MAT1856/APM466 Assignment #4

Assignment #4: Options

Professor: Luis Seco, TA: Jonathan Mostovoy

Due: April 12, 2021, at 10PM EST. Submissions accepted up to 7 days late at a 1% penalty

a day. No submissions accepted after April 19, 2021.

Please bring any questions about this assignment to your TA’s, Jonathan’s, weekly (virtual) office hour or

on Piazza.

Expectations

1. Please have your final report typeset using LATEX and using this template: https://www.overleaf.

com/read/hvymwrqhkcbw. Please also structure your answers in line with the mock answers provided.

2. You may, and are encouraged, to discuss how to do these questions with your peers. However, your

write-up must be done individually, and the sharing of your write-up before April 19th is prohibited.

Additional Notes: Marks will be awarded for each question as either full-, half-, or zero-marks according to if

the question was answered with a few small mistakes, substantial mistakes but fundamental idea still correct, or

fundamental idea wrong / no answer respectively. -10 marks if not typeset in LATEXusing the template provided as

intended.

2 Questions- 100 points

The following are all True/False Questions (exception Q6 - full derivation required for any marks there).

Please clearly write TRUE/FALSE without any explanation.

For the following questions, suppose that V is the value of a European Call Option priced using Black￾Scholes. It would be wise to thoroughly familiarize yourself with the mathematical derivation of the

Black-Scholes model, and how a sensitivity analysis of an Option amounts to analyzing “The Greeks”.

1. True/False: (20 points) Black-Scholes depends on a Gaussian Distribution and is therefore well-posed

for accounting for and pricing V in accordance with tail-risk events like recessions.

2. True/False: (20 points) Everything else being equal, V increases as the underlying stock’s drift term,

µ, increases.

3. True/False: (20 points) The strike price, K, is ultimately irrelevant for the Black-Scholes formula

because of the Put-Call Parity.

4. True/False: (20 points) Everything else being equal, V will decrease as we get closed to the option’s

expiry date. (Hint: The Greek “Θ”.)

5. True/False: (20 points) Everything else being equal, as an options gets deeper “in- or out-of-the￾money”, the more volatile V will be (I.e., rate of change / comparative change in V increases). (Hint:

The Greek “Γ”.)

6. (BONUS: 20 points) Derive the Delta (∂SV ) for a European Call Option priced using Black-Scholes

directly (do not use Put-Call Parity). Then use this quantity to explain Delta Hedging. No part

marks awarded for part-answers (only fully completed answers accepted.)

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