MTH359 Tutor-Marked Assignment 01

This assignment is worth 20 % of the final mark for MTH359 Applied Financial Mathematics I

Learning Outcome :

● Differentiate between the types of options: Puts & Calls, European & American.
● Compute the expected value of a financial contract using binomial tree model.
● Construct the Itô’s integral.
● Set up hedging strategies to minimise risks.
● Solve pricing problems with the application of Black-Scholes formula.
● Calculate the implied volatility for an option contract.

What the MTH359 Tutor-Marked Assignment 01 asks you to do

MTH359 Applied Financial Mathematics I introduces the mathematics used to price and hedge derivatives. You will work with options, discrete-time binomial models, stochastic calculus and the continuous-time Black-Scholes framework, and learn how these tools are used to manage risk in real markets.

This TMA is worth 20% of the final mark for MTH359. It tests whether you can classify option contracts, compute prices using binomial trees and Black-Scholes, work with Itô integrals, design hedging strategies and back out implied volatility. Markers look for correct methods, clear working and sensible interpretation of your numbers.

MTH359 learning outcomes explained

Each outcome below links to the type of working your marker expects to see.

How to structure your MTH359 TMA01

1. Read each question carefully – note the option type, maturity, interest rate convention and whether dividends apply.
2. State the model and assumptions – for example no-arbitrage, continuous compounding or a recombining tree.
3. Write the formula before substituting – this earns method marks even if an arithmetic slip occurs.
4. Show working clearly – lay out trees, tables or iterations so every step can be checked.
5. Interpret the result – explain what the price, delta or implied volatility tells you financially.
6. Check consistency – verify answers with put-call parity, bounds on option prices or a quick spreadsheet.

Key concepts to revise for MTH359

• Option payoffs – max(S − K, 0) for calls and max(K − S, 0) for puts underpin every pricing question.
• No-arbitrage principle – the basis for replication, risk-neutral pricing and put-call parity.
• Risk-neutral probability – q = (e^(rΔt) − d)/(u − d) drives binomial tree valuation.
• Brownian motion – its independent, normally distributed increments are essential for stochastic calculus.
• Itô’s lemma – needed to derive the dynamics of functions of the stock price.
• Black-Scholes formula – know the inputs, d1 and d2, and the model’s assumptions.
• The Greeks – delta in particular links pricing to hedging.
• Numerical root-finding – bisection and Newton-Raphson for implied volatility.

Common mistakes to avoid

• Mixing up time units, such as using months instead of years for maturity or volatility.
• Forgetting to discount at each step of the binomial tree, or checking early exercise only at maturity for American options.
• Treating the Itô integral like an ordinary Riemann integral and missing the extra second-order term.
• Reading normal distribution values incorrectly or rounding too early in Black-Scholes calculations.
• Giving final numbers with no explanation of what they mean for the investor or hedger.

MTH359 TMA01 FAQs

What is the MTH359 TMA01 about?

It covers option types, binomial tree pricing, Itô integrals, hedging, the Black-Scholes formula and implied volatility, and is worth 20% of your final mark.

How much working should I show?

Show enough for a marker to follow each step: formulas, substituted values, intermediate results and your final answer. Clear working protects your method marks.

Can I use Excel or Python for calculations?

Software is useful for checking trees and iterations, but always present the method and key steps in your answer rather than only the final output.

Can I get help with my MTH359 assignment?

Yes. Our Singapore-based subject tutors can guide you through the brief, explain the methods and help with presentation and referencing so you can submit with confidence.