Markets & Quants
Markets. Mathematics. Independent judgement.

Understand the market.Defend your thinking.

Understand investing, trading and quantitative finance. Learn the ideas, work through the models and put your knowledge into practice.

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INVESTINGTRADINGQUANTITATIVE FINANCE
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Markets & QuantsKnowledge. Perspective. Practice.

Find your subject.

The Markets & Quants approach

Follow the consequences.

Illustrative central-bank hall with stone columns, a bronze globe and strong sunlight leading toward a modern financial district.
Observe the world. Work through the mechanism.
A teaching question · illustrative example

What has to change before a bond price moves?

A policy headline arrives. Start with what was already in the price, then follow what the new information changes. Economics, mathematics and judgement meet in the same question.

An announcement alone does not determine the outcome. Expectations and risk premia matter.

Work through the bond example

  1. Read the announcement.

    Suppose a central bank signals tighter policy. Ask what the market had already expected.

  2. Trace the expectations.

    A revised path for future rates can change required yields. Credit and liquidity risk also matter.

  3. Reprice the cash flows.

    For fixed promised cash flows, a higher required yield means a lower present value, and vice versa.

  4. Challenge the conclusion.

    Compare the maturity, coupon and risk exposure. Explain which assumptions your answer depends on.

The question to carry forwardWhat would change your conclusion?

Our teaching philosophy
Question the model

Which assumption
moves the price?

Read the Black–Scholes surface as an argument about a European call. Follow the effect of spot and volatility, then ask which real-world risks this model leaves outside the frame.

C/K = (S/K) Φ(d₁) − e−rT Φ(d₂)
Explore derivatives
BLACK–SCHOLESEUROPEAN CALL / 01
The Black–Scholes call surfaceCalculated Black–Scholes European call value divided by strike, across spot-to-strike ratios from 0.65 to 1.50 and annual volatility from 8 to 55 percent. One year to expiry, continuously compounded risk-free rate 3 percent, no dividends. The surface rises with spot and volatility. Copper highlights the at-the-money slice. Animation is decorative and does not change the values.0.651.001.508%30%55%0.30.6SPOT / STRIKE · S/KVOLATILITY · σCALL / STRIKE · C/K010203
Calculated model · illustrative inputs
01

Price creates the slope.

A higher spot price raises the call value, with other inputs fixed.

02

Uncertainty adds value.

In this model, higher volatility lifts the European call surface.

03

The bend tells a story.

Near the strike, the option’s response to price changes becomes especially visible.

Fixed assumptions: one year to expiry · 3% continuously compounded risk-free rate · no dividends. Constant volatility for each valuation. A model illustration, not observed prices or a forecast. The moving highlight changes no calculated value.

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An argument worth working through.

Start with a question. Follow the evidence, inspect the calculation and decide whether the conclusion holds.

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In preparation

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A look at the courses we are preparing. Enrolment opens when each course is ready.

Learning in practice

What does your model leave out?

Change the assumptions in this Monte Carlo experiment. Compare the range of outcomes, then ask what the simulation cannot tell you.

Quantitative finance · Interactive study

Explore the range of outcomes.

A market model describes possibilities. Change the assumptions and examine how uncertainty evolves over time.

Simulated market paths

40 paths shown · 2,000 simulated
Simulated market pathsGeometric Brownian motion: 2000 simulated paths, starting index 100, assumed drift 6.0 percent per year, volatility 20.0 percent and horizon 5 years. The logarithmic index chart displays 40 representative paths, the pointwise fifth to ninety-fifth percentile band, and the median at each month.50100200400Today1y2y3y4y5yIndex level · logarithmic scale
Median5th–95th percentile bandRepresentative paths
Median ending index122.1Starting index: 100
5th–95th percentile56.8 – 262.8Range of terminal outcomes
Finishes below 10034.7%Share of simulated scenarios

The shaded band contains the middle 90% of simulated index levels at each point in time. Individual paths can move outside it.

Model & assumptions
St+Δt=Stexp⁡ ⁣[(μ−12σ2)Δt+σΔt Z],Z∼N(0,1)S_{t+\Delta t}=S_t\exp\!\left[\left(\mu-\tfrac12\sigma^2\right)\Delta t+\sigma\sqrt{\Delta t}\,Z\right],\quad Z\sim\mathcal N(0,1)

μ is the assumed annual drift; σ is annual volatility. The model uses exact lognormal transitions at monthly intervals and 2,000 paths generated with paired, opposite random shocks. Parameters are constant. Changing an input reuses the same random draws; running again changes them.

This is an illustrative index model, not a portfolio or a market forecast. It omits jumps, changing volatility, fees, tax and inflation. The percentile band is pointwise and is not a confidence interval for a forecast.

Study the mathematics

A more guided path

Bring a question.
Build a defensible answer.

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Learn by doing

Try a lesson.

One idea. A worked example. A question to make it yours.

WORKED EXAMPLE / 01ILLUSTRATIVE INPUTS

What is a future payment worth today?

Suppose you will receive ₹110 in one year. At a required return of 10%, its present value is ₹100. Change the required return and the value changes.

₹100Present value at 10%
Present value of ₹110 received in one year: ₹104.76 at 5%, ₹100 at 10%, and ₹95.65 at 15%.PRESENT VALUE · ₹050100104.765%100.0010%95.6515%REQUIRED RETURN

Present value = ₹110 ÷ (1 + required return)

One future payment · one year · no other cash flows

Check your understanding
If the required return rises, what happens to today’s value?
Continue with valuation

A short example from our teaching approach. Take it at your own pace.