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Enter Your Details to Start the Quiz

If solving these puzzles was exciting for you, imagine how rewarding it would be to solve real financial problems. Financial markets can be complex, like mazes. Risks are not always obvious, and opportunities come to those who know how to find them.

Our Master of Science in Quantitative Finance programme helps you turn your problem-solving skills into strong analytical abilities. It prepares you for careers in investment banking, asset management, fintech, and more.

Are you an Arbitrage Architect?

The Scenario: You are a Junior Quant at a high-frequency trading firm. You observe two derivative contracts, Alpha and Beta, which track the same underlying volatility index. Usually, they move in lockstep. However, a sudden liquidity crunch has caused a temporary "dislocation."

  • Contract Alpha is trading at $102.
  • Contract Beta is trading at $98.
  • Your model proves that by the end of the trading day (i.e. in 2 hours from now), there is an 80% probability that both contracts will converge to the mean price of $100, and a 20% probability that they will both crash to $90 due to a systemic shock.
To capture the "spread" (the difference) while minimizing the risk of the 20% "crash" scenario, which of the following actions is the most mathematically sound?
×

Think about Delta-Neutrality. In a "Pairs Trade," you want to profit from the prices coming back together (convergence). Calculate your profit/loss for both the "Convergence" scenario ($100) and the "Crash" scenario ($90) if you are "Long" the cheap asset and "Short" the expensive one.

Solution Apply to MS Quantitative Finance

The Solution

Correct Answer: A (Buy 100 units of Beta and Sell 100 units of Alpha)

The Logic: This is a classic Long/Short Mean Reversion play.

  1. Cost to Enter: You sell Alpha at $102 (cash inflow $102) and buy Beta at $98 (cash spend $98). You actually start with a +$4 net credit per pair.
  2. Scenario 1: Convergence (80% prob):
    • Alpha drops from $102 to $100 (You gain $2 on your Short).
    • Beta rises from $98 to $100 (You gain $2 on your Long).
    • Total Profit: $4.
  3. Scenario 2: Systemic Crash (20% prob)
    • Alpha drops from $102 to $90 (You gain $12 on your Short).
    • Beta drops from $98 to $90 (You lose $8 on your Long).
    • Total Profit: $4.

There is an 80% chance you will make $4 profit and 20% chance that you will make a $4 profit i.e. a 100% chance that you will make $4 profit in the above case.

The "Quant" Insight: Because you are "Market Neutral" (Shorting the overpriced and Buying the underpriced), the absolute direction of the market doesn't matter. Whether the market goes to $100 or crashes to $90, you lock in the $4 spread in the above example. This is the essence of Arbitrage!

To showcase how this works in a separate scenario, assume that the 20% probability case was one where BOTH the stocks ended up @ $105 (i.e. the convergence hypothesis breaks down) and even in that case, you would expect to end up in a profit. An 80% chance of a $4 profit and a 20% chance that you end up with a $2 profit!

Next Puzzle Apply to MS Quantitative Finance

Can you successfully do the Arbitrage?

The Scenario:You notice the following quotes for the same stock in two markets.

  • Market A: ₹100 per share.
  • Market B: ₹102 per share

Transaction costs are ₹1 per share.

Is there an arbitrage opportunity? If yes, how many shares would you buy/sell to make a profit of ₹100?
×

Think about buying in the cheaper market, selling in the more expensive one, and remember to account for transaction costs.

Solution Apply to MS Quantitative Finance

The Solution

Correct Answer: A Buy in Market A at ₹100, sell in Market B at ₹102.

  • Buy in Market A at ₹100, sell in Market B at ₹102.
  • Transaction cost = ₹1 per share (remember, this applies to both buy and sell transactions).
  • Net profit per share = (Sell price – Buy price – Costs) = 102 – 100 – 2 = ₹0

Conclusion: No arbitrage profit exists because transaction costs wipe out the gain. Always account for costs before jumping into what you think is an arbitrage!

Next Puzzle Apply to MS Quantitative Finance

Monte Carlo Simulation Challenge

The Scenario:A stock currently trades at ₹200. You want to estimate the probability that it will be above ₹220 in 1 year.

Assume

  • Expected annual return = 8%
  • Volatility = 20%
  • Risk-free rate = 5%
How would you set up a Monte Carlo simulation to estimate this probability?
Hint
×

Think about simulating random paths using geometric Brownian motion and counting the proportion of paths ending above ₹220.

Solution Apply to MS Quantitative Finance

The Solution

Correct Answer: B approx. 37%

Use the Geometric Brownian Motion (GBM) formula

  • where Z is a random draw from a standard normal distribution.
  • Simulate thousands of paths for 1 year.
  • Count how many paths end with
  • Probability ≈ (Number of successful paths ÷ Total paths).

This shows how Monte Carlo is often used to estimate probabilities in option pricing and risk management.

Next Puzzle Apply to MS Quantitative Finance

Probability Puzzle (Option Pricing Intuition)

The Scenario:You hold a European call option with strike price ₹50. The underlying asset has a 60% chance of ending at ₹70 and a 40% chance of ending at ₹40 at maturity.

What is the expected payoff of the option?
Hint
×

Payoff = Max (Stock Price – Strike, 0). Multiply each payoff by its probability and sum them.

Solution Apply to MS Quantitative Finance

The Solution

  • Payoff if stock ends at ₹70: max (70 – 50, 0) = ₹20.
  • Payoff if stock ends at ₹40: max (40 – 50, 0) = ₹0.
  • Expected payoff = (0.6 × 20) + (0.4 × 0) = ₹12.

This demonstrates how expected value under probabilities drives option pricing intuition.

Apply to MS Quantitative Finance

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