 + C_3 \ge 2C_2$ . Here $4 + 2.75 = 6.75 < 7 = 2 \times 3.5$ , so convexity is violated, creating an arbitrage.

Construct a butterfly spread: buy one call at strike 1000, buy one call at strike 1020, and sell two calls at strike 1010. The net premium is

C_1 + C_3 - 2C_2 = 4 + 2.75 - 2(3.5) = 6.75 - 7 = -0.25,

so the position generates an upfront credit of $0.25$ .

The payoff at expiration $S_T$ is

V(S_T) = \max(S_T-1000,0) + \max(S_T-1020,0) - 2\max(S_T-1010,0).

Evaluating piecewise:

$S_T \le 1000$ : all options expire worthless, $V=0$ .
$1000 < S_T \le 1010$ : $V = (S_T-1000) \ge 0$ .
$1010 < S_T \le 1020$ : $V = (S_T-1000) - 2(S_T-1010) = 1020 - S_T \ge 0$ .
$S_T > 1020$ : $V = (S_T-1000)+(S_T-1020)-2(S_T-1010)=0$ .

The payoff is non-negative for all $S_T$ and strictly positive for $1000 < S_T < 1020$ . Since the position was entered at a net credit of $0.25$ , the guaranteed profit is $0.25$ dollars (25 cents).

Binomial option pricing

OptionsWarmupAkunaJane StreetCitadel

Assume the risk-free rate is zero. A stock currently priced at $100 will be worth either$ 130 or $70 in one year, with probabilities 0.80 and 0.20 respectively. No dividends are paid. What is the value of a one-year European call option with a strike price of$ 110?

Approach

Set up the one-period binomial tree with the given up and down factors.

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Trailing zeros of 100!

CombinatoricsWarmupAkunaJane StreetCitadel

Without computing $100!$ explicitly, find the number of trailing zeros in its decimal representation.

Approach

Think about what a trailing zero represents in terms of the prime factors of the number.

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Pricing a reciprocal-payoff contract

OptionsEasyAkunaCitadelSIG

Assume a zero interest rate and a stock whose current price is 1 and follows a geometric Brownian motion. Determine the value of a contract that pays, at maturity $T$ , the reciprocal of the stock price observed at that time.

Verification. For the special case where σ²T = ln 2, what is the contract value?

Approach

Express the contract value as the risk-neutral expectation of the reciprocal of the stock price at maturity.

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Random volatility vs constant volatility

OptionsEasyAkunaSIGOptiver

A deep out-of-the-money European call option is priced either with a constant volatility of 30% or with a volatility drawn from a random distribution whose mean is 30%, independent of the Brownian motion driving the stock price. Which option is more expensive?

Approach

Consider how the Black–Scholes call price changes when volatility increases versus when it decreases by the same amount.

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Barrier option comparison

OptionsMediumAkunaSIGOptiver

Consider a non-dividend-paying stock with current price $20$ and a strike price of $30$ . The risk-free interest rate is zero. Option A is a one-touch digital option that pays $1 if the stock price ever exceeds $30$ within the next year. Option B is a European digital option that pays $1 if the stock price is above $30$ at the end of one year. How are the values of the two options related?

Approach

Consider the payoff conditions for each option on a single price path: when does Option B pay \$1, and does that imply Option A also pays \$1?

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Optimal stopping comparison

OptionsMediumAkunaCitadelSIG

Under what circumstances is it optimal to exercise an American call option on a stock that pays no dividends? What about an American put option?

Approach

Think about the no-arbitrage lower bound for a European option and how it relates to the payoff from immediate exercise.

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Risk-neutral option pricing

OptionsMediumAkunaCitadelSIG

Derive the Black-Scholes formula for a European call option on a non-dividend-paying stock using the risk-neutral probability measure.

Approach

Start by writing the risk-neutral pricing formula for the call option as a discounted expectation under the equivalent martingale measure.

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Q10

At-the-money call option approximation

OptionsMediumAkunaSIGOptiver

Estimate the value of an at-the-money call option on a non-dividend-paying stock, assuming a low interest rate and short maturity.

Verification. Using the approximation derived above, what is the approximate ATM call value when S_0 = 100, σ = 0.2, and T = 0.25?

Approach

Start with the Black–Scholes formula for a call option, setting the stock price equal to the strike price for the at-the-money condition.

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Q11

Call spread limit

OptionsMediumAkunaCitadelSIG

A European digital option (binary option) pays a fixed amount $H$ if the stock price at expiration is above the strike price $X$ , and zero otherwise. Find the price of this option and describe how it is related to the price of a standard Black-Scholes European call option. Provide a careful explanation.

Approach

Write the binary option's payoff as an indicator function and apply risk-neutral pricing.

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Q12

Risk-neutral pricing

OptionsMediumAkunaJane StreetCitadel

A stock currently priced at $50 will be worth either $60 or $40 in three months, each with equal probability. The value of a three-month at-the-money put on this stock is $4. If the probability of an up move to $60 becomes $75\%$ and the probability of a down move to $40 becomes $25\%$ , does the value of the three-month ATM put increase or decrease, and by how much?

Approach

Recall that in an arbitrage-free complete market, option prices are determined by the risk-neutral probabilities, not the real-world ones.

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Q13

Gamma P&L

OptionsMediumAkunaCitadelSIG

I write a one-month put option using $28\%$ implied volatility and delta-hedge the position continuously until maturity. The realized volatility over the month is $16\%$ . Do I make or lose money?

Approach

Write the P&L of a delta-hedged option position over an infinitesimal time step using the Black-Scholes framework.

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Q14

Relative position

Mental mathWarmupAkunaOptiverJane Street

What is the angle, in degrees, between the minute hand and the hour hand of an analog clock at $3:25$ ?

Approach

Compute the position of each hand relative to 12 o'clock, using the fact that the minute hand moves 6° per minute and the hour hand moves 0.5° per minute.

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Q15

Discrete call pricing

Market makingEasyAkunaJane StreetSIG

A call option settles to the product of two fair six-sided dice rolls. Quote a market $2$ units wide centered on the option's fair value, for a strike of $19$ . Report the sum of your bid and ask prices. For instance, if your market were $5$ @ $7$ , you would enter $12$ .

Approach

List all ordered pairs of dice rolls whose product exceeds 19 and compute the payoff for each.

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Other firms & topics

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Frequently asked questions

How many Akuna Capital interview questions are on QuantGrind?

200 questions are tagged to Akuna Capital across our 2,516-problem set, concentrated in options, probability, and combinatorics. 15 are free to preview on this page; the full set unlocks with a membership, each with hints, the accepted answer, and a worked solution.

How hard is the Akuna Capital quant interview?

Expect a phone screen heavy on mental math and probability, then an onsite or final round mixing brainteasers, market-making games, and topic depth. The bar is less about exotic tricks and more about speed, accuracy, and explaining your thinking clearly under time pressure.

How should I prepare for the Akuna Capital quant interview?

Practice timed, out loud, and without a calculator. Rebuild each answer from first principles rather than recognizing it, and review the ones you got slowly — interview signal comes from how fast and cleanly you reason, not whether you've seen the exact prompt before.

Practice the full Akuna Capital set

Every question comes with progressive hints, the accepted answer, and a full worked solution. 100 free to start — no card required.

Open Akuna Capital in the app → See membership